From 1161e41cc42b9ed05f0c16664b605519922ebffe Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Dennis=20M=C3=BCller?= <d.mueller@jacobs-university.de>
Date: Tue, 25 Apr 2017 08:16:09 +0200
Subject: [PATCH] Added errors folder

---
 .../$Continuity$Equation$Electrons.omdoc      |   78 -
 .../$Continuity$Equation$Holes.omdoc          |   68 -
 .../continuity/$Current$Electrons.omdoc       |  118 -
 .../Models/continuity/$Current$Holes.omdoc    |  118 -
 .../MitM/Models/continuity/$Mobilities.omdoc  |   29 -
 .../densities/$Bandstructure$Parameters.omdoc |   29 -
 .../Models/densities/$Density$Electrons.omdoc |   44 -
 .../Models/densities/$Density$Holes.omdoc     |   44 -
 .../densities/$Electrostatic$Potential.omdoc  |   13 -
 .../$Fermi$Potential$Electrons.omdoc          |   21 -
 .../densities/$Fermi$Potential$Holes.omdoc    |   21 -
 .../MitM/Models/poisson/$Charge.omdoc         |   48 -
 .../MitM/Models/poisson/$Displacement.omdoc   |   35 -
 .../$Poisson$Boundary$Conditions.omdoc        |   22 +-
 .../Models/poisson/$Poisson$Equation.omdoc    |   15 +-
 .../poisson/$Thermodynamic$Equilibrium.omdoc  |   19 +-
 errors/mmt-omdoc/.err                         |    2 +
 errors/mmt-omdoc/mmt/.err                     |    2 +
 errors/mmt-omdoc/mmt/Quantities.mmt.err       |  268 +
 errors/mmt-omdoc/mmt/VanRoosbroeck.mmt.err    | 1024 ++++
 errors/mmt-omdoc/mmt/band.mmt.err             |  199 +
 errors/mmt-omdoc/mmt/constants.mmt.err        |  136 +
 errors/mmt-omdoc/mmt/continuity.mmt.err       | 1069 ++++
 errors/mmt-omdoc/mmt/densities.mmt.err        |  201 +
 errors/mmt-omdoc/mmt/device.mmt.err           |  470 ++
 errors/mmt-omdoc/mmt/poisson.mmt.err          | 4616 +++++++++++++++++
 errors/mmt-omdoc/mmt/recombination.mmt.err    | 1815 +++++++
 errors/mmt-omdoc/mmt/species.mmt.err          |    2 +
 export/html/content/.html                     |    1 -
 export/html/content/http..mathhub.info/.html  |    1 -
 .../content/http..mathhub.info/MitM/.html     |    1 -
 .../http..mathhub.info/MitM/Models/$Base.html |    1 -
 .../MitM/Models/$Physical$Constants.html      |    1 -
 .../http..mathhub.info/MitM/Models/.html      |    1 -
 .../Models/VanRoosbroeck/$Van$Roosbroeck.html |    1 -
 .../MitM/Models/VanRoosbroeck/.html           |    1 -
 ...tinuity$Boundary$Conditions$Electrons.html |    1 -
 ...$Continuity$Boundary$Conditions$Holes.html |    1 -
 .../$Continuity$Equation$Electrons.html       |    1 -
 .../$Continuity$Equation$Holes.html           |    1 -
 .../Models/continuity/$Current$Electrons.html |    1 -
 .../Models/continuity/$Current$Holes.html     |    1 -
 .../MitM/Models/continuity/$Mobilities.html   |    1 -
 .../MitM/Models/continuity/.html              |    1 -
 .../densities/$Bandstructure$Parameters.html  |    1 -
 .../Models/densities/$Density$Electrons.html  |    1 -
 .../MitM/Models/densities/$Density$Holes.html |    1 -
 .../densities/$Electrostatic$Potential.html   |    1 -
 .../densities/$Fermi$Potential$Electrons.html |    1 -
 .../densities/$Fermi$Potential$Holes.html     |    1 -
 .../MitM/Models/densities/.html               |    1 -
 .../MitM/Models/device/$Device$Geometry.html  |    1 -
 .../device/$Device$Operation$State.html       |    1 -
 .../MitM/Models/device/$Device.html           |    1 -
 .../MitM/Models/device/$Doping$Profile.html   |    1 -
 .../MitM/Models/device/.html                  |    1 -
 .../MitM/Models/poisson/$Charge.html          |    1 -
 .../MitM/Models/poisson/$Displacement.html    |    1 -
 .../poisson/$Poisson$Boundary$Conditions.html |    1 -
 .../Models/poisson/$Poisson$Equation.html     |    1 -
 .../Models/poisson/$Poisson$Parameters.html   |    1 -
 .../poisson/$Thermodynamic$Equilibrium.html   |    1 -
 .../MitM/Models/poisson/.html                 |    1 -
 .../Models/recombination/$Recombination.html  |    1 -
 .../$Spontaneous$Recombination.html           |    1 -
 .../MitM/Models/recombination/.html           |    1 -
 export/html/narration/.html                   |    1 -
 export/html/narration/VanRoosbroeck.html      |    1 -
 export/html/narration/constants.html          |    1 -
 export/html/narration/continuity.html         |    1 -
 export/html/narration/densities.html          |    1 -
 export/html/narration/device.html             |    1 -
 export/html/narration/poisson.html            |    1 -
 export/html/narration/recombination.html      |    1 -
 export/mh-html/content/.html                  |    1 -
 .../mh-html/content/http..mathhub.info/.html  |    1 -
 .../content/http..mathhub.info/MitM/.html     |    1 -
 .../http..mathhub.info/MitM/Models/$Base.html |    1 -
 .../MitM/Models/$Physical$Constants.html      |    1 -
 .../http..mathhub.info/MitM/Models/.html      |    1 -
 .../Models/VanRoosbroeck/$Van$Roosbroeck.html |    1 -
 .../MitM/Models/VanRoosbroeck/.html           |    1 -
 ...tinuity$Boundary$Conditions$Electrons.html |    1 -
 ...$Continuity$Boundary$Conditions$Holes.html |    1 -
 .../$Continuity$Equation$Electrons.html       |    1 -
 .../$Continuity$Equation$Holes.html           |    1 -
 .../Models/continuity/$Current$Electrons.html |    1 -
 .../Models/continuity/$Current$Holes.html     |    1 -
 .../MitM/Models/continuity/$Mobilities.html   |    1 -
 .../MitM/Models/continuity/.html              |    1 -
 .../densities/$Bandstructure$Parameters.html  |    1 -
 .../Models/densities/$Density$Electrons.html  |    1 -
 .../MitM/Models/densities/$Density$Holes.html |    1 -
 .../densities/$Electrostatic$Potential.html   |    1 -
 .../densities/$Fermi$Potential$Electrons.html |    1 -
 .../densities/$Fermi$Potential$Holes.html     |    1 -
 .../MitM/Models/densities/.html               |    1 -
 .../MitM/Models/device/$Device$Geometry.html  |    1 -
 .../device/$Device$Operation$State.html       |    1 -
 .../MitM/Models/device/$Device.html           |    1 -
 .../MitM/Models/device/$Doping$Profile.html   |    1 -
 .../MitM/Models/device/.html                  |    1 -
 .../MitM/Models/poisson/$Charge.html          |    1 -
 .../MitM/Models/poisson/$Displacement.html    |    1 -
 .../poisson/$Poisson$Boundary$Conditions.html |    1 -
 .../Models/poisson/$Poisson$Equation.html     |    1 -
 .../Models/poisson/$Poisson$Parameters.html   |    1 -
 .../poisson/$Thermodynamic$Equilibrium.html   |    1 -
 .../MitM/Models/poisson/.html                 |    1 -
 .../Models/recombination/$Recombination.html  |    1 -
 .../$Spontaneous$Recombination.html           |    1 -
 .../MitM/Models/recombination/.html           |    1 -
 export/mh-html/narration/.html                |    1 -
 export/mh-html/narration/VanRoosbroeck.html   |    1 -
 export/mh-html/narration/constants.html       |    1 -
 export/mh-html/narration/continuity.html      |    1 -
 export/mh-html/narration/densities.html       |    1 -
 export/mh-html/narration/device.html          |    1 -
 export/mh-html/narration/poisson.html         |    1 -
 export/mh-html/narration/recombination.html   |    1 -
 export/planetary/content/.html                |    1 -
 .../content/http..mathhub.info/.html          |    1 -
 .../content/http..mathhub.info/MitM/.html     |    1 -
 .../http..mathhub.info/MitM/Models/$Base.html |    1 -
 .../MitM/Models/$Physical$Constants.html      |    1 -
 .../http..mathhub.info/MitM/Models/.html      |    1 -
 .../Models/VanRoosbroeck/$Van$Roosbroeck.html |    1 -
 .../MitM/Models/VanRoosbroeck/.html           |    1 -
 ...tinuity$Boundary$Conditions$Electrons.html |    1 -
 ...$Continuity$Boundary$Conditions$Holes.html |    1 -
 .../$Continuity$Equation$Electrons.html       |    1 -
 .../$Continuity$Equation$Holes.html           |    1 -
 .../Models/continuity/$Current$Electrons.html |    1 -
 .../Models/continuity/$Current$Holes.html     |    1 -
 .../MitM/Models/continuity/$Mobilities.html   |    1 -
 .../MitM/Models/continuity/.html              |    1 -
 .../densities/$Bandstructure$Parameters.html  |    1 -
 .../Models/densities/$Density$Electrons.html  |    1 -
 .../MitM/Models/densities/$Density$Holes.html |    1 -
 .../densities/$Electrostatic$Potential.html   |    1 -
 .../densities/$Fermi$Potential$Electrons.html |    1 -
 .../densities/$Fermi$Potential$Holes.html     |    1 -
 .../MitM/Models/densities/.html               |    1 -
 .../MitM/Models/device/$Device$Geometry.html  |    1 -
 .../device/$Device$Operation$State.html       |    1 -
 .../MitM/Models/device/$Device.html           |    1 -
 .../MitM/Models/device/$Doping$Profile.html   |    1 -
 .../MitM/Models/device/.html                  |    1 -
 .../MitM/Models/poisson/$Charge.html          |    1 -
 .../MitM/Models/poisson/$Displacement.html    |    1 -
 .../poisson/$Poisson$Boundary$Conditions.html |    1 -
 .../Models/poisson/$Poisson$Equation.html     |    1 -
 .../Models/poisson/$Poisson$Parameters.html   |    1 -
 .../poisson/$Thermodynamic$Equilibrium.html   |    1 -
 .../MitM/Models/poisson/.html                 |    1 -
 .../Models/recombination/$Recombination.html  |    1 -
 .../$Spontaneous$Recombination.html           |    1 -
 .../MitM/Models/recombination/.html           |    1 -
 export/planetary/narration/.html              |    1 -
 export/planetary/narration/VanRoosbroeck.html |    1 -
 export/planetary/narration/constants.html     |    1 -
 export/planetary/narration/continuity.html    |    1 -
 export/planetary/narration/densities.html     |    1 -
 export/planetary/narration/device.html        |    1 -
 export/planetary/narration/poisson.html       |    1 -
 export/planetary/narration/recombination.html |    1 -
 narration/VanRoosbroeck.omdoc                 |   11 -
 narration/constants.omdoc                     |    2 -
 narration/continuity.omdoc                    |    5 -
 narration/densities.omdoc                     |   11 -
 narration/device.omdoc                        |    3 -
 narration/poisson.omdoc                       |    5 -
 narration/recombination.omdoc                 |    3 -
 relational/VanRoosbroeck.rel                  |    3 -
 relational/constants.rel                      |    4 -
 relational/continuity.rel                     |   15 -
 relational/densities.rel                      |   13 -
 relational/device.rel                         |    9 -
 .../$Continuity$Equation$Electrons.rel        |    4 -
 .../continuity/$Continuity$Equation$Holes.rel |   29 -
 .../Models/continuity/$Current$Electrons.rel  |   21 -
 .../MitM/Models/continuity/$Current$Holes.rel |   24 -
 .../MitM/Models/continuity/$Mobilities.rel    |    6 -
 .../densities/$Bandstructure$Parameters.rel   |   11 -
 .../Models/densities/$Density$Electrons.rel   |    9 -
 .../MitM/Models/densities/$Density$Holes.rel  |    9 -
 .../densities/$Electrostatic$Potential.rel    |    6 -
 .../densities/$Fermi$Potential$Electrons.rel  |    5 -
 .../densities/$Fermi$Potential$Holes.rel      |    5 -
 .../MitM/Models/poisson/$Charge.rel           |   16 -
 .../MitM/Models/poisson/$Displacement.rel     |    8 -
 .../poisson/$Poisson$Boundary$Conditions.rel  |   23 -
 .../MitM/Models/poisson/$Poisson$Equation.rel |   22 -
 .../poisson/$Thermodynamic$Equilibrium.rel    |   22 -
 relational/poisson.rel                        |   13 -
 relational/recombination.rel                  |    5 -
 196 files changed, 9813 insertions(+), 1173 deletions(-)
 delete mode 100644 content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/continuity/$Current$Holes.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/continuity/$Mobilities.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/densities/$Density$Electrons.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/densities/$Density$Holes.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/poisson/$Charge.omdoc
 delete mode 100644 content/http..mathhub.info/MitM/Models/poisson/$Displacement.omdoc
 create mode 100644 errors/mmt-omdoc/.err
 create mode 100644 errors/mmt-omdoc/mmt/.err
 create mode 100644 errors/mmt-omdoc/mmt/Quantities.mmt.err
 create mode 100644 errors/mmt-omdoc/mmt/VanRoosbroeck.mmt.err
 create mode 100644 errors/mmt-omdoc/mmt/band.mmt.err
 create mode 100644 errors/mmt-omdoc/mmt/constants.mmt.err
 create mode 100644 errors/mmt-omdoc/mmt/continuity.mmt.err
 create mode 100644 errors/mmt-omdoc/mmt/densities.mmt.err
 create mode 100644 errors/mmt-omdoc/mmt/device.mmt.err
 create mode 100644 errors/mmt-omdoc/mmt/poisson.mmt.err
 create mode 100644 errors/mmt-omdoc/mmt/recombination.mmt.err
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diff --git a/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.omdoc b/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.omdoc
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-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ContinuityEquationElectrons" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#887.29.0:1140.35.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#938.31.1:1015.31.78"/></metadata>Formulation of the continuity equation for electrons in divergence form.</opaque><constant name="continuity_equation">
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-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ContinuityEquationHoles" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2405.63.0:2841.74.1"/></metadata><import from="http://mathhub.info/MitM/Models/continuity?CurrentHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2451.64.1:2473.64.23"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2476.65.1:2511.65.36"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2514.66.1:2556.66.43"/></metadata></import><import from="http://mathhub.info/MitM/Models/recombination?Recombination"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2559.67.1:2595.67.37"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2598.68.1:2639.68.42"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2644.70.1:2717.70.74"/></metadata>Formulation of the continuity equation for holes in divergence form.</opaque><constant name="continuity_equation_holes">
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-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="CurrentElectrons" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#572.15.0:1261.29.1"/></metadata><import from="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#611.16.1:653.16.43"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#656.17.1:697.17.42"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#700.18.1:735.18.36"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?Mobilities"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#738.19.1:758.19.21"/></metadata></import><import from="http://mathhub.info/MitM/Models?CurrentDensity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#761.20.1:789.20.29"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#794.22.1:973.24.53"/></metadata>Definition of the electron current in gradient form. 
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-                 <om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1741.43.12:1779.43.50"/></metadata>
-                 <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
-                 <om:OMBVAR><om:OMV name="x"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1742.43.13:1742.43.13"/></metadata><type><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/x/8"></om:OMV><om:OMV name="P"></om:OMV><om:OMV name="f"></om:OMV><om:OMV name="g"></om:OMV>
-      </om:OMA></type></om:OMV></om:OMBVAR>
-                 <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1745.43.16:1779.43.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QEMul"></om:OMS><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/I/6"></om:OMV><om:OMV name="P"></om:OMV><om:OMV name="f"></om:OMV><om:OMV name="g"></om:OMV><om:OMV name="x"></om:OMV>
-      </om:OMA><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/I/7"></om:OMV><om:OMV name="P"></om:OMV><om:OMV name="f"></om:OMV><om:OMV name="g"></om:OMV><om:OMV name="x"></om:OMV>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1745.43.16:1770.43.41"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QEMul"></om:OMS><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/I/2"></om:OMV><om:OMV name="P"></om:OMV><om:OMV name="f"></om:OMV><om:OMV name="g"></om:OMV><om:OMV name="x"></om:OMV>
-      </om:OMA><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/I/3"></om:OMV><om:OMV name="P"></om:OMV><om:OMV name="f"></om:OMV><om:OMV name="g"></om:OMV><om:OMV name="x"></om:OMV>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1745.43.16:1752.43.23"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QEMul"></om:OMS><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/I/0"></om:OMV><om:OMV name="P"></om:OMV><om:OMV name="f"></om:OMV><om:OMV name="g"></om:OMV><om:OMV name="x"></om:OMV>
-      </om:OMA><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/I/1"></om:OMV><om:OMV name="P"></om:OMV><om:OMV name="f"></om:OMV><om:OMV name="g"></om:OMV><om:OMV name="x"></om:OMV>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1745.43.16:1746.43.17"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/smglom/arithmetics" module="realarith" name="uminus"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="elementary_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1746.43.17:1746.43.17"/></metadata></om:OMS>
-      </om:OMA><om:OMS base="http://mathhub.info/MitM/Models/continuity" module="Mobilities" name="mobility_holes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1750.43.21:1752.43.23"/></metadata></om:OMS>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1756.43.27:1770.43.41"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityHoles" name="density_holes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1757.43.28:1757.43.28"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1759.43.30:1763.43.34"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="f"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1760.43.31:1760.43.31"/></metadata></om:OMV><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1762.43.33:1762.43.33"/></metadata></om:OMV>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1765.43.36:1769.43.40"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="g"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1766.43.37:1766.43.37"/></metadata></om:OMV><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1768.43.39:1768.43.39"/></metadata></om:OMV>
-      </om:OMA>
-      </om:OMA>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1774.43.45:1779.43.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1775.43.46:1776.43.47"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/smglom/calculus" module="derivative" name="derivative"></om:OMS><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/I/4"></om:OMV><om:OMV name="P"></om:OMV><om:OMV name="f"></om:OMV><om:OMV name="g"></om:OMV><om:OMV name="x"></om:OMV>
-      </om:OMA><om:OMV name="g"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1775.43.46:1775.43.46"/></metadata></om:OMV><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/I/5"></om:OMV><om:OMV name="P"></om:OMV><om:OMV name="f"></om:OMV><om:OMV name="g"></om:OMV><om:OMV name="x"></om:OMV>
-      </om:OMA>
-      </om:OMA><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1778.43.49:1778.43.49"/></metadata></om:OMV>
-      </om:OMA>
-      </om:OMA>
-      </om:OMBIND>
-      </om:OMBIND>
-      </om:OMBIND>
-      </om:OMBIND></om:OMOBJ></definition>
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="j_p 2 3"> <scope languages="" priority="0"/> </notation></notations>
-     </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/continuity/$Mobilities.omdoc b/content/http..mathhub.info/MitM/Models/continuity/$Mobilities.omdoc
deleted file mode 100644
index 46deda8..0000000
--- a/content/http..mathhub.info/MitM/Models/continuity/$Mobilities.omdoc
+++ /dev/null
@@ -1,29 +0,0 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Mobilities" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#190.6.0:491.11.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#223.7.1:285.7.63"/></metadata>The electron mobility parameter usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/continuity" module="Mobilities" name="mobility_electrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#278.-1.-1:280.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="mobility_electrons">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#287.8.1:359.8.73"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#308.8.22:348.8.62"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#308.8.22:309.8.23"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#311.8.25:348.8.62"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Area"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#312.8.26:315.8.29"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#320.8.34:347.8.61"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimTimes"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#321.8.35:337.8.51"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItime"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#341.8.55:346.8.60"/></metadata></om:OMS>
-      </om:OMA>
-      </om:OMA>
-      </om:OMA></om:OMOBJ></type>
-       
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="μ_n"> <scope languages="" priority="0"/> </notation></notations>
-     </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#361.9.1:419.9.59"/></metadata>The hole mobility parameter usually denoted by <unparsed>None</unparsed>.</opaque><constant name="mobility_holes">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#421.10.1:489.10.69"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#438.10.18:478.10.58"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#438.10.18:439.10.19"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#441.10.21:478.10.58"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Area"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#442.10.22:445.10.25"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#450.10.30:477.10.57"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimTimes"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#451.10.31:467.10.47"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItime"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#471.10.51:476.10.56"/></metadata></om:OMS>
-      </om:OMA>
-      </om:OMA>
-      </om:OMA></om:OMOBJ></type>
-       
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="μ_p"> <scope languages="" priority="0"/> </notation></notations>
-     </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.omdoc b/content/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.omdoc
deleted file mode 100644
index 5c7d442..0000000
--- a/content/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.omdoc
+++ /dev/null
@@ -1,29 +0,0 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="BandstructureParameters" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#209.6.0:878.19.1"/></metadata><import from="http://mathhub.info/MitM/Models?Density"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#256.7.1:277.7.22"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#280.8.1:373.9.32"/></metadata>The effective density of states for the conduction bands 
-     usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="effective_density_of_states_conduction_bands"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#366.-1.-1:368.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="effective_density_of_states_conduction_bands">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#375.10.1:443.10.69"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="Density" name="density_dim"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#422.10.48:432.10.58"/></metadata></om:OMS></om:OMOBJ></type>
-       
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="N_c"> <scope languages="" priority="0"/> </notation></notations>
-     </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#446.11.2:536.12.32"/></metadata>The effective density of states for the valence bands 
-     usually denoted by <unparsed>None</unparsed>.</opaque><constant name="effective_density_of_states_valence_bands">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#538.13.1:603.13.66"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="Density" name="density_dim"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#582.13.45:592.13.55"/></metadata></om:OMS></om:OMOBJ></type>
-       
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="N_v"> <scope languages="" priority="0"/> </notation></notations>
-     </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#606.14.2:661.14.57"/></metadata>The conduction band edge usually denoted by <unparsed>None</unparsed>.</opaque><constant name="conduction_band_edge">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#663.15.1:705.15.43"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#686.15.24:694.15.32"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#686.15.24:687.15.25"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Energy"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#689.15.27:694.15.32"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></type>
-       
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="E_c"> <scope languages="" priority="0"/> </notation></notations>
-     </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#708.16.2:760.16.54"/></metadata>The valence band edge usually denoted by <unparsed>None</unparsed>.</opaque><constant name="valence_band_edge">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#762.17.1:801.17.40"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#782.17.21:790.17.29"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#782.17.21:783.17.22"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Energy"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#785.17.24:790.17.29"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></type>
-       
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="E_v"> <scope languages="" priority="0"/> </notation></notations>
-     </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#804.18.2:876.18.74"/></metadata>N.B.: The band gap of the semiconductor is given by Eg = <unparsed>None</unparsed>.</opaque></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/densities/$Density$Electrons.omdoc b/content/http..mathhub.info/MitM/Models/densities/$Density$Electrons.omdoc
deleted file mode 100644
index 66ef8ba..0000000
--- a/content/http..mathhub.info/MitM/Models/densities/$Density$Electrons.omdoc
+++ /dev/null
@@ -1,44 +0,0 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="DensityElectrons" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2053.57.0:2368.65.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceOperationState"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2092.58.1:2128.58.37"/></metadata></import><import from="http://mathhub.info/MitM/Models?PhysicalConstants"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2131.59.1:2162.59.32"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?BandstructureParameters"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2166.60.1:2199.60.34"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2204.62.1:2274.62.71"/></metadata>Formula for the electron density for the Boltzmann approximation.</opaque><constant name="density_electrons">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2276.63.1:2366.64.52"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2304.63.29:2304.63.29"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></type>
-       <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
-                 <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="unknown"></om:OMS>
-                 <om:OMBVAR><om:OMV name="/y/2"></om:OMV><om:OMV name="/x/1"></om:OMV><om:OMV name="/I/0"></om:OMV></om:OMBVAR>
-                 <om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50"/></metadata>
-                 <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
-                 <om:OMBVAR><om:OMV name="x"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2319.64.5:2319.64.5"/></metadata><type><om:OMV name="/x/1"></om:OMV></type></om:OMV><om:OMV name="y"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2321.64.7:2321.64.7"/></metadata><type><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/y/2"></om:OMV><om:OMV name="x"></om:OMV>
-      </om:OMA></type></om:OMV></om:OMBVAR>
-                 <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="multiplication"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="effective_density_of_states_conduction_bands"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2326.64.12"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2364.64.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="exp"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2332.64.18"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2334.64.20:2364.64.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="real_div"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2335.64.21:2353.64.39"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="bin_minus"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2346.64.32"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="multiplication"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="elementary_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2336.64.22"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2340.64.26:2346.64.32"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="bin_minus"></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2341.64.27:2341.64.27"/></metadata></om:OMV><om:OMV name="y"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2345.64.31:2345.64.31"/></metadata></om:OMV>
-      </om:OMA>
-      </om:OMA><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="conduction_band_edge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2350.64.36:2352.64.38"/></metadata></om:OMS>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2363.64.49"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="multiplication"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="Boltzmann_constant"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2359.64.45"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="temperatur"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2363.64.49:2363.64.49"/></metadata></om:OMS>
-      </om:OMA><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/I/0"></om:OMV><om:OMV name="x"></om:OMV><om:OMV name="y"></om:OMV>
-      </om:OMA>
-      </om:OMA>
-      </om:OMA>
-      </om:OMA>
-      </om:OMBIND>
-      </om:OMBIND></om:OMOBJ></definition>
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="n"> <scope languages="" priority="0"/> </notation></notations>
-     </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/densities/$Density$Holes.omdoc b/content/http..mathhub.info/MitM/Models/densities/$Density$Holes.omdoc
deleted file mode 100644
index c827996..0000000
--- a/content/http..mathhub.info/MitM/Models/densities/$Density$Holes.omdoc
+++ /dev/null
@@ -1,44 +0,0 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="DensityHoles" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2496.71.0:2797.78.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceOperationState"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2531.72.1:2567.72.37"/></metadata></import><import from="http://mathhub.info/MitM/Models?PhysicalConstants"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2570.73.1:2601.73.32"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?BandstructureParameters"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2605.74.1:2638.74.34"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2641.75.1:2707.75.67"/></metadata>Formula for the hole density for the Boltzmann approximation.</opaque><constant name="density_holes">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2709.76.1:2795.77.52"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2733.76.25:2733.76.25"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></type>
-       <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
-                 <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="unknown"></om:OMS>
-                 <om:OMBVAR><om:OMV name="/y/2"></om:OMV><om:OMV name="/x/1"></om:OMV><om:OMV name="/I/0"></om:OMV></om:OMBVAR>
-                 <om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50"/></metadata>
-                 <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
-                 <om:OMBVAR><om:OMV name="x"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2748.77.5:2748.77.5"/></metadata><type><om:OMV name="/x/1"></om:OMV></type></om:OMV><om:OMV name="y"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2750.77.7:2750.77.7"/></metadata><type><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/y/2"></om:OMV><om:OMV name="x"></om:OMV>
-      </om:OMA></type></om:OMV></om:OMBVAR>
-                 <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2793.77.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="multiplication"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="effective_density_of_states_valence_bands"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2755.77.12"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2793.77.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="exp"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2761.77.18"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2763.77.20:2793.77.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="real_div"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2764.77.21:2782.77.39"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="addition"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2775.77.32"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="multiplication"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="elementary_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2765.77.22"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2769.77.26:2775.77.32"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="bin_minus"></om:OMS><om:OMV name="y"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2770.77.27:2770.77.27"/></metadata></om:OMV><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2774.77.31:2774.77.31"/></metadata></om:OMV>
-      </om:OMA>
-      </om:OMA><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="valence_band_edge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2779.77.36:2781.77.38"/></metadata></om:OMS>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2792.77.49"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="multiplication"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="Boltzmann_constant"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2788.77.45"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="temperatur"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2792.77.49:2792.77.49"/></metadata></om:OMS>
-      </om:OMA><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMV name="/I/0"></om:OMV><om:OMV name="x"></om:OMV><om:OMV name="y"></om:OMV>
-      </om:OMA>
-      </om:OMA>
-      </om:OMA>
-      </om:OMA>
-      </om:OMBIND>
-      </om:OMBIND></om:OMOBJ></definition>
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="p"> <scope languages="" priority="0"/> </notation></notations>
-     </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.omdoc b/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.omdoc
deleted file mode 100644
index e9c6c99..0000000
--- a/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.omdoc
+++ /dev/null
@@ -1,13 +0,0 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ElectrostaticPotential" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1432.36.0:1657.42.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1477.37.1:1507.37.31"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1511.39.1:1593.40.29"/></metadata>Spatial variation of the electrostatic potential,
-	   usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1588.-1.-1:1588.-1.-1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="electrostatic_potential">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1595.41.1:1655.41.61"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1621.41.27:1646.41.52"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1621.41.27:1621.41.27"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1625.41.31:1646.41.52"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1626.41.32:1627.41.33"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1629.41.35:1645.41.51"/></metadata></om:OMS>
-      </om:OMA>
-      </om:OMA></om:OMOBJ></type>
-       
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ψ"> <scope languages="" priority="0"/> </notation></notations>
-     </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.omdoc b/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.omdoc
deleted file mode 100644
index d884294..0000000
--- a/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.omdoc
+++ /dev/null
@@ -1,21 +0,0 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="FermiPotentialElectrons" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1049.25.0:1293.30.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1095.26.1:1125.26.31"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1129.27.2:1229.28.31"/></metadata>Spatial variation of the quasi-Fermi potential for the electrons,
-	   usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialElectrons" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1222.-1.-1:1224.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="quasi_Fermi_potential">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1231.29.1:1291.29.61"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
-                 <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="unknown"></om:OMS>
-                 <om:OMBVAR><om:OMV name="/Ω/0"></om:OMV></om:OMBVAR>
-                 <om:OMBIND>
-                 <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="free"></om:OMS>
-                 <om:OMBVAR><om:OMV name="Ω"><type><om:OMV name="/Ω/0"></om:OMV></type></om:OMV></om:OMBVAR>
-                 <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1255.29.25:1280.29.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
-              <om:OMV name="Ω"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1255.29.25:1255.29.25"/></metadata></om:OMV><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1259.29.29:1280.29.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1260.29.30:1261.29.31"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1263.29.33:1279.29.49"/></metadata></om:OMS>
-      </om:OMA>
-      </om:OMA>
-      </om:OMBIND>
-      </om:OMBIND></om:OMOBJ></type>
-       
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="φ_n"> <scope languages="" priority="0"/> </notation></notations>
-     </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.omdoc b/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.omdoc
deleted file mode 100644
index 559afad..0000000
--- a/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.omdoc
+++ /dev/null
@@ -1,21 +0,0 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="FermiPotentialHoles" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1475.36.0:1710.41.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1517.37.1:1547.37.31"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1550.38.1:1646.39.31"/></metadata>Spatial variation of the quasi-Fermi potential for the holes,
-	   usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialHoles" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1639.-1.-1:1641.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="quasi_Fermi_potential">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1648.40.1:1708.40.61"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
-                 <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="unknown"></om:OMS>
-                 <om:OMBVAR><om:OMV name="/Ω/0"></om:OMV></om:OMBVAR>
-                 <om:OMBIND>
-                 <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="free"></om:OMS>
-                 <om:OMBVAR><om:OMV name="Ω"><type><om:OMV name="/Ω/0"></om:OMV></type></om:OMV></om:OMBVAR>
-                 <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1672.40.25:1697.40.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
-              <om:OMV name="Ω"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1672.40.25:1672.40.25"/></metadata></om:OMV><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1676.40.29:1697.40.50"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1677.40.30:1678.40.31"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1680.40.33:1696.40.49"/></metadata></om:OMS>
-      </om:OMA>
-      </om:OMA>
-      </om:OMBIND>
-      </om:OMBIND></om:OMOBJ></type>
-       
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="φ_p"> <scope languages="" priority="0"/> </notation></notations>
-     </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/poisson/$Charge.omdoc b/content/http..mathhub.info/MitM/Models/poisson/$Charge.omdoc
deleted file mode 100644
index 07442c2..0000000
--- a/content/http..mathhub.info/MitM/Models/poisson/$Charge.omdoc
+++ /dev/null
@@ -1,48 +0,0 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Charge" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#599.15.0:1185.30.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#628.16.1:658.16.31"/></metadata></import><import from="http://mathhub.info/MitM/Models/device?DopingProfile"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#661.17.1:690.17.30"/></metadata></import><import from="http://mathhub.info/MitM/Models/poisson?PoissonParameters"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#693.18.1:720.18.28"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#723.19.1:758.19.36"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#761.20.1:803.20.43"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#806.21.1:847.21.42"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#850.22.1:881.22.32"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#884.23.1:922.23.39"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#927.25.1:1087.27.32"/></metadata>The total charge denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="Charge" name="total_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#959.-1.-1:959.-1.-1"/></metadata></om:OMS></om:OMOBJ> composed of doping profile <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DopingProfile" name="doping_profile"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#990.-1.-1:990.-1.-1"/></metadata></om:OMS></om:OMOBJ> and 
-     electron and hole densities <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityElectrons" name="density_electrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1032.-1.-1:1032.-1.-1"/></metadata></om:OMS></om:OMOBJ> and <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityHoles" name="density_holes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1040.-1.-1:1040.-1.-1"/></metadata></om:OMS></om:OMOBJ>, defined by
-     <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="Charge" name="total_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1061.-1.-1:1061.-1.-1"/></metadata></om:OMS></om:OMOBJ> = <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="elementary_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1067.-1.-1:1067.-1.-1"/></metadata></om:OMS></om:OMOBJ>(<om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DopingProfile" name="doping_profile"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1071.-1.-1:1071.-1.-1"/></metadata></om:OMS></om:OMOBJ>+<om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityHoles" name="density_holes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1075.-1.-1:1075.-1.-1"/></metadata></om:OMS></om:OMOBJ> - <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityElectrons" name="density_electrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1081.-1.-1:1081.-1.-1"/></metadata></om:OMS></om:OMOBJ>).</opaque><constant name="total_charge">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1089.28.1:1183.29.65"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1104.28.16:1104.28.16"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1108.28.20:1108.28.20"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></type>
-       <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28"/></metadata>
-                 <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
-                 <om:OMBVAR><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1123.29.5:1123.29.5"/></metadata><type><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1127.29.9:1127.29.9"/></metadata></om:OMS></type></om:OMV></om:OMBVAR>
-                 <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="multiplication"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1131.29.13"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="uminus"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="elementary_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1131.29.13:1131.29.13"/></metadata></om:OMS>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="bin_minus"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="addition"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1140.29.22"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/device" module="DopingProfile" name="doping_profile"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1137.29.19:1137.29.19"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1139.29.21:1139.29.21"/></metadata></om:OMV>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityHoles" name="density_holes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1145.29.27:1145.29.27"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1147.29.29:1151.29.33"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1148.29.30:1148.29.30"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1150.29.32:1150.29.32"/></metadata></om:OMV>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1153.29.35:1159.29.41"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialHoles" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1154.29.36:1156.29.38"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1158.29.40:1158.29.40"/></metadata></om:OMV>
-      </om:OMA>
-      </om:OMA>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityElectrons" name="density_electrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1165.29.47:1165.29.47"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1167.29.49:1171.29.53"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1168.29.50:1168.29.50"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1170.29.52:1170.29.52"/></metadata></om:OMV>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1173.29.55:1179.29.61"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialElectrons" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1174.29.56:1176.29.58"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1178.29.60:1178.29.60"/></metadata></om:OMV>
-      </om:OMA>
-      </om:OMA>
-      </om:OMA>
-      </om:OMA>
-      </om:OMBIND></om:OMOBJ></definition>
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="Q"> <scope languages="" priority="0"/> </notation></notations>
-     </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/poisson/$Displacement.omdoc b/content/http..mathhub.info/MitM/Models/poisson/$Displacement.omdoc
deleted file mode 100644
index ef9baa7..0000000
--- a/content/http..mathhub.info/MitM/Models/poisson/$Displacement.omdoc
+++ /dev/null
@@ -1,35 +0,0 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Displacement" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1252.34.0:1505.41.1"/></metadata><import from="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1287.35.1:1328.35.42"/></metadata></import><import from="http://mathhub.info/MitM/Models/poisson?PoissonParameters"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1331.36.1:1358.36.28"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1363.38.1:1439.38.77"/></metadata>Expression for electric displacement denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="Displacement" name="electric_displacement"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1415.-1.-1:1415.-1.-1"/></metadata></om:OMS></om:OMOBJ> = <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1421.-1.-1:1425.-1.3"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="uminus"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="PoissonParameters" name="dielectric_permitivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1423.-1.1:1425.-1.3"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ> d/dx <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1434.-1.-1:1434.-1.-1"/></metadata></om:OMS></om:OMOBJ></opaque><constant name="electric_displacement">
-       <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1441.39.1:1503.40.30"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1469.39.29:1469.39.29"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></type>
-       <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22"/></metadata>
-                 <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
-                 <om:OMBVAR><om:OMV name="x"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1478.40.5:1478.40.5"/></metadata><type><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"></om:OMS></type></om:OMV></om:OMBVAR>
-                 <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1494.40.21"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="multiplication"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1484.40.11"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="uminus"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="PoissonParameters" name="dielectric_permitivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11"/></metadata></om:OMS>
-      </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1488.40.15:1494.40.21"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1491.40.18"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="der"></om:OMS><om:OMBIND>
-                 <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
-                 <om:OMBVAR><om:OMV name="z"><type><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></type></om:OMV></om:OMBVAR>
-                 <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain_prop"></om:OMS><om:OMV name="z"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56"/></metadata></om:OMV>
-      </om:OMA>
-      </om:OMBIND><om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1489.40.16"/></metadata></om:OMS>
-      </om:OMA><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1493.40.20:1493.40.20"/></metadata></om:OMV>
-      </om:OMA>
-      </om:OMA>
-      </om:OMBIND></om:OMOBJ></definition>
-       <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="D"> <scope languages="" priority="0"/> </notation></notations>
-     </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.omdoc b/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.omdoc
index 0b23979..89d6d56 100644
--- a/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.omdoc
+++ b/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.omdoc
@@ -1,26 +1,14 @@
 <omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PoissonBoundaryConditions" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2396.72.0:2876.81.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2444.73.1:2478.73.35"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2481.74.1:2580.75.37"/></metadata>Boundary value for electrostatic potential at top contact 
-	     for an applied voltage <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2573.-1.-1:2575.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="potential_top">
+	     for an applied voltage <unparsed>None</unparsed>.</opaque><constant name="potential_top">
        <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2582.76.1:2644.76.63"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2598.76.17:2617.76.36"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2598.76.17:2599.76.18"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2601.76.20:2617.76.36"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></type>
-       <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2623.76.42:2633.76.52"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/smglom/arithmetics" module="realarith" name="addition"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2623.76.42:2627.76.46"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2631.76.50:2633.76.52"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></definition>
+       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[QE ElectricPotential]]></om:text></om:OMSF></om:OMOBJ></type>
+       <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[ψ_0_1 + U_1]]></om:text></om:OMSF></om:OMOBJ></definition>
        <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ψ_1"> <scope languages="" priority="0"/> </notation></notations>
      </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2646.77.1:2807.79.60"/></metadata>Boundary value for electrostatic potential at bottom contact 
 	     for an applied voltage <unparsed>None</unparsed>.
 	     N.B.: the applied bias voltage is U_bias = <unparsed>None</unparsed></opaque><constant name="potential_bottom">
        <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2809.80.1:2874.80.66"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2828.80.20:2847.80.39"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2828.80.20:2829.80.21"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2831.80.23:2847.80.39"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></type>
-       <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2853.80.45:2863.80.55"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/smglom/arithmetics" module="realarith" name="addition"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2853.80.45:2857.80.49"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2861.80.53:2863.80.55"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></definition>
+       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[QE ElectricPotential]]></om:text></om:OMSF></om:OMOBJ></type>
+       <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[ψ_0_2 + U_2]]></om:text></om:OMSF></om:OMOBJ></definition>
        <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ψ_2"> <scope languages="" priority="0"/> </notation></notations>
      </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.omdoc b/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.omdoc
index 17d8ce0..155433e 100644
--- a/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.omdoc
+++ b/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.omdoc
@@ -1,20 +1,7 @@
 <omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PoissonEquation" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1529.43.0:1732.51.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?Charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1567.44.1:1583.44.17"/></metadata></import><import from="http://mathhub.info/MitM/Models/poisson?Displacement"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1586.45.1:1608.45.23"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1613.47.1:1698.48.29"/></metadata>Defintion of the Poisson equation with total charge 
        as right hand side.</opaque><constant name="poisson_equation">
        <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1700.49.1:1729.49.30"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
-                 <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="unknown"></om:OMS>
-                 <om:OMBVAR><om:OMV name="/I/2"></om:OMV><om:OMV name="/I/1"></om:OMV><om:OMV name="/I/0"></om:OMV></om:OMBVAR>
-                 <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1719.49.20:1727.49.28"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="ded"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1721.49.22:1727.49.28"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="eq"></om:OMS><om:OMV name="/I/2"></om:OMV><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1721.49.22:1723.49.24"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MitM/smglom/calculus" module="derivative" name="derivative"></om:OMS><om:OMV name="/I/0"></om:OMV><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="Displacement" name="electric_displacement"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1721.49.22:1721.49.22"/></metadata></om:OMS><om:OMV name="/I/1"></om:OMV>
-      </om:OMA><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="Charge" name="total_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1727.49.28:1727.49.28"/></metadata></om:OMS>
-      </om:OMA>
-      </om:OMA>
-      </om:OMBIND></om:OMOBJ></type>
+       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[⊦ D ' ≐ Q]]></om:text></om:OMSF></om:OMOBJ></type>
        
        
      </constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.omdoc b/content/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.omdoc
index 970fde8..08d022e 100644
--- a/content/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.omdoc
+++ b/content/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.omdoc
@@ -1,27 +1,14 @@
 <omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ThermodynamicEquilibrium" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1826.56.0:2308.68.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?Charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1873.57.1:1889.57.17"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1894.59.1:1991.60.34"/></metadata>Value of build-in potential ψ_0 at top contact guranteeing 
        local charge neutrality.</opaque><constant name="equilibrium_potential_top">
        <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1993.61.1:2053.61.61"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2021.61.29:2040.61.48"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2021.61.29:2022.61.30"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2024.61.32:2040.61.48"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></type>
+       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[QE ElectricPotential]]></om:text></om:OMSF></om:OMOBJ></type>
        
        <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ψ_0_2"> <scope languages="" priority="0"/> </notation></notations>
      </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2057.63.1:2235.65.79"/></metadata>Value of build-in potential ψ_0 at bottom contact guranteeing 
        local charge neutrality. 
-       N.B. the build-in potential is given as U_b = <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
-                 <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="unknown"></om:OMS>
-                 <om:OMBVAR><om:OMV name="/I/0"></om:OMV></om:OMBVAR>
-                 <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2210.-1.-1:2222.-1.11"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QESubtract"></om:OMS><om:OMV name="/I/0"></om:OMV><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2210.-1.-1:2214.-1.3"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2218.-1.7:2222.-1.11"/></metadata></om:OMS>
-      </om:OMA>
-      </om:OMBIND></om:OMOBJ> (Check!)</opaque><constant name="equilibrium_potential_bottom">
+       N.B. the build-in potential is given as U_b = <unparsed>None</unparsed> (Check!)</opaque><constant name="equilibrium_potential_bottom">
        <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2243.67.1:2306.67.64"/></metadata>
-       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2274.67.32:2293.67.51"/></metadata>
-              <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
-              <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2274.67.32:2275.67.33"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2277.67.35:2293.67.51"/></metadata></om:OMS>
-      </om:OMA></om:OMOBJ></type>
+       <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[QE ElectricPotential]]></om:text></om:OMSF></om:OMOBJ></type>
        
        <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ψ_0_1"> <scope languages="" priority="0"/> </notation></notations>
      </constant></theory></omdoc>
\ No newline at end of file
diff --git a/errors/mmt-omdoc/.err b/errors/mmt-omdoc/.err
new file mode 100644
index 0000000..a003a31
--- /dev/null
+++ b/errors/mmt-omdoc/.err
@@ -0,0 +1,2 @@
+<errors>
+</errors>
diff --git a/errors/mmt-omdoc/mmt/.err b/errors/mmt-omdoc/mmt/.err
new file mode 100644
index 0000000..a003a31
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/.err
@@ -0,0 +1,2 @@
+<errors>
+</errors>
diff --git a/errors/mmt-omdoc/mmt/Quantities.mmt.err b/errors/mmt-omdoc/mmt/Quantities.mmt.err
new file mode 100644
index 0000000..68e0cd8
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/Quantities.mmt.err
@@ -0,0 +1,268 @@
+<errors>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models?RecombinationRate?recombinationrate_dim?definition: Judgment  |- DimNone/'(Volume*SItime) : type" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$1.apply(RuleBasedChecker.scala:83)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$1.apply(RuleBasedChecker.scala:82)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:82)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$7.apply(MMTStructureChecker.scala:316)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$7.apply(MMTStructureChecker.scala:296)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:296)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models?RecombinationRate?recombinationrate?type: Judgment  |- Ω→QE recombinationrate_dim INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$1.apply(RuleBasedChecker.scala:83)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$1.apply(RuleBasedChecker.scala:82)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:82)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/Quantities.mmt#1740.57.0:1741.57.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: Cannot find resource http://mathhub.info/MitM/Models/SpatialPotential/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/SpatialPotential not found or not accessible" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/Quantities.mmt#1740.57.0:1741.57.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error 
+  type="info.kwarc.mmt.api.BackendError" shortMsg="Cannot find resource http://mathhub.info/MitM/Models/SpatialPotential/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/SpatialPotential not found or not accessible" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.backend.LocalCopy.load(Storage.scala:147)</element>
+      <element>info.kwarc.mmt.api.archives.Archive.load(Archive.scala:81)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:58)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:54)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.backend.Backend.load(Backend.scala:54)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:382)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.optional(Lookup.scala:31)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getO(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getComponent(Lookup.scala:81)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:37)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:36)</element>
+      <element>scala.Option.map(Option.scala:146)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:36)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:123)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:121)</element>
+      <element>scala.Option.foreach(Option.scala:257)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:121)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:116)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter.check(TextInterpreter.scala:116)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:164)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:419)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:422)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+</error>
+</error>
+
+</errors>
diff --git a/errors/mmt-omdoc/mmt/VanRoosbroeck.mmt.err b/errors/mmt-omdoc/mmt/VanRoosbroeck.mmt.err
new file mode 100644
index 0000000..73ca509
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/VanRoosbroeck.mmt.err
@@ -0,0 +1,1024 @@
+<errors>
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#702.15.1:734.15.33" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#702.15.1:734.15.33
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#737.16.1:779.16.43" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#737.16.1:779.16.43
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#782.17.1:829.17.48" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#782.17.1:829.17.48
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#832.18.1:875.18.44" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#832.18.1:875.18.44
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#878.19.1:935.19.58" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#878.19.1:935.19.58
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#938.20.1:991.20.54" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#938.20.1:991.20.54
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#994.21.1:1041.21.48" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#994.21.1:1041.21.48
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#1043.22.0:1044.22.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#1043.22.0:1044.22.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheckExtendContext(MMTStructureChecker.scala:86)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:411)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+</errors>
diff --git a/errors/mmt-omdoc/mmt/band.mmt.err b/errors/mmt-omdoc/mmt/band.mmt.err
new file mode 100644
index 0000000..edc6cdf
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/band.mmt.err
@@ -0,0 +1,199 @@
+<errors>
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/band.mmt#621.16.0:622.16.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: Cannot find resource http://mathhub.info/MitM/Models/BandstructureParameters/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/BandstructureParameters not found or not accessible" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/band.mmt#621.16.0:622.16.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error 
+  type="info.kwarc.mmt.api.BackendError" shortMsg="Cannot find resource http://mathhub.info/MitM/Models/BandstructureParameters/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/BandstructureParameters not found or not accessible" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.backend.LocalCopy.load(Storage.scala:147)</element>
+      <element>info.kwarc.mmt.api.archives.Archive.load(Archive.scala:81)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:58)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:54)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.backend.Backend.load(Backend.scala:54)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:382)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.optional(Lookup.scala:31)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getO(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getComponent(Lookup.scala:81)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:37)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:36)</element>
+      <element>scala.Option.map(Option.scala:146)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:36)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:123)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:121)</element>
+      <element>scala.Option.foreach(Option.scala:257)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:121)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:116)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter.check(TextInterpreter.scala:116)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:164)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:419)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:422)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+</error>
+</error>
+
+<error target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/band.mmt#744.21.12:744.21.12" type="info.kwarc.mmt.api.SourceError" shortMsg="expected ':', '=', '#', '##', '@', 'role', found " level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/band.mmt#744.21.12:744.21.12
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readConstant$3.apply(StructureParser.scala:875)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readConstant$3.apply(StructureParser.scala:875)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.errorCont(StructureParser.scala:156)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:875)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readStructure$1.apply$mcV$sp(StructureParser.scala:924)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readStructure$1.apply(StructureParser.scala:924)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readStructure$1.apply(StructureParser.scala:924)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readStructure(StructureParser.scala:923)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:493)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+</errors>
diff --git a/errors/mmt-omdoc/mmt/constants.mmt.err b/errors/mmt-omdoc/mmt/constants.mmt.err
new file mode 100644
index 0000000..7c40c4b
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/constants.mmt.err
@@ -0,0 +1,136 @@
+<errors>
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/constants.mmt#701.15.0:702.15.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: Cannot find resource http://mathhub.info/MitM/Models/PhysicalConstants/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/PhysicalConstants not found or not accessible" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/constants.mmt#701.15.0:702.15.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error 
+  type="info.kwarc.mmt.api.BackendError" shortMsg="Cannot find resource http://mathhub.info/MitM/Models/PhysicalConstants/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/PhysicalConstants not found or not accessible" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.backend.LocalCopy.load(Storage.scala:147)</element>
+      <element>info.kwarc.mmt.api.archives.Archive.load(Archive.scala:81)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:58)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:54)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.backend.Backend.load(Backend.scala:54)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:382)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.optional(Lookup.scala:31)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getO(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getComponent(Lookup.scala:81)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:37)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:36)</element>
+      <element>scala.Option.map(Option.scala:146)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:36)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:123)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:121)</element>
+      <element>scala.Option.foreach(Option.scala:257)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:121)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:116)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter.check(TextInterpreter.scala:116)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:164)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:419)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:422)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+</error>
+</error>
+
+</errors>
diff --git a/errors/mmt-omdoc/mmt/continuity.mmt.err b/errors/mmt-omdoc/mmt/continuity.mmt.err
new file mode 100644
index 0000000..b884f2f
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/continuity.mmt.err
@@ -0,0 +1,1069 @@
+<errors>
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/continuity.mmt#273.8.0:274.8.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: Cannot find resource http://mathhub.info/MitM/Models/continuity/Mobility/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/continuity/Mobility not found or not accessible" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/continuity.mmt#273.8.0:274.8.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error 
+  type="info.kwarc.mmt.api.BackendError" shortMsg="Cannot find resource http://mathhub.info/MitM/Models/continuity/Mobility/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/continuity/Mobility not found or not accessible" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.backend.LocalCopy.load(Storage.scala:147)</element>
+      <element>info.kwarc.mmt.api.archives.Archive.load(Archive.scala:81)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:58)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:54)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.backend.Backend.load(Backend.scala:54)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:382)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.optional(Lookup.scala:31)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getO(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getComponent(Lookup.scala:81)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:37)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:36)</element>
+      <element>scala.Option.map(Option.scala:146)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:36)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:123)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:121)</element>
+      <element>scala.Option.foreach(Option.scala:257)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:121)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:116)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter.check(TextInterpreter.scala:116)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:164)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:419)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:422)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+</error>
+</error>
+
+<error target="parser" sref="http://mathhub.info/MitM/Models/mmt/continuity.mmt#797.24.50:797.24.50" type="info.kwarc.mmt.api.SourceError" shortMsg="unbound token: '" level="2">
+  source error (parser) at http://mathhub.info/MitM/Models/mmt/continuity.mmt#797.24.50:797.24.50
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeError(NotationBasedParser.scala:81)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:304)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>scala.collection.immutable.List.map(List.scala:273)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.logGroup(NotationBasedParser.scala:57)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:204)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?CurrentLaw?current_law?type: Judgment n:/n/8 |- {x:(oneOf  /A/0 Ω Ω)}⊦j x≐((-q⋅μ)⋅(n x))⋅φ (' x) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?CurrentLaw?current_law?type: Judgment n:/n/8 |- {x:(oneOf  /A/0 Ω Ω)}⊦j x≐((-q⋅μ)⋅(n x))⋅φ (' x) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?CurrentLaw?current_law?type: Judgment n:/n/8 |- {x:(oneOf  /A/0 Ω Ω)}⊦j x≐((-q⋅μ)⋅(n x))⋅φ (' x) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?CurrentLaw?current_law?type: Judgment n:/n/8 |- {x:(oneOf  /A/0 Ω Ω)}⊦j x≐((-q⋅μ)⋅(n x))⋅φ (' x) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?CurrentLaw?current_law?type: Judgment n:/n/8 |- {x:(oneOf  /A/0 Ω Ω)}⊦j x≐((-q⋅μ)⋅(n x))⋅φ (' x) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?CurrentLaw?current_law?type: Judgment n:/n/8 |- {x:(oneOf  /A/0 Ω Ω)}⊦j x≐((-q⋅μ)⋅(n x))⋅φ (' x) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error target="parser" sref="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1119.36.15:1119.36.15" type="info.kwarc.mmt.api.SourceError" shortMsg="unbound token: '" level="2">
+  source error (parser) at http://mathhub.info/MitM/Models/mmt/continuity.mmt#1119.36.15:1119.36.15
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeError(NotationBasedParser.scala:81)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:304)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>scala.collection.immutable.List.map(List.scala:273)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.logGroup(NotationBasedParser.scala:57)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:204)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?ContinuityEquation?continuity_equation?type: Judgment  |- {x:(oneOf  /A/0 Ω Ω Ω)}⊦(j ' x)≐-(z (R x)) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?ContinuityEquation?continuity_equation?type: Judgment  |- {x:(oneOf  /A/0 Ω Ω Ω)}⊦(j ' x)≐-(z (R x)) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?ContinuityEquation?continuity_equation?type: Judgment  |- {x:(oneOf  /A/0 Ω Ω Ω)}⊦(j ' x)≐-(z (R x)) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?ContinuityEquation?continuity_equation?type: Judgment  |- {x:(oneOf  /A/0 Ω Ω Ω)}⊦(j ' x)≐-(z (R x)) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/continuity?ContinuityEquation?continuity_equation?type: Judgment  |- {x:(oneOf  /A/0 Ω Ω Ω)}⊦(j ' x)≐-(z (R x)) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+</errors>
diff --git a/errors/mmt-omdoc/mmt/densities.mmt.err b/errors/mmt-omdoc/mmt/densities.mmt.err
new file mode 100644
index 0000000..681108e
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/densities.mmt.err
@@ -0,0 +1,201 @@
+<errors>
+<error target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/densities.mmt#508.13.12:508.13.12" type="info.kwarc.mmt.api.SourceError" shortMsg="expected ':', '=', '#', '##', '@', 'role', found " level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/densities.mmt#508.13.12:508.13.12
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readConstant$3.apply(StructureParser.scala:875)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readConstant$3.apply(StructureParser.scala:875)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.errorCont(StructureParser.scala:156)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:875)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readStructure$1.apply$mcV$sp(StructureParser.scala:924)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readStructure$1.apply(StructureParser.scala:924)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readStructure$1.apply(StructureParser.scala:924)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readStructure(StructureParser.scala:923)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:493)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/densities?DensityLaw?density_law?type: Judgment ψ:/ψ/16, n:/n/17 |- {x:(oneOf  /A/0 Ω Ω Ω)}⊦(n x)≐N⋅((oneOf  /A/1 exponentiation exponentiation exponentiation exponentiation) (scalar (((((-q⋅z)⋅((ψ x)-(oneOf  /A/4 φ x φ x)))-E))/(k_B))⋅T)) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/densities?DensityLaw?density_law?type: Judgment ψ:/ψ/16, n:/n/17 |- {x:(oneOf  /A/0 Ω Ω Ω)}⊦(n x)≐N⋅((oneOf  /A/1 exponentiation exponentiation exponentiation exponentiation) (scalar (((((-q⋅z)⋅((ψ x)-(oneOf  /A/4 φ x φ x)))-E))/(k_B))⋅T)) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+</errors>
diff --git a/errors/mmt-omdoc/mmt/device.mmt.err b/errors/mmt-omdoc/mmt/device.mmt.err
new file mode 100644
index 0000000..c8a9b3c
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/device.mmt.err
@@ -0,0 +1,470 @@
+<errors>
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/device.mmt#566.16.0:567.16.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: Cannot find resource http://mathhub.info/MitM/Models/device/DeviceGeometry/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/device/DeviceGeometry not found or not accessible" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/device.mmt#566.16.0:567.16.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error 
+  type="info.kwarc.mmt.api.BackendError" shortMsg="Cannot find resource http://mathhub.info/MitM/Models/device/DeviceGeometry/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/device/DeviceGeometry not found or not accessible" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.backend.LocalCopy.load(Storage.scala:147)</element>
+      <element>info.kwarc.mmt.api.archives.Archive.load(Archive.scala:81)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:58)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:54)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.backend.Backend.load(Backend.scala:54)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:382)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.optional(Lookup.scala:31)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getO(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getComponent(Lookup.scala:81)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:37)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:36)</element>
+      <element>scala.Option.map(Option.scala:146)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:36)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:123)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:121)</element>
+      <element>scala.Option.foreach(Option.scala:257)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:121)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:116)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter.check(TextInterpreter.scala:116)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:164)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:419)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:422)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+</error>
+</error>
+
+<error type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile?type: Judgment  |- Ω→density_dim INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/device.mmt#1310.45.0:1311.45.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: Cannot find resource http://mathhub.info/MitM/Models/device/DopingProfile/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/device/DopingProfile not found or not accessible" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/device.mmt#1310.45.0:1311.45.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error 
+  type="info.kwarc.mmt.api.BackendError" shortMsg="Cannot find resource http://mathhub.info/MitM/Models/device/DopingProfile/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/device/DopingProfile not found or not accessible" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.backend.LocalCopy.load(Storage.scala:147)</element>
+      <element>info.kwarc.mmt.api.archives.Archive.load(Archive.scala:81)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:58)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:54)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.backend.Backend.load(Backend.scala:54)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:382)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.optional(Lookup.scala:31)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getO(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getComponent(Lookup.scala:81)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:37)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:36)</element>
+      <element>scala.Option.map(Option.scala:146)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:36)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:123)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:121)</element>
+      <element>scala.Option.foreach(Option.scala:257)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:121)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:116)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter.check(TextInterpreter.scala:116)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:164)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:419)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:422)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+</error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/device.mmt#1924.62.0:1925.62.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: Cannot find resource http://mathhub.info/MitM/Models/device/DeviceOperationState/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/device/DeviceOperationState not found or not accessible" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/device.mmt#1924.62.0:1925.62.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error 
+  type="info.kwarc.mmt.api.BackendError" shortMsg="Cannot find resource http://mathhub.info/MitM/Models/device/DeviceOperationState/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/device/DeviceOperationState not found or not accessible" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.backend.LocalCopy.load(Storage.scala:147)</element>
+      <element>info.kwarc.mmt.api.archives.Archive.load(Archive.scala:81)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:58)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:54)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.backend.Backend.load(Backend.scala:54)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:382)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.optional(Lookup.scala:31)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getO(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getComponent(Lookup.scala:81)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:37)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:36)</element>
+      <element>scala.Option.map(Option.scala:146)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:36)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:123)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:121)</element>
+      <element>scala.Option.foreach(Option.scala:257)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:121)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:116)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter.check(TextInterpreter.scala:116)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:164)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:419)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:422)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+</error>
+</error>
+
+</errors>
diff --git a/errors/mmt-omdoc/mmt/poisson.mmt.err b/errors/mmt-omdoc/mmt/poisson.mmt.err
new file mode 100644
index 0000000..afbf9ff
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/poisson.mmt.err
@@ -0,0 +1,4616 @@
+<errors>
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#564.12.0:565.12.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: Cannot find resource http://mathhub.info/MitM/Models/poisson/PoissonParameters/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/poisson/PoissonParameters not found or not accessible" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#564.12.0:565.12.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error 
+  type="info.kwarc.mmt.api.BackendError" shortMsg="Cannot find resource http://mathhub.info/MitM/Models/poisson/PoissonParameters/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/poisson/PoissonParameters not found or not accessible" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.backend.LocalCopy.load(Storage.scala:147)</element>
+      <element>info.kwarc.mmt.api.archives.Archive.load(Archive.scala:81)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:58)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:54)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.backend.Backend.load(Backend.scala:54)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:382)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.optional(Lookup.scala:31)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getO(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getComponent(Lookup.scala:81)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:37)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:36)</element>
+      <element>scala.Option.map(Option.scala:146)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:36)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:123)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:121)</element>
+      <element>scala.Option.foreach(Option.scala:257)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:121)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:116)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter.check(TextInterpreter.scala:116)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:164)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:419)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:422)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+</error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1066.26.24:1166.26.124" type="info.kwarc.mmt.api.SourceError" shortMsg="during parsing: get error: backend: no backend available that is applicable to http://cds.omdoc.org/mmt?mmt?oneOf" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1066.26.24:1166.26.124
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:145)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://cds.omdoc.org/mmt?mmt?oneOf" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getAs$1.apply(Lookup.scala:41)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getAs$1.apply(Lookup.scala:41)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.as(Lookup.scala:21)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getAs(Lookup.scala:41)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier$$anonfun$4$$anonfun$apply$6.apply(ElaborationBasedSimplifier.scala:199)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier$$anonfun$4$$anonfun$apply$6.apply(ElaborationBasedSimplifier.scala:195)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier$$anonfun$4.apply(ElaborationBasedSimplifier.scala:195)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier$$anonfun$4.apply(ElaborationBasedSimplifier.scala:191)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.info$kwarc$mmt$api$uom$ElaborationBasedSimplifier$$flattenDeclaration(ElaborationBasedSimplifier.scala:191)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier$$anonfun$flatten$3.apply(ElaborationBasedSimplifier.scala:101)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier$$anonfun$flatten$3.apply(ElaborationBasedSimplifier.scala:101)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.flatten(ElaborationBasedSimplifier.scala:101)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.info$kwarc$mmt$api$uom$ElaborationBasedSimplifier$$flattenDeclaration(ElaborationBasedSimplifier.scala:167)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier$$anonfun$flatten$3.apply(ElaborationBasedSimplifier.scala:101)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier$$anonfun$flatten$3.apply(ElaborationBasedSimplifier.scala:101)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.flatten(ElaborationBasedSimplifier.scala:101)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.info$kwarc$mmt$api$uom$ElaborationBasedSimplifier$$flattenDeclaration(ElaborationBasedSimplifier.scala:167)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier$$anonfun$flatten$3.apply(ElaborationBasedSimplifier.scala:101)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier$$anonfun$flatten$3.apply(ElaborationBasedSimplifier.scala:101)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.flatten(ElaborationBasedSimplifier.scala:101)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.apply(ElaborationBasedSimplifier.scala:48)</element>
+      <element>info.kwarc.mmt.api.uom.StructureSimplifier$class.apply(Simplifier.scala:24)</element>
+      <element>info.kwarc.mmt.api.uom.Simplifier.apply(Simplifier.scala:39)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$getRules$1.apply(NotationBasedParser.scala:221)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$getRules$1.apply(NotationBasedParser.scala:220)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.getRules(NotationBasedParser.scala:220)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:180)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/poisson?ChargeLaw?total_charge_density?type: Judgment  |- {x : Ω} ⊦ Q x ≐ -q ⋅ ((C x) + (holes/z ⋅ (holes/density x)) + (electrons/z ⋅ (electrons/density x)) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1168.27.0:1169.27.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: Cannot find resource http://mathhub.info/MitM/Models/poisson/ChargeLaw/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/poisson/ChargeLaw not found or not accessible" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1168.27.0:1169.27.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error 
+  type="info.kwarc.mmt.api.BackendError" shortMsg="Cannot find resource http://mathhub.info/MitM/Models/poisson/ChargeLaw/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/poisson/ChargeLaw not found or not accessible" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.backend.LocalCopy.load(Storage.scala:147)</element>
+      <element>info.kwarc.mmt.api.archives.Archive.load(Archive.scala:81)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:58)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:54)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.backend.Backend.load(Backend.scala:54)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:382)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.optional(Lookup.scala:31)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getO(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getComponent(Lookup.scala:81)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:37)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:36)</element>
+      <element>scala.Option.map(Option.scala:146)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:36)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:123)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:121)</element>
+      <element>scala.Option.foreach(Option.scala:257)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:121)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:116)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter.check(TextInterpreter.scala:116)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:164)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:419)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:422)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+</error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1209.30.1:1250.30.42" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1209.30.1:1250.30.42
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1253.31.1:1280.31.28" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1253.31.1:1280.31.28
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1283.32.1:1305.32.23" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1283.32.1:1305.32.23
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1310.34.1:1386.34.77" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1310.34.1:1386.34.77
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1414.36.25:1435.36.46" type="info.kwarc.mmt.api.SourceError" shortMsg="during parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1414.36.25:1435.36.46
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:145)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.flatten(ElaborationBasedSimplifier.scala:94)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.apply(ElaborationBasedSimplifier.scala:48)</element>
+      <element>info.kwarc.mmt.api.uom.StructureSimplifier$class.apply(Simplifier.scala:24)</element>
+      <element>info.kwarc.mmt.api.uom.Simplifier.apply(Simplifier.scala:39)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$getRules$1.apply(NotationBasedParser.scala:221)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$getRules$1.apply(NotationBasedParser.scala:220)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.getRules(NotationBasedParser.scala:220)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:180)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1441.37.4:1460.37.23" type="info.kwarc.mmt.api.SourceError" shortMsg="during parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1441.37.4:1460.37.23
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:145)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:856)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$7.apply(NotationBasedParser.scala:223)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$7.apply(NotationBasedParser.scala:223)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.getRules(NotationBasedParser.scala:223)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:180)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:856)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1390.36.1:1467.37.30" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1390.36.1:1467.37.30
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1468.38.0:1469.38.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1468.38.0:1469.38.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheckExtendContext(MMTStructureChecker.scala:86)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:411)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1567.44.1:1583.44.17" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1567.44.1:1583.44.17
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1586.45.1:1608.45.23" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1586.45.1:1608.45.23
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1613.47.1:1698.48.29" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1613.47.1:1698.48.29
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1719.49.20:1728.49.29" type="info.kwarc.mmt.api.SourceError" shortMsg="during parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1719.49.20:1728.49.29
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:145)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.flatten(ElaborationBasedSimplifier.scala:94)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.apply(ElaborationBasedSimplifier.scala:48)</element>
+      <element>info.kwarc.mmt.api.uom.StructureSimplifier$class.apply(Simplifier.scala:24)</element>
+      <element>info.kwarc.mmt.api.uom.Simplifier.apply(Simplifier.scala:39)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$getRules$1.apply(NotationBasedParser.scala:221)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$getRules$1.apply(NotationBasedParser.scala:220)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.getRules(NotationBasedParser.scala:220)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:180)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1700.49.1:1729.49.30" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1700.49.1:1729.49.30
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1731.51.0:1732.51.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1731.51.0:1732.51.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Displacement" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheckExtendContext(MMTStructureChecker.scala:86)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:411)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1873.57.1:1889.57.17" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1873.57.1:1889.57.17
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1894.59.1:1991.60.34" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1894.59.1:1991.60.34
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2021.61.29:2042.61.50" type="info.kwarc.mmt.api.SourceError" shortMsg="during parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2021.61.29:2042.61.50
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:145)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.flatten(ElaborationBasedSimplifier.scala:94)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.apply(ElaborationBasedSimplifier.scala:48)</element>
+      <element>info.kwarc.mmt.api.uom.StructureSimplifier$class.apply(Simplifier.scala:24)</element>
+      <element>info.kwarc.mmt.api.uom.Simplifier.apply(Simplifier.scala:39)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$getRules$1.apply(NotationBasedParser.scala:221)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$getRules$1.apply(NotationBasedParser.scala:220)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.getRules(NotationBasedParser.scala:220)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:180)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1993.61.1:2053.61.61" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#1993.61.1:2053.61.61
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2057.63.1:2235.65.79" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2057.63.1:2235.65.79
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2274.67.32:2295.67.53" type="info.kwarc.mmt.api.SourceError" shortMsg="during parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2274.67.32:2295.67.53
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:145)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$7.apply(NotationBasedParser.scala:223)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$7.apply(NotationBasedParser.scala:223)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.getRules(NotationBasedParser.scala:223)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:180)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2243.67.1:2306.67.64" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2243.67.1:2306.67.64
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2307.68.0:2308.68.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2307.68.0:2308.68.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheckExtendContext(MMTStructureChecker.scala:86)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:411)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2444.73.1:2478.73.35" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2444.73.1:2478.73.35
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:480)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2481.74.1:2580.75.37" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2481.74.1:2580.75.37
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2598.76.17:2619.76.38" type="info.kwarc.mmt.api.SourceError" shortMsg="during parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2598.76.17:2619.76.38
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:145)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.flatten(ElaborationBasedSimplifier.scala:94)</element>
+      <element>info.kwarc.mmt.api.uom.ElaborationBasedSimplifier.apply(ElaborationBasedSimplifier.scala:48)</element>
+      <element>info.kwarc.mmt.api.uom.StructureSimplifier$class.apply(Simplifier.scala:24)</element>
+      <element>info.kwarc.mmt.api.uom.Simplifier.apply(Simplifier.scala:39)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$getRules$1.apply(NotationBasedParser.scala:221)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$getRules$1.apply(NotationBasedParser.scala:220)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.getRules(NotationBasedParser.scala:220)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:180)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2623.76.42:2635.76.54" type="info.kwarc.mmt.api.SourceError" shortMsg="during parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2623.76.42:2635.76.54
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:145)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:856)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$7.apply(NotationBasedParser.scala:223)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$7.apply(NotationBasedParser.scala:223)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.getRules(NotationBasedParser.scala:223)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:180)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:856)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2582.76.1:2644.76.63" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2582.76.1:2644.76.63
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2646.77.1:2807.79.60" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2646.77.1:2807.79.60
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:553)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2828.80.20:2849.80.41" type="info.kwarc.mmt.api.SourceError" shortMsg="during parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2828.80.20:2849.80.41
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:145)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$7.apply(NotationBasedParser.scala:223)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$7.apply(NotationBasedParser.scala:223)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.getRules(NotationBasedParser.scala:223)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:180)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2853.80.45:2865.80.57" type="info.kwarc.mmt.api.SourceError" shortMsg="during parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2853.80.45:2865.80.57
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:145)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:856)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$7.apply(NotationBasedParser.scala:223)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$7.apply(NotationBasedParser.scala:223)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.getRules(NotationBasedParser.scala:223)</element>
+      <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:180)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:856)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2809.80.1:2874.80.66" type="info.kwarc.mmt.api.SourceError" shortMsg="after parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2809.80.1:2874.80.66
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:98)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectRules(Rule.scala:124)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheck(MMTStructureChecker.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:53)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2875.81.0:2876.81.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/poisson.mmt#2875.81.0:2876.81.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error type="info.kwarc.mmt.api.GetError" shortMsg="get error: backend: no backend available that is applicable to http://mathhub.info/MitM/Models/poisson?Charge" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:386)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.getDeclarationsInScope(Controller.scala:324)</element>
+      <element>sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:133)</element>
+      <element>info.kwarc.mmt.api.RuleSet$$anonfun$1.apply(Rule.scala:132)</element>
+      <element>scala.collection.immutable.List.flatMap(List.scala:327)</element>
+      <element>info.kwarc.mmt.api.RuleSet$.collectAdditionalRules(Rule.scala:132)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.prepareCheckExtendContext(MMTStructureChecker.scala:86)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:411)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+  </error>
+</error>
+
+</errors>
diff --git a/errors/mmt-omdoc/mmt/recombination.mmt.err b/errors/mmt-omdoc/mmt/recombination.mmt.err
new file mode 100644
index 0000000..c38f7df
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/recombination.mmt.err
@@ -0,0 +1,1815 @@
+<errors>
+<error target="parser" sref="http://mathhub.info/MitM/Models/mmt/recombination.mmt#477.14.6:500.14.29" type="info.kwarc.mmt.api.SourceError" shortMsg="unbound token: electrons/spatialdensity" level="2">
+  source error (parser) at http://mathhub.info/MitM/Models/mmt/recombination.mmt#477.14.6:500.14.29
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeError(NotationBasedParser.scala:81)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:304)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>scala.collection.immutable.List.map(List.scala:273)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.logGroup(NotationBasedParser.scala:57)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:204)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error target="parser" sref="http://mathhub.info/MitM/Models/mmt/recombination.mmt#506.14.35:525.14.54" type="info.kwarc.mmt.api.SourceError" shortMsg="unbound token: holes/spatialdensity" level="2">
+  source error (parser) at http://mathhub.info/MitM/Models/mmt/recombination.mmt#506.14.35:525.14.54
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeError(NotationBasedParser.scala:81)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:304)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>scala.collection.immutable.List.map(List.scala:273)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.logGroup(NotationBasedParser.scala:57)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:204)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error target="parser" sref="http://mathhub.info/MitM/Models/mmt/recombination.mmt#534.14.63:557.14.86" type="info.kwarc.mmt.api.SourceError" shortMsg="unbound token: electrons/spatialdensity" level="2">
+  source error (parser) at http://mathhub.info/MitM/Models/mmt/recombination.mmt#534.14.63:557.14.86
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeError(NotationBasedParser.scala:81)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:304)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>scala.collection.immutable.List.map(List.scala:273)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.logGroup(NotationBasedParser.scala:57)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:204)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error target="parser" sref="http://mathhub.info/MitM/Models/mmt/recombination.mmt#565.14.94:584.14.113" type="info.kwarc.mmt.api.SourceError" shortMsg="unbound token: holes/spatialdensity" level="2">
+  source error (parser) at http://mathhub.info/MitM/Models/mmt/recombination.mmt#565.14.94:584.14.113
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeError(NotationBasedParser.scala:81)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:304)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>scala.collection.immutable.List.map(List.scala:273)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.logGroup(NotationBasedParser.scala:57)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:204)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error target="parser" sref="http://mathhub.info/MitM/Models/mmt/recombination.mmt#618.15.29:642.15.53" type="info.kwarc.mmt.api.SourceError" shortMsg="unbound token: electrons/fermi/potential" level="2">
+  source error (parser) at http://mathhub.info/MitM/Models/mmt/recombination.mmt#618.15.29:642.15.53
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeError(NotationBasedParser.scala:81)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:304)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>scala.collection.immutable.List.map(List.scala:273)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>scala.collection.immutable.List.map(List.scala:277)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.logGroup(NotationBasedParser.scala:57)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:204)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error target="parser" sref="http://mathhub.info/MitM/Models/mmt/recombination.mmt#650.15.61:670.15.81" type="info.kwarc.mmt.api.SourceError" shortMsg="unbound token: holes/fermi/potential" level="2">
+  source error (parser) at http://mathhub.info/MitM/Models/mmt/recombination.mmt#650.15.61:670.15.81
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeError(NotationBasedParser.scala:81)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:304)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>scala.collection.immutable.List.map(List.scala:273)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$14.apply(NotationBasedParser.scala:327)</element>
+    <element>scala.collection.immutable.List.map(List.scala:277)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:327)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$doFoundContent$1(NotationBasedParser.scala:426)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:489)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$makeTermFromMatchedList$1.apply(NotationBasedParser.scala:486)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:486)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:311)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.info$kwarc$mmt$api$parser$NotationBasedParser$$makeTerm(NotationBasedParser.scala:317)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser$$anonfun$5.apply(NotationBasedParser.scala:205)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.logGroup(NotationBasedParser.scala:57)</element>
+    <element>info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:204)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:142)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:285)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:290)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:850)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:603)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+type="info.kwarc.mmt.api.InvalidUnit" shortMsg="invalid unit: http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate?type: Judgment T:/T/15, exponential:/exponential/16 |- {x:Ω}⊦(R x)≐(((r (electrons/spatialdensity x) (holes/spatialdensity x))⋅(electrons/spatialdensity x))⋅(holes/spatialdensity x))⋅(1-(exponential ((q⋅((electrons/fermi/potential x)-(holes/fermi/potential x))))/((k_B⋅T)))) INHABITABLE" level="2">
+  <stacktrace>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:88)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1$$anonfun$apply$mcV$sp$2.apply(RuleBasedChecker.scala:86)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply$mcV$sp(RuleBasedChecker.scala:86)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$apply$1.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.logGroup(RuleBasedChecker.scala:16)</element>
+    <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:276)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$check$5.apply(MMTStructureChecker.scala:269)</element>
+    <element>scala.Option.foreach(Option.scala:257)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:269)</element>
+    <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementBegin(MMTStructureChecker.scala:56)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElement(Interpreter.scala:73)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.seCont(StructureParser.scala:94)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.addDeclaration$1(StructureParser.scala:453)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:604)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:433)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply$mcV$sp(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$readTheory$1.apply(StructureParser.scala:687)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:686)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+</error>
+
+<error 
+target="structure-parser" sref="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1103.26.0:1104.26.1" type="info.kwarc.mmt.api.SourceError" shortMsg="error while parsing: Cannot find resource http://mathhub.info/MitM/Models/recombination/SpontaneousRecombination/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/recombination/SpontaneousRecombination not found or not accessible" level="2">
+  source error (structure-parser) at http://mathhub.info/MitM/Models/mmt/recombination.mmt#1103.26.0:1104.26.1
+  <stacktrace>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.makeError(StructureParser.scala:160)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:415)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+    <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+    <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+    <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+    <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+    <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+    <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+    <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+    <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+    <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+    <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+    <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+    <element>Debug$.run(Debug.scala:32)</element>
+    <element>Test.main(preamble.scala:48)</element>
+    <element>Debug.main(Debug.scala)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+    <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+    <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+    <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+    <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+  </stacktrace>
+  <error 
+  type="info.kwarc.mmt.api.BackendError" shortMsg="Cannot find resource http://mathhub.info/MitM/Models/recombination/SpontaneousRecombination/: file/folder /home/jazzpirate/work/MathHub/MitM/Models/narration/recombination/SpontaneousRecombination not found or not accessible" level="2">
+    <stacktrace>
+      <element>info.kwarc.mmt.api.backend.LocalCopy.load(Storage.scala:147)</element>
+      <element>info.kwarc.mmt.api.archives.Archive.load(Archive.scala:81)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:58)</element>
+      <element>info.kwarc.mmt.api.backend.Backend$$anonfun$load$2.apply(Backend.scala:54)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.backend.Backend.load(Backend.scala:54)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply$mcV$sp(Controller.scala:382)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$retrieve$1.apply(Controller.scala:379)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.logGroup(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.retrieve(Controller.scala:378)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply$mcV$sp(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anonfun$iterate$1.apply(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:357)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:369)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.iterate(Controller.scala:349)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller$$anon$3.handler(Controller.scala:320)</element>
+      <element>info.kwarc.mmt.api.libraries.LookupWithNotFoundHandler.get(Lookup.scala:197)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup$$anonfun$getO$1.apply(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.optional(Lookup.scala:31)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getO(Lookup.scala:36)</element>
+      <element>info.kwarc.mmt.api.libraries.Lookup.getComponent(Lookup.scala:81)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:37)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker$$anonfun$2.apply(RuleBasedChecker.scala:36)</element>
+      <element>scala.Option.map(Option.scala:146)</element>
+      <element>info.kwarc.mmt.api.checking.RuleBasedChecker.apply(RuleBasedChecker.scala:36)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:123)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1$$anonfun$apply$4.apply(TextInterpreter.scala:121)</element>
+      <element>scala.Option.foreach(Option.scala:257)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:121)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter$$anonfun$check$1.apply(TextInterpreter.scala:116)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.opaque.TextInterpreter.check(TextInterpreter.scala:116)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$check(MMTStructureChecker.scala:164)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:419)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker$$anonfun$info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1$1.apply(MMTStructureChecker.scala:416)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.info$kwarc$mmt$api$checking$MMTStructureChecker$$doDoc$1(MMTStructureChecker.scala:416)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.checkElementEnd(MMTStructureChecker.scala:422)</element>
+      <element>info.kwarc.mmt.api.checking.MMTStructureChecker.applyElementEnd(MMTStructureChecker.scala:64)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter$$anon$1.onElementEnd(Interpreter.scala:76)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.end(StructureParser.scala:109)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.readTheory(StructureParser.scala:689)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.info$kwarc$mmt$api$parser$KeywordBasedParser$$readInDocument(StructureParser.scala:387)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply$mcV$sp(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser$$anonfun$apply$1.apply(StructureParser.scala:176)</element>
+      <element>info.kwarc.mmt.api.frontend.Logger$class.logGroup(Log.scala:34)</element>
+      <element>info.kwarc.mmt.api.parser.Parser.logGroup(Parser.scala:225)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:175)</element>
+      <element>info.kwarc.mmt.api.parser.KeywordBasedParser.apply(StructureParser.scala:166)</element>
+      <element>info.kwarc.mmt.api.checking.TwoStepInterpreter.apply(Interpreter.scala:79)</element>
+      <element>info.kwarc.mmt.api.checking.Interpreter.importDocument(Interpreter.scala:40)</element>
+      <element>info.kwarc.mmt.api.archives.Importer.buildFile(Index.scala:39)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.runBuildTask(BuildTarget.scala:526)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.checkOrRunBuildTask(BuildTarget.scala:453)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:182)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager$$anonfun$addTasks$1.apply(BuildQueue.scala:181)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.archives.TrivialBuildManager.addTasks(BuildQueue.scala:181)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:374)</element>
+      <element>info.kwarc.mmt.api.archives.TraversingBuildTarget.build(BuildTarget.scala:368)</element>
+      <element>info.kwarc.mmt.api.archives.BuildTarget.apply(BuildTarget.scala:214)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:309)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$$anonfun$archiveBuildAction$1.apply(ActionHandling.scala:286)</element>
+      <element>scala.collection.immutable.List.foreach(List.scala:381)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.archiveBuildAction(ActionHandling.scala:286)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.archiveBuildAction(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handle(ActionHandling.scala:66)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handle(Controller.scala:64)</element>
+      <element>info.kwarc.mmt.api.frontend.ActionHandling$class.handleLine(ActionHandling.scala:29)</element>
+      <element>info.kwarc.mmt.api.frontend.Controller.handleLine(Controller.scala:64)</element>
+      <element>Debug$.run(Debug.scala:32)</element>
+      <element>Test.main(preamble.scala:48)</element>
+      <element>Debug.main(Debug.scala)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)</element>
+      <element>sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)</element>
+      <element>sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)</element>
+      <element>java.lang.reflect.Method.invoke(Method.java:498)</element>
+      <element>com.intellij.rt.execution.application.AppMain.main(AppMain.java:147)</element>
+    </stacktrace>
+</error>
+</error>
+
+</errors>
diff --git a/errors/mmt-omdoc/mmt/species.mmt.err b/errors/mmt-omdoc/mmt/species.mmt.err
new file mode 100644
index 0000000..a003a31
--- /dev/null
+++ b/errors/mmt-omdoc/mmt/species.mmt.err
@@ -0,0 +1,2 @@
+<errors>
+</errors>
diff --git a/export/html/content/.html b/export/html/content/.html
deleted file mode 100644
index 7869b21..0000000
--- a/export/html/content/.html
+++ /dev/null
@@ -1 +0,0 @@
-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../html.js"></script></head><body><div class="namespace"><div class="subnamespace"><a href="http..mathhub.info/.html">http://mathhub.info/</a></div></div></body></html>
\ No newline at end of file
diff --git a/export/html/content/http..mathhub.info/.html b/export/html/content/http..mathhub.info/.html
deleted file mode 100644
index d5c0930..0000000
--- a/export/html/content/http..mathhub.info/.html
+++ /dev/null
@@ -1 +0,0 @@
-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../html.js"></script></head><body><div class="namespace"><div class="subnamespace"><a href="MitM/.html">http://mathhub.info/MitM</a></div></div></body></html>
\ No newline at end of file
diff --git a/export/html/content/http..mathhub.info/MitM/.html b/export/html/content/http..mathhub.info/MitM/.html
deleted file mode 100644
index d94deb0..0000000
--- a/export/html/content/http..mathhub.info/MitM/.html
+++ /dev/null
@@ -1 +0,0 @@
-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../html.js"></script></head><body><div class="namespace"><div class="subnamespace"><a href="Models/.html">http://mathhub.info/MitM/Models</a></div></div></body></html>
\ No newline at end of file
diff --git a/export/html/content/http..mathhub.info/MitM/Models/$Base.html b/export/html/content/http..mathhub.info/MitM/Models/$Base.html
deleted file mode 100644
index 648b66c..0000000
--- a/export/html/content/http..mathhub.info/MitM/Models/$Base.html
+++ /dev/null
@@ -1 +0,0 @@
-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Base</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#574.15.1:601.15.28">http://mathhub.info/MitM/Models/constants.mmt#574.15.1:601.15.28</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma">LFSigma</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma">?LFSigma</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#604.16.1:631.16.28">http://mathhub.info/MitM/Models/constants.mmt#604.16.1:631.16.28</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://gl.mathhub.info/MMT/LFX/Sigma?TypedSigma">TypedSigma</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://gl.mathhub.info/MMT/LFX/Sigma?TypedSigma]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?TypedSigma">?TypedSigma</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols">Symbols</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://gl.mathhub.info/MMT/LFX/Sigma?Symbols]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols">?Symbols</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://gl.mathhub.info/MMT/LFX/Sigma?Rules">Rules</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://gl.mathhub.info/MMT/LFX/Sigma?Rules]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Rules">?Rules</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?LF">LF</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?LF]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LF">?LF</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?TermsTypesKinds">TermsTypesKinds</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?TermsTypesKinds]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?TermsTypesKinds">?TermsTypesKinds</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/mmt?Errors">Errors</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/mmt?Errors]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/mmt?Errors">?Errors</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/mmt?ModExp">ModExp</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/mmt?ModExp]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/mmt?ModExp">?ModExp</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/mmt?mmt">mmt</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/mmt?mmt]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/mmt?mmt">?mmt</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?Typed">Typed</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?Typed]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed">?Typed</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?Kinded">Kinded</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?Kinded]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Kinded">?Kinded</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?TypedConstants">TypedConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?TypedConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?TypedConstants">?TypedConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?KindedConstants">KindedConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?KindedConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?KindedConstants">?KindedConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?LambdaPi">LambdaPi</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?LambdaPi]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi">?LambdaPi</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?LFRules">LFRules</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?LFRules]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LFRules">?LFRules</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?exp">exp</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?exp" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#640.17.7:644.17.11" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#640.17.7:644.17.11" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#640.17.7:644.17.11" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#634.17.1:647.17.14">http://mathhub.info/MitM/Models/constants.mmt#634.17.1:647.17.14</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?der">der</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?der" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#655.18.7:696.18.48" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#656.18.8:656.18.8" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#656.18.8:656.18.8" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#660.18.12:667.18.19" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#660.18.12:667.18.19" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#664.18.16:667.18.19" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#655.18.7:696.18.48" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#655.18.7:696.18.48" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:696.18.48" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:681.18.33" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#671.18.23:676.18.28" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#676.18.28:676.18.28" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:681.18.33" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:681.18.33" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:696.18.48" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:696.18.48" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#685.18.37:696.18.48" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#691.18.43:691.18.43" data-mmt-position="2_2_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#685.18.37:696.18.48" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#685.18.37:696.18.48" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>b ' (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#649.18.1:707.18.59">http://mathhub.info/MitM/Models/constants.mmt#649.18.1:707.18.59</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?Real_vec_space2">Real_vec_space2</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#793.21.19:796.21.22">type</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ℝ2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#775.21.1:816.21.42">http://mathhub.info/MitM/Models/constants.mmt#775.21.1:816.21.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?Real_vec_space3">Real_vec_space3</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#836.22.19:839.22.22">type</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ℝ3 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#818.22.1:863.22.46">http://mathhub.info/MitM/Models/constants.mmt#818.22.1:863.22.46</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?comp1">comp1</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#875.24.9:880.24.14" data-mmt-position="1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#875.24.9:880.24.14" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#875.24.9:880.24.14" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#887.24.21:887.24.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#887.24.21:887.24.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#890.24.24:893.24.27" data-mmt-position="2_0">πl</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#893.24.27:893.24.27" data-mmt-position="2_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#867.24.1:896.24.30">http://mathhub.info/MitM/Models/constants.mmt#867.24.1:896.24.30</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?comp2">comp2</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#906.25.9:911.25.14" data-mmt-position="1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#906.25.9:911.25.14" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#906.25.9:911.25.14" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#918.25.21:918.25.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#918.25.21:918.25.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#921.25.24:929.25.32" data-mmt-position="2_0">πl</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#921.25.24:929.25.32" data-mmt-position="2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#924.25.27:929.25.32" data-mmt-position="2_1_0">πr</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#928.25.31:928.25.31" data-mmt-position="2_1_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#898.25.1:932.25.35">http://mathhub.info/MitM/Models/constants.mmt#898.25.1:932.25.35</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?comp3">comp3</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#942.26.9:947.26.14" data-mmt-position="1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#942.26.9:947.26.14" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#942.26.9:947.26.14" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#954.26.21:954.26.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#954.26.21:954.26.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#957.26.24:965.26.32" data-mmt-position="2_0">πr</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#957.26.24:965.26.32" data-mmt-position="2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#960.26.27:965.26.32" data-mmt-position="2_1_0">πr</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#964.26.31:964.26.31" data-mmt-position="2_1_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#934.26.1:968.26.35">http://mathhub.info/MitM/Models/constants.mmt#934.26.1:968.26.35</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?pred_as_sub2">pred_as_sub2</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#987.28.16:1004.28.33" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#993.28.22:996.28.25" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#987.28.16:1004.28.33" data-mmt-position="0">→</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1001.28.30:1004.28.33" data-mmt-position="2">type</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1011.28.40:1011.28.40" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1011.28.40:1011.28.40" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#993.28.22:996.28.25" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">⟨</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_1">ℝ2</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">|</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52" data-mmt-position="2_2_1">z</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52" data-mmt-position="2_2_1_1">ℝ2</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59" data-mmt-position="2_2_2_1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59" data-mmt-position="2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1028.28.57" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1030.28.59" data-mmt-position="2_2_2_2_0"></mspace><mi data-mmt-varref="2_2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1030.28.59:1030.28.59" data-mmt-position="2_2_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">⟩</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>pred2 a (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#972.28.1:1048.28.77">http://mathhub.info/MitM/Models/constants.mmt#972.28.1:1048.28.77</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?pred_as_sub3">pred_as_sub3</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1065.29.16:1082.29.33" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-position="1_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1071.29.22:1074.29.25" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1065.29.16:1082.29.33" data-mmt-position="0">→</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1079.29.30:1082.29.33" data-mmt-position="2">type</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-position="1_1_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1071.29.22:1074.29.25" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">⟨</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">|</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52" data-mmt-position="2_2_1">z</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52" data-mmt-position="2_2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59" data-mmt-position="2_2_2_1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59" data-mmt-position="2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1106.29.57" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1108.29.59" data-mmt-position="2_2_2_2_0"></mspace><mi data-mmt-varref="2_2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1108.29.59:1108.29.59" data-mmt-position="2_2_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">⟩</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>pred3 a (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1050.29.1:1126.29.77">http://mathhub.info/MitM/Models/constants.mmt#1050.29.1:1126.29.77</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three">lift_type_one_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1155.31.26:1178.31.49" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1160.31.31:1163.31.34" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1155.31.26:1178.31.49" data-mmt-position="0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1155.31.26:1178.31.49" data-mmt-position="2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1168.31.39:1178.31.49" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1168.31.39:1178.31.49" data-mmt-position="2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1174.31.45:1177.31.48" data-mmt-position="2_2">bool</mo><mo class="operator brackets">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1160.31.31:1163.31.34" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9" data-mmt-position="2_1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9" data-mmt-position="2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1195.32.13:1195.32.13" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24" data-mmt-position="2_2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24" data-mmt-position="2_2_2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1198.32.16:1202.32.20" data-mmt-position="2_2_2_2_2_1">comp1</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1197.32.15:1205.32.23" data-mmt-position="2_2_2_2_2_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1204.32.22:1204.32.22" data-mmt-position="2_2_2_2_2_2">v</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_1">∧</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1215.32.33" data-mmt-position="2_2_2_3_3_1">comp2</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1217.32.35" data-mmt-position="2_2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1217.32.35:1217.32.35" data-mmt-position="2_2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_2_3_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_1">∧</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1231.32.49" data-mmt-position="2_2_3_3_1">comp3</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1233.32.51" data-mmt-position="2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1233.32.51:1233.32.51" data-mmt-position="2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_3_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>t1↑ a (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1130.31.1:1252.32.70">http://mathhub.info/MitM/Models/constants.mmt#1130.31.1:1252.32.70</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three">lift_type_two_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1279.33.26:1303.33.50" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1285.33.32:1288.33.35" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1279.33.26:1303.33.50" data-mmt-position="0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1279.33.26:1303.33.50" data-mmt-position="2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1293.33.40:1303.33.50" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1293.33.40:1303.33.50" data-mmt-position="2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1299.33.46:1302.33.49" data-mmt-position="2_2">bool</mo><mo class="operator brackets">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1285.33.32:1288.33.35" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9" data-mmt-position="2_1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9" data-mmt-position="2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1320.34.13:1320.34.13" data-mmt-position="2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35" data-mmt-position="2_2_2_2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">⟨</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1328.34.21" data-mmt-position="2_2_2_2_1_1">comp1</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1330.34.23" data-mmt-position="2_2_2_2_1_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1330.34.23:1330.34.23" data-mmt-position="2_2_2_2_1_2">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">,</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1337.34.30" data-mmt-position="2_2_2_2_2_1">comp2</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1339.34.32" data-mmt-position="2_2_2_2_2_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1339.34.32:1339.34.32" data-mmt-position="2_2_2_2_2_2">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">⟩</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_1">∧</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1351.34.44" data-mmt-position="2_2_3_3_1">comp3</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1353.34.46" data-mmt-position="2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1353.34.46:1353.34.46" data-mmt-position="2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_3_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>t2↑ a (precedence -1)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1254.33.1:1380.34.73">http://mathhub.info/MitM/Models/constants.mmt#1254.33.1:1380.34.73</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_function_one_to_three">lift_function_one_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_function_one_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1414.36.30:1461.36.77" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1415.36.31:1415.36.31" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1415.36.31:1415.36.31" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1419.36.35:1426.36.42" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1419.36.35:1426.36.42" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1423.36.39:1426.36.42" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1414.36.30:1461.36.77" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1414.36.30:1461.36.77" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1461.36.77" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1439.36.55" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1429.36.45:1434.36.50" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1434.36.50:1434.36.50" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1439.36.55" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1439.36.55" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1461.36.77" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1461.36.77" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1443.36.59:1461.36.77" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1444.36.60:1456.36.72" data-mmt-position="2_2_1_1">pred3</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1444.36.60:1456.36.72" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1450.36.66:1456.36.72" data-mmt-position="2_2_1_2_1">t1↑</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1455.36.71:1455.36.71" data-mmt-position="2_2_1_2_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1443.36.59:1461.36.77" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1443.36.59:1461.36.77" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>f1↑ b (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1385.36.1:1510.37.45">http://mathhub.info/MitM/Models/constants.mmt#1385.36.1:1510.37.45</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_function_two_to_three">lift_function_two_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_function_two_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1541.38.30:1590.38.79" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1542.38.31:1542.38.31" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1542.38.31:1542.38.31" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1546.38.35:1554.38.43" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1546.38.35:1554.38.43" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1551.38.40:1554.38.43" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1541.38.30:1590.38.79" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1541.38.30:1590.38.79" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1590.38.79" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1568.38.57" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1557.38.46:1563.38.52" data-mmt-position="2_1_1_1">pred2</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1563.38.52:1563.38.52" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1568.38.57" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1568.38.57" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1590.38.79" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1590.38.79" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1572.38.61:1590.38.79" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1573.38.62:1585.38.74" data-mmt-position="2_2_1_1">pred3</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1573.38.62:1585.38.74" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1579.38.68:1585.38.74" data-mmt-position="2_2_1_2_1">t2↑</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1584.38.73:1584.38.73" data-mmt-position="2_2_1_2_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1572.38.61:1590.38.79" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1572.38.61:1590.38.79" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>f2↑ b (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1512.38.1:1650.39.56">http://mathhub.info/MitM/Models/constants.mmt#1512.38.1:1650.39.56</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PhysicalConstants</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The vaccuum dielectric permitivity constant (usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-position="">ε_0</mo></math>)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity">vacuum_dielectric_permitivity</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ε_0 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#326.7.1:369.7.44">http://mathhub.info/MitM/Models/constants.mmt#326.7.1:369.7.44</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The elementary charge (denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-position="">q</mo></math>)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge">elementary_charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>q (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#417.9.1:446.9.30">http://mathhub.info/MitM/Models/constants.mmt#417.9.1:446.9.30</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The Boltzmann constant (usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-position="">k_B</mo></math>)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant">Boltzmann_constant</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>k_B (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#506.11.1:538.11.33">http://mathhub.info/MitM/Models/constants.mmt#506.11.1:538.11.33</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../html.js"></script></head><body><div class="namespace"><div class="subnamespace"><a href="VanRoosbroeck/.html">http://mathhub.info/MitM/Models/VanRoosbroeck</a></div><div class="subnamespace"><a href="continuity/.html">http://mathhub.info/MitM/Models/continuity</a></div><div class="subnamespace"><a href="densities/.html">http://mathhub.info/MitM/Models/densities</a></div><div class="subnamespace"><a href="device/.html">http://mathhub.info/MitM/Models/device</a></div><div class="subnamespace"><a href="poisson/.html">http://mathhub.info/MitM/Models/poisson</a></div><div class="subnamespace"><a href="recombination/.html">http://mathhub.info/MitM/Models/recombination</a></div><div class="submodule"><a href="$Base.html">http://mathhub.info/MitM/Models?Base</a></div><div class="submodule"><a href="$Physical$Constants.html">http://mathhub.info/MitM/Models?PhysicalConstants</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">VanRoosbroeck</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonEquation">PoissonEquation</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?PoissonEquation]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonEquation">?PoissonEquation</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#702.15.1:734.15.33">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#702.15.1:734.15.33</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?Charge]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">?Charge</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Displacement">Displacement</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?Displacement]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement">?Displacement</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions">PoissonBoundaryConditions</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions">?PoissonBoundaryConditions</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#737.16.1:779.16.43">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#737.16.1:779.16.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">ThermodynamicEquilibrium</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">?ThermodynamicEquilibrium</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons">ContinuityEquationElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons">?ContinuityEquationElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#782.17.1:829.17.48">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#782.17.1:829.17.48</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">CurrentElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?CurrentElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">?CurrentElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles">ContinuityEquationHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles">?ContinuityEquationHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#832.18.1:875.18.44">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#832.18.1:875.18.44</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentHoles">CurrentHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?CurrentHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles">?CurrentHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons">ContinuityBoundaryConditionsElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons">?ContinuityBoundaryConditionsElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#878.19.1:935.19.58">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#878.19.1:935.19.58</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles">ContinuityBoundaryConditionsHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles">?ContinuityBoundaryConditionsHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#938.20.1:991.20.54">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#938.20.1:991.20.54</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination">SpontaneousRecombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination">?SpontaneousRecombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#994.21.1:1041.21.48">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#994.21.1:1041.21.48</a></td></tr></table></div></div></div></div></body></html>
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diff --git a/export/html/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Electrons.html b/export/html/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Electrons.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityBoundaryConditionsElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2985.81.1:3021.81.37">http://mathhub.info/MitM/Models/continuity.mmt#2985.81.1:3021.81.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the top contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top">potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_n_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3071.83.1:3108.83.38">http://mathhub.info/MitM/Models/continuity.mmt#3071.83.1:3108.83.38</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the bottom contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom">potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_n_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3160.85.1:3200.85.41">http://mathhub.info/MitM/Models/continuity.mmt#3160.85.1:3200.85.41</a></td></tr></table></div></div></div></div></body></html>
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diff --git a/export/html/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Holes.html b/export/html/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Holes.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityBoundaryConditionsHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3386.92.1:3422.92.37">http://mathhub.info/MitM/Models/continuity.mmt#3386.92.1:3422.92.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the top contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top">potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_p_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3471.94.1:3508.94.38">http://mathhub.info/MitM/Models/continuity.mmt#3471.94.1:3508.94.38</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the bottom contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom">potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_p_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3559.96.1:3599.96.41">http://mathhub.info/MitM/Models/continuity.mmt#3559.96.1:3599.96.41</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityEquationElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">CurrentElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/continuity?CurrentElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">?CurrentElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1879.50.1:1905.50.27">http://mathhub.info/MitM/Models/continuity.mmt#1879.50.1:1905.50.27</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1908.51.1:1939.51.32">http://mathhub.info/MitM/Models/continuity.mmt#1908.51.1:1939.51.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1942.52.1:1980.52.39">http://mathhub.info/MitM/Models/continuity.mmt#1942.52.1:1980.52.39</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1983.53.1:2019.53.37">http://mathhub.info/MitM/Models/continuity.mmt#1983.53.1:2019.53.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2022.54.1:2063.54.42">http://mathhub.info/MitM/Models/continuity.mmt#2022.54.1:2063.54.42</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formulation of the continuity equation for electrons in divergence form.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation_electrons">continuity_equation_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation_electrons" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2188.59.2:2272.59.86" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2188.59.2:2272.59.86" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2272.59.86" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2202.59.16" data-mmt-position="2_3_3"><mo class="operator brackets">(</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_1">j_n</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">[</mo><mi data-mmt-position="2_3_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">]</mo><mrow data-mmt-position="2_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_3_2_2_0"></mspace><mi data-mmt-varref="2_3_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_3">ψ</mo><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_4">φ_n</mo><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2202.59.16" data-mmt-position="2_3_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2202.59.16" data-mmt-position="2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">[</mo><mi data-mmt-position="2_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">]</mo><mrow data-mmt-position="2_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="2_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2272.59.86" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2272.59.86" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">[</mo><mi data-mmt-position="2_2_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">]</mo><mrow data-mmt-position="2_2_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_2_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_2_1_2_2_0"></mspace><mi data-mmt-varref="2_2_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_2_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets 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data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2221.59.35:2237.59.51" data-mmt-position="2_4_2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2221.59.35:2237.59.51" data-mmt-position="2_4_2_3_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2230.59.44:2236.59.50" data-mmt-position="2_4_2_3_2_3_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2230.59.44:2236.59.50" data-mmt-position="2_4_2_3_2_3_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2235.59.49:2235.59.49" data-mmt-position="2_4_2_3_2_3_2">x</mi><mo class="operator 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class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2242.59.56:2246.59.60" data-mmt-position="2_4_2_3_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2242.59.56:2246.59.60" data-mmt-position="2_4_2_3_3_2_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2245.59.59:2245.59.59" data-mmt-position="2_4_2_3_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2239.59.53:2255.59.69" data-mmt-position="2_4_2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2239.59.53:2255.59.69" 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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityEquationHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentHoles">CurrentHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/continuity?CurrentHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles">?CurrentHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2403.65.1:2425.65.23">http://mathhub.info/MitM/Models/continuity.mmt#2403.65.1:2425.65.23</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2428.66.1:2463.66.36">http://mathhub.info/MitM/Models/continuity.mmt#2428.66.1:2463.66.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2466.67.1:2508.67.43">http://mathhub.info/MitM/Models/continuity.mmt#2466.67.1:2508.67.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2511.68.1:2547.68.37">http://mathhub.info/MitM/Models/continuity.mmt#2511.68.1:2547.68.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2550.69.1:2591.69.42">http://mathhub.info/MitM/Models/continuity.mmt#2550.69.1:2591.69.42</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formulation of the continuity equation for holes in divergence form.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes">continuity_equation_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2703.74.2:2788.74.87" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2703.74.2:2788.74.87" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2717.74.16" data-mmt-position="2_3_3"><mo class="operator brackets">(</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_1">j_p</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">[</mo><mi data-mmt-position="2_3_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">]</mo><mrow data-mmt-position="2_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_3_2_2_0"></mspace><mi data-mmt-varref="2_3_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_3">ψ</mo><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_4">φ_p</mo><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2717.74.16" data-mmt-position="2_3_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2717.74.16" data-mmt-position="2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">[</mo><mi data-mmt-position="2_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">]</mo><mrow data-mmt-position="2_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="2_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">[</mo><mi data-mmt-position="2_2_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">]</mo><mrow data-mmt-position="2_2_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_2_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_2_1_2_2_0"></mspace><mi data-mmt-varref="2_2_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_2_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow></mrow></mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_4"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2721.74.20:2788.74.87" data-mmt-position="2_4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2722.74.21:2722.74.21" data-mmt-position="2_4_1">x</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2722.74.21:2722.74.21" data-mmt-position="2_4_1_1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2721.74.20:2788.74.87" data-mmt-position="2_4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2721.74.20:2788.74.87" data-mmt-position="2_4_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2788.74.87" data-mmt-position="2_4_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2730.74.29" data-mmt-position="2_4_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2730.74.29" data-mmt-position="2_4_2_2_2">q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2788.74.87" data-mmt-position="2_4_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2788.74.87" data-mmt-position="2_4_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_1">R</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_1">n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2740.74.39:2744.74.43" data-mmt-position="2_4_2_3_2_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2740.74.39:2744.74.43" data-mmt-position="2_4_2_3_2_2_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2743.74.42:2743.74.42" data-mmt-position="2_4_2_3_2_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2746.74.45:2752.74.51" data-mmt-position="2_4_2_3_2_3_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2746.74.45:2752.74.51" data-mmt-position="2_4_2_3_2_3_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2751.74.50:2751.74.50" data-mmt-position="2_4_2_3_2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2758.74.57:2762.74.61" data-mmt-position="2_4_2_3_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2758.74.57:2762.74.61" data-mmt-position="2_4_2_3_3_2_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2761.74.60:2761.74.60" data-mmt-position="2_4_2_3_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2764.74.63:2770.74.69" data-mmt-position="2_4_2_3_3_3_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2764.74.63:2770.74.69" data-mmt-position="2_4_2_3_3_3_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2769.74.68:2769.74.68" data-mmt-position="2_4_2_3_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_4"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2773.74.72:2779.74.78" data-mmt-position="2_4_2_3_4_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2773.74.72:2779.74.78" data-mmt-position="2_4_2_3_4_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2778.74.77:2778.74.77" data-mmt-position="2_4_2_3_4_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_5"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2781.74.80:2787.74.86" data-mmt-position="2_4_2_3_5_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2781.74.80:2787.74.86" data-mmt-position="2_4_2_3_5_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2786.74.85:2786.74.85" data-mmt-position="2_4_2_3_5_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2672.73.1:2791.74.90">http://mathhub.info/MitM/Models/continuity.mmt#2672.73.1:2791.74.90</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">CurrentElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#531.16.1:573.16.43">http://mathhub.info/MitM/Models/continuity.mmt#531.16.1:573.16.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#576.17.1:617.17.42">http://mathhub.info/MitM/Models/continuity.mmt#576.17.1:617.17.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#620.18.1:655.18.36">http://mathhub.info/MitM/Models/continuity.mmt#620.18.1:655.18.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#658.19.1:678.19.21">http://mathhub.info/MitM/Models/continuity.mmt#658.19.1:678.19.21</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Definition of the electron current in gradient form. <br/>     The driving force of the current are the negative gradients of <br/>     the quasi-Fermi potential, here denoted by j_n.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons">current_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#966.26.21:1021.26.76" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#967.26.22:967.26.22" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#967.26.22:967.26.22" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#974.26.29:977.26.32" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#966.26.21:1021.26.76" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#966.26.21:1021.26.76" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:991.26.46" data-mmt-position="2_1_1"><mo class="operator opt-brackets 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data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1011.26.66:1016.26.71" data-mmt-position="2_3_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1016.26.71:1016.26.71" data-mmt-position="2_3_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1010.26.65:1021.26.76" data-mmt-position="2_3_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1010.26.65:1021.26.76" data-mmt-position="2_3_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math 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data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">]</mo><mrow data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1033.27.8:1033.27.8" data-mmt-position="2_1">f</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1033.27.8:1033.27.8" data-mmt-position="2_1_1"><mrow data-mmt-position="2_1_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#981.26.36:986.26.41" data-mmt-position="2_1_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#986.26.41:986.26.41" data-mmt-position="2_1_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_1_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1035.27.10:1035.27.10" data-mmt-position="2_2">g</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1035.27.10:1035.27.10" data-mmt-position="2_2_1"><mrow data-mmt-position="2_2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#996.26.51:1001.26.56" data-mmt-position="2_2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1001.26.56:1001.26.56" data-mmt-position="2_2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1037.27.12:1075.27.50" data-mmt-position="2_3_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1038.27.13:1038.27.13" data-mmt-position="2_3_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1038.27.13:1038.27.13" data-mmt-position="2_3_1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_3_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1016.26.71:1016.26.71" data-mmt-position="2_3_1_1_2">P</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1037.27.12:1075.27.50" data-mmt-position="2_3_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1037.27.12:1075.27.50" data-mmt-position="2_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1075.27.50" data-mmt-position="2_3_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1066.27.41" data-mmt-position="2_3_2_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1048.27.23" data-mmt-position="2_3_2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1042.27.17" data-mmt-position="2_3_2_2_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1042.27.17" data-mmt-position="2_3_2_2_2_2_2">q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1048.27.23" data-mmt-position="2_3_2_2_2_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1048.27.23" data-mmt-position="2_3_2_2_2_3">μ_n</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1066.27.41" data-mmt-position="2_3_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1066.27.41" data-mmt-position="2_3_2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_1">n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1056.27.31:1056.27.31" data-mmt-position="2_3_2_2_3_2_1">f</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1055.27.30:1059.27.34" data-mmt-position="2_3_2_2_3_2_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1058.27.33:1058.27.33" data-mmt-position="2_3_2_2_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1062.27.37:1062.27.37" data-mmt-position="2_3_2_2_3_3_1">g</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1061.27.36:1065.27.40" data-mmt-position="2_3_2_2_3_3_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1064.27.39:1064.27.39" data-mmt-position="2_3_2_2_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1075.27.50" data-mmt-position="2_3_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1075.27.50" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1070.27.45:1075.27.50" data-mmt-position="2_3_2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1071.27.46:1071.27.46" data-mmt-position="2_3_2_3_1_3">g</mi><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1071.27.46:1072.27.47" data-mmt-position="2_3_2_3_1_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1071.27.46:1072.27.47" data-mmt-position="2_3_2_3_1_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">[</mo><mi data-mmt-position="2_3_2_3_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_3_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">]</mo><mrow data-mmt-position="2_3_2_3_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7824.214.54" data-mmt-position="2_3_2_3_1_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_0"></mspace><mi data-mmt-varref="2_3_2_3_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" 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href="http://mathhub.info/MitM/Models/continuity.mmt#946.26.1:1089.27.64">http://mathhub.info/MitM/Models/continuity.mmt#946.26.1:1089.27.64</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">CurrentHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1201.33.1:1239.33.39">http://mathhub.info/MitM/Models/continuity.mmt#1201.33.1:1239.33.39</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1242.34.1:1283.34.42">http://mathhub.info/MitM/Models/continuity.mmt#1242.34.1:1283.34.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1286.35.1:1317.35.32">http://mathhub.info/MitM/Models/continuity.mmt#1286.35.1:1317.35.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1320.36.1:1340.36.21">http://mathhub.info/MitM/Models/continuity.mmt#1320.36.1:1340.36.21</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Defintion of the hole current in gradient form. <br/>     The driving force of the current are the negative gradient of <br/>     the quasi-Fermi potential, here denoted by j_p.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes">current_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1622.43.17:1677.43.72" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1623.43.18:1623.43.18" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1623.43.18:1623.43.18" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1630.43.25:1633.43.28" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1622.43.17:1677.43.72" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1622.43.17:1677.43.72" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1647.43.42" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1637.43.32:1642.43.37" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1642.43.37:1642.43.37" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1647.43.42" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1647.43.42" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1651.43.46:1662.43.57" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1652.43.47:1657.43.52" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1657.43.52:1657.43.52" data-mmt-position="2_2_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1651.43.46:1662.43.57" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1651.43.46:1662.43.57" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1666.43.61:1677.43.72" data-mmt-position="2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1667.43.62:1672.43.67" data-mmt-position="2_3_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1672.43.67:1672.43.67" data-mmt-position="2_3_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1666.43.61:1677.43.72" data-mmt-position="2_3_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1666.43.61:1677.43.72" data-mmt-position="2_3_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1686.44.5:1686.44.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1686.44.5:1686.44.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1630.43.25:1633.43.28" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">]</mo><mrow data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1689.44.8:1689.44.8" data-mmt-position="2_1">f</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1689.44.8:1689.44.8" data-mmt-position="2_1_1"><mrow data-mmt-position="2_1_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1637.43.32:1642.43.37" data-mmt-position="2_1_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1642.43.37:1642.43.37" data-mmt-position="2_1_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_1_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1691.44.10:1691.44.10" data-mmt-position="2_2">g</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1691.44.10:1691.44.10" data-mmt-position="2_2_1"><mrow data-mmt-position="2_2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1652.43.47:1657.43.52" data-mmt-position="2_2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1657.43.52:1657.43.52" data-mmt-position="2_2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1694.44.13:1694.44.13" data-mmt-position="2_3_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1694.44.13:1694.44.13" data-mmt-position="2_3_1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_3_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1672.43.67:1672.43.67" data-mmt-position="2_3_1_1_2">P</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1698.44.17" data-mmt-position="2_3_2_2_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1698.44.17" data-mmt-position="2_3_2_2_2_2_2">q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_3">μ_p</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1712.44.31:1712.44.31" data-mmt-position="2_3_2_2_3_2_1">f</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1711.44.30:1715.44.34" data-mmt-position="2_3_2_2_3_2_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1714.44.33:1714.44.33" data-mmt-position="2_3_2_2_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1718.44.37:1718.44.37" data-mmt-position="2_3_2_2_3_3_1">g</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1717.44.36:1721.44.40" data-mmt-position="2_3_2_2_3_3_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1720.44.39:1720.44.39" data-mmt-position="2_3_2_2_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1726.44.45:1731.44.50" data-mmt-position="2_3_2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1727.44.46:1727.44.46" data-mmt-position="2_3_2_3_1_3">g</mi><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1727.44.46:1728.44.47" data-mmt-position="2_3_2_3_1_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1727.44.46:1728.44.47" data-mmt-position="2_3_2_3_1_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">[</mo><mi data-mmt-position="2_3_2_3_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_3_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">]</mo><mrow data-mmt-position="2_3_2_3_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7824.214.54" data-mmt-position="2_3_2_3_1_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_0"></mspace><mi data-mmt-varref="2_3_2_3_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1726.44.45:1731.44.50" data-mmt-position="2_3_2_3_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1730.44.49:1730.44.49" data-mmt-position="2_3_2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>j_p b c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1606.43.1:1745.44.64">http://mathhub.info/MitM/Models/continuity.mmt#1606.43.1:1745.44.64</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Mobilities</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The electron mobility parameter usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-position="">μ_n</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons">mobility_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>μ_n (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#287.8.1:319.8.33">http://mathhub.info/MitM/Models/continuity.mmt#287.8.1:319.8.33</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The hole mobility parameter usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-position="">μ_p</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes">mobility_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>μ_p (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#381.10.1:409.10.29">http://mathhub.info/MitM/Models/continuity.mmt#381.10.1:409.10.29</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Continuity$Boundary$Conditions$Electrons.html">http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons</a></div><div class="submodule"><a href="$Continuity$Boundary$Conditions$Holes.html">http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles</a></div><div class="submodule"><a href="$Continuity$Equation$Electrons.html">http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons</a></div><div class="submodule"><a href="$Continuity$Equation$Holes.html">http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles</a></div><div class="submodule"><a href="$Current$Electrons.html">http://mathhub.info/MitM/Models/continuity?CurrentElectrons</a></div><div class="submodule"><a href="$Current$Holes.html">http://mathhub.info/MitM/Models/continuity?CurrentHoles</a></div><div class="submodule"><a href="$Mobilities.html">http://mathhub.info/MitM/Models/continuity?Mobilities</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">BandstructureParameters</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The effective density of states for the conduction bands <br/>     usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-position="">N_c</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands">effective_density_of_states_conduction_bands</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>N_c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#340.9.1:398.9.59">http://mathhub.info/MitM/Models/densities.mmt#340.9.1:398.9.59</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The effective density of states for the valence bands <br/>     usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-position="">N_v</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands">effective_density_of_states_valence_bands</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>N_v (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#493.12.1:548.12.56">http://mathhub.info/MitM/Models/densities.mmt#493.12.1:548.12.56</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The conduction band edge usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-position="">E_c</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge">conduction_band_edge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>E_c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#608.14.1:642.14.35">http://mathhub.info/MitM/Models/densities.mmt#608.14.1:642.14.35</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The valence band edge usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-position="">E_v</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge">valence_band_edge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>E_v (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#699.16.1:730.16.32">http://mathhub.info/MitM/Models/densities.mmt#699.16.1:730.16.32</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">N.B.: The band gap of the semiconductor is given by Eg = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:800.-1.5" data-mmt-position="2">E_c</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:800.-1.5" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:800.-1.5" data-mmt-position="3">E_v</mo></mrow></math>.</div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DensityElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2092.58.1:2128.58.37">http://mathhub.info/MitM/Models/densities.mmt#2092.58.1:2128.58.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2131.59.1:2162.59.32">http://mathhub.info/MitM/Models/densities.mmt#2131.59.1:2162.59.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2166.60.1:2199.60.34">http://mathhub.info/MitM/Models/densities.mmt#2166.60.1:2199.60.34</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formula for the electron density for the Boltzmann approximation.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons">density_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/mmt?mmt?unknown">unknown</mo><mspace width=".2em"></mspace><mo>[</mo><mi data-mmt-position="1">y/2</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="2">x/1</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="3">I/0</mi><mo>]</mo><mspace width=".2em"></mspace><mrow data-mmt-position="4"><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2319.64.5:2319.64.5" data-mmt-position="4_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mi data-mmt-position="4_1_1">x/1</mi></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2321.64.7:2321.64.7" data-mmt-position="4_2">y</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2321.64.7:2321.64.7" data-mmt-position="4_2_1"><mi data-mmt-position="4_2_1_1">y/2</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_2_1_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_2_1_2">x</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_2">N_c</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2332.64.18" data-mmt-position="4_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2364.64.50" data-mmt-position="4_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2364.64.50" data-mmt-position="4_3_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mfrac><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2334.64.20:2364.64.50" data-mmt-position="4_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2335.64.21:2353.64.39" data-mmt-position="4_3_3_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2346.64.32" data-mmt-position="4_3_3_2_2_2_2">q</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2346.64.32" data-mmt-position="4_3_3_2_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2346.64.32" data-mmt-position="4_3_3_2_2_2_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="4_1" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2341.64.27:2341.64.27" data-mmt-position="4_3_3_2_2_2_3_2">x</mi><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2340.64.26:2346.64.32" data-mmt-position="4_3_3_2_2_2_3_1">-</mo><mi data-mmt-varref="4_2" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2345.64.31:2345.64.31" data-mmt-position="4_3_3_2_2_2_3_3">y</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2335.64.21:2353.64.39" data-mmt-position="4_3_3_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2335.64.21:2353.64.39" data-mmt-position="4_3_3_2_2_3">E_c</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2334.64.20:2364.64.50" data-mmt-position="4_3_3_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2363.64.49" data-mmt-position="4_3_3_2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2363.64.49" data-mmt-position="4_3_3_2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2363.64.49" data-mmt-position="4_3_3_2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mfrac><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2334.64.20:2364.64.50" data-mmt-position="4_3_3_2_4"><mo class="operator brackets">(</mo><mi data-mmt-position="4_3_3_2_4_1">I/0</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_3_3_2_4_2">x</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_2" data-mmt-position="4_3_3_2_4_3">y</mi><mo class="operator brackets">)</mo></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mo class="operator brackets">)</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>n (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2276.63.1:2366.64.52">http://mathhub.info/MitM/Models/densities.mmt#2276.63.1:2366.64.52</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DensityHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2531.72.1:2567.72.37">http://mathhub.info/MitM/Models/densities.mmt#2531.72.1:2567.72.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2570.73.1:2601.73.32">http://mathhub.info/MitM/Models/densities.mmt#2570.73.1:2601.73.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2605.74.1:2638.74.34">http://mathhub.info/MitM/Models/densities.mmt#2605.74.1:2638.74.34</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formula for the hole density for the Boltzmann approximation.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes">density_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/mmt?mmt?unknown">unknown</mo><mspace width=".2em"></mspace><mo>[</mo><mi data-mmt-position="1">y/2</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="2">x/1</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="3">I/0</mi><mo>]</mo><mspace width=".2em"></mspace><mrow data-mmt-position="4"><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2748.77.5:2748.77.5" data-mmt-position="4_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mi data-mmt-position="4_1_1">x/1</mi></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2750.77.7:2750.77.7" data-mmt-position="4_2">y</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2750.77.7:2750.77.7" data-mmt-position="4_2_1"><mi data-mmt-position="4_2_1_1">y/2</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_2_1_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_2_1_2">x</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2793.77.50" data-mmt-position="4_3_2">N_v</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2793.77.50" data-mmt-position="4_3_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2793.77.50" data-mmt-position="4_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2761.77.18" data-mmt-position="4_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2793.77.50" data-mmt-position="4_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2793.77.50" data-mmt-position="4_3_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mfrac><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2763.77.20:2793.77.50" data-mmt-position="4_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2764.77.21:2782.77.39" data-mmt-position="4_3_3_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2775.77.32" data-mmt-position="4_3_3_2_2_2_2">q</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2775.77.32" data-mmt-position="4_3_3_2_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2775.77.32" data-mmt-position="4_3_3_2_2_2_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="4_2" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2770.77.27:2770.77.27" data-mmt-position="4_3_3_2_2_2_3_2">y</mi><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2769.77.26:2775.77.32" data-mmt-position="4_3_3_2_2_2_3_1">-</mo><mi data-mmt-varref="4_1" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2774.77.31:2774.77.31" data-mmt-position="4_3_3_2_2_2_3_3">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2764.77.21:2782.77.39" data-mmt-position="4_3_3_2_2_1">+</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2764.77.21:2782.77.39" data-mmt-position="4_3_3_2_2_3">E_v</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2763.77.20:2793.77.50" data-mmt-position="4_3_3_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2792.77.49" data-mmt-position="4_3_3_2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2792.77.49" data-mmt-position="4_3_3_2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2792.77.49" data-mmt-position="4_3_3_2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mfrac><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2763.77.20:2793.77.50" data-mmt-position="4_3_3_2_4"><mo class="operator brackets">(</mo><mi data-mmt-position="4_3_3_2_4_1">I/0</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_3_3_2_4_2">x</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_2" data-mmt-position="4_3_3_2_4_3">y</mi><mo class="operator brackets">)</mo></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mo class="operator brackets">)</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>p (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2709.76.1:2795.77.52">http://mathhub.info/MitM/Models/densities.mmt#2709.76.1:2795.77.52</a></td></tr></table></div></div></div></div></body></html>
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diff --git a/export/html/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.html b/export/html/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ElectrostaticPotential</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1766.47.1:1796.47.31">http://mathhub.info/MitM/Models/densities.mmt#1766.47.1:1796.47.31</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Spatial variation of the electrostatic potential,<br/>	   usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-position="">ψ</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential">electrostatic_potential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1884.51.1:1923.51.40">http://mathhub.info/MitM/Models/densities.mmt#1884.51.1:1923.51.40</a></td></tr></table></div></div></div></div></body></html>
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diff --git a/export/html/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.html b/export/html/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">FermiPotentialElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1011.25.1:1041.25.31">http://mathhub.info/MitM/Models/densities.mmt#1011.25.1:1041.25.31</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Spatial variation of the quasi-Fermi potential for the electrons,<br/>	   usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-position="">φ_n</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential">quasi_Fermi_potential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_n (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1147.28.1:1186.28.40">http://mathhub.info/MitM/Models/densities.mmt#1147.28.1:1186.28.40</a></td></tr></table></div></div></div></div></body></html>
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diff --git a/export/html/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.html b/export/html/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">FermiPotentialHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1397.36.1:1427.36.31">http://mathhub.info/MitM/Models/densities.mmt#1397.36.1:1427.36.31</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Spatial variation of the quasi-Fermi potential for the holes,<br/>	   usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-position="">φ_p</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential">quasi_Fermi_potential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_p (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1528.39.1:1567.39.40">http://mathhub.info/MitM/Models/densities.mmt#1528.39.1:1567.39.40</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Bandstructure$Parameters.html">http://mathhub.info/MitM/Models/densities?BandstructureParameters</a></div><div class="submodule"><a href="$Density$Electrons.html">http://mathhub.info/MitM/Models/densities?DensityElectrons</a></div><div class="submodule"><a href="$Density$Holes.html">http://mathhub.info/MitM/Models/densities?DensityHoles</a></div><div class="submodule"><a href="$Electrostatic$Potential.html">http://mathhub.info/MitM/Models/densities?ElectrostaticPotential</a></div><div class="submodule"><a href="$Fermi$Potential$Electrons.html">http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons</a></div><div class="submodule"><a href="$Fermi$Potential$Holes.html">http://mathhub.info/MitM/Models/densities?FermiPotentialHoles</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DeviceGeometry</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#292.8.1:308.8.17">http://mathhub.info/MitM/Models/device.mmt#292.8.1:308.8.17</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop">domain_prop</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#355.10.15:362.10.22" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#355.10.15:362.10.22" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#359.10.19:362.10.22" data-mmt-position="2">bool</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#341.10.1:365.10.25">http://mathhub.info/MitM/Models/device.mmt#341.10.1:365.10.25</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The one-dimensional spatial domain of the device (denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="">Ω</mo></math>).</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain">domain</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type">type</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#506.13.19:521.13.34" data-mmt-position="1">pred</mo><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#511.13.24:521.13.34" data-mmt-position="2">domain_prop</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>Ω (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#488.13.1:530.13.43">http://mathhub.info/MitM/Models/device.mmt#488.13.1:530.13.43</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DeviceOperationState</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1410.49.1:1434.49.25">http://mathhub.info/MitM/Models/device.mmt#1410.49.1:1434.49.25</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">The global temperature of the device denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-position="">T</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur">temperatur</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>T (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1528.52.1:1550.52.23">http://mathhub.info/MitM/Models/device.mmt#1528.52.1:1550.52.23</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The applied voltage at the bottom contact denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom">voltage_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>U_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1618.54.1:1646.54.29">http://mathhub.info/MitM/Models/device.mmt#1618.54.1:1646.54.29</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The applied voltage at the top contact denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top">voltage_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>U_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1711.56.1:1736.56.26">http://mathhub.info/MitM/Models/device.mmt#1711.56.1:1736.56.26</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf">prf</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1780.59.7:1792.59.19" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1780.59.7:1792.59.19" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1792.59.19" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1788.59.15" data-mmt-position="2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1788.59.15" data-mmt-position="2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1788.59.15" data-mmt-position="2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?neq" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1792.59.19" data-mmt-position="2_1">≠</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1792.59.19" data-mmt-position="2_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1774.59.1:1795.59.22">http://mathhub.info/MitM/Models/device.mmt#1774.59.1:1795.59.22</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Device</span></div><div class="document-body"></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DopingProfile</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DopingProfile?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1128.39.1:1152.39.25">http://mathhub.info/MitM/Models/device.mmt#1128.39.1:1152.39.25</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DopingProfile?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">The doping profile, denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-position="">C</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile">doping_profile</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>C (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1198.41.1:1229.41.32">http://mathhub.info/MitM/Models/device.mmt#1198.41.1:1229.41.32</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Device$Geometry.html">http://mathhub.info/MitM/Models/device?DeviceGeometry</a></div><div class="submodule"><a href="$Device$Operation$State.html">http://mathhub.info/MitM/Models/device?DeviceOperationState</a></div><div class="submodule"><a href="$Device.html">http://mathhub.info/MitM/Models/device?Device</a></div><div class="submodule"><a href="$Doping$Profile.html">http://mathhub.info/MitM/Models/device?DopingProfile</a></div></div></body></html>
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diff --git a/export/html/content/http..mathhub.info/MitM/Models/poisson/$Charge.html b/export/html/content/http..mathhub.info/MitM/Models/poisson/$Charge.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Charge</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#628.16.1:658.16.31">http://mathhub.info/MitM/Models/poisson.mmt#628.16.1:658.16.31</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#661.17.1:690.17.30">http://mathhub.info/MitM/Models/poisson.mmt#661.17.1:690.17.30</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#693.18.1:720.18.28">http://mathhub.info/MitM/Models/poisson.mmt#693.18.1:720.18.28</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#723.19.1:758.19.36">http://mathhub.info/MitM/Models/poisson.mmt#723.19.1:758.19.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#761.20.1:803.20.43">http://mathhub.info/MitM/Models/poisson.mmt#761.20.1:803.20.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#806.21.1:847.21.42">http://mathhub.info/MitM/Models/poisson.mmt#806.21.1:847.21.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#850.22.1:881.22.32">http://mathhub.info/MitM/Models/poisson.mmt#850.22.1:881.22.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#884.23.1:922.23.39">http://mathhub.info/MitM/Models/poisson.mmt#884.23.1:922.23.39</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The total charge denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-position="">Q</mo></math> composed of doping profile <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-position="">C</mo></math> and <br/>     electron and hole densities <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-position="">n</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-position="">p</mo></math>, defined by<br/>     <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-position="">Q</mo></math> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-position="">q</mo></math>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-position="">C</mo></math>+<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-position="">p</mo></math> - <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-position="">n</mo></math>).</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge?total_charge">total_charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1123.29.5:1123.29.5" data-mmt-position="1">x</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1123.29.5:1123.29.5" data-mmt-position="1_1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1131.29.13" data-mmt-position="2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1131.29.13" data-mmt-position="2_2_2">q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1140.29.22" data-mmt-position="2_3_2_2_1">C</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1140.29.22" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1139.29.21:1139.29.21" data-mmt-position="2_3_2_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_1">+</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1147.29.29:1151.29.33" data-mmt-position="2_3_2_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1147.29.29:1151.29.33" data-mmt-position="2_3_2_3_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1150.29.32:1150.29.32" data-mmt-position="2_3_2_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1153.29.35:1159.29.41" data-mmt-position="2_3_2_3_3_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1153.29.35:1159.29.41" data-mmt-position="2_3_2_3_3_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1158.29.40:1158.29.40" data-mmt-position="2_3_2_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_1">-</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_1">n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1167.29.49:1171.29.53" data-mmt-position="2_3_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1167.29.49:1171.29.53" data-mmt-position="2_3_3_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1170.29.52:1170.29.52" data-mmt-position="2_3_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1173.29.55:1179.29.61" data-mmt-position="2_3_3_3_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1173.29.55:1179.29.61" data-mmt-position="2_3_3_3_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1178.29.60:1178.29.60" data-mmt-position="2_3_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>Q (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1089.28.1:1183.29.65">http://mathhub.info/MitM/Models/poisson.mmt#1089.28.1:1183.29.65</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Displacement</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1287.35.1:1328.35.42">http://mathhub.info/MitM/Models/poisson.mmt#1287.35.1:1328.35.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1331.36.1:1358.36.28">http://mathhub.info/MitM/Models/poisson.mmt#1331.36.1:1358.36.28</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Expression for electric displacement denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-position="">D</mo></math> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1421.-1.-1:1425.-1.3" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1421.-1.-1:1425.-1.3" data-mmt-position="2">ε_s</mo></mrow></math> d/dx <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-position="">ψ</mo></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement">electric_displacement</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1478.40.5:1478.40.5" data-mmt-position="1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1478.40.5:1478.40.5" data-mmt-position="1_1">Ω</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1494.40.21" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1484.40.11" data-mmt-position="2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1484.40.11" data-mmt-position="2_2_2">ε_s</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1494.40.21" data-mmt-position="2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1494.40.21" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1488.40.15:1494.40.21" data-mmt-position="2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1491.40.18" data-mmt-position="2_3_1_3">ψ</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1491.40.18" data-mmt-position="2_3_1_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1491.40.18" data-mmt-position="2_3_1_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_1_2_0">[</mo><mi data-mmt-position="2_3_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_1_2_0">]</mo><mrow data-mmt-position="2_3_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_1_2_2_0"></mspace><mi data-mmt-varref="2_3_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1488.40.15:1494.40.21" data-mmt-position="2_3_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1493.40.20:1493.40.20" data-mmt-position="2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>D (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1441.39.1:1503.40.30">http://mathhub.info/MitM/Models/poisson.mmt#1441.39.1:1503.40.30</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PoissonBoundaryConditions</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">ThermodynamicEquilibrium</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">?ThermodynamicEquilibrium</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2439.75.1:2473.75.35">http://mathhub.info/MitM/Models/poisson.mmt#2439.75.1:2473.75.35</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/poisson?Charge]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">?Charge</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary value for electrostatic potential at top contact <br/>	     for an applied voltage <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top">potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2609.78.33" data-mmt-position="2">ψ_0_1</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2609.78.33" data-mmt-position="1">+</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2609.78.33" data-mmt-position="3">U_1</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2577.78.1:2620.78.44">http://mathhub.info/MitM/Models/poisson.mmt#2577.78.1:2620.78.44</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary value for electrostatic potential at bottom contact <br/>	     for an applied voltage <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math>.<br/>	     N.B.: the applied bias voltage is U_bias = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2779.-1.5" data-mmt-position="2">U_2</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2779.-1.5" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2779.-1.5" data-mmt-position="3">U_1</mo></mrow></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom">potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36" data-mmt-position="2">ψ_0_2</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36" data-mmt-position="1">+</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36" data-mmt-position="3">U_2</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2785.82.1:2831.82.47">http://mathhub.info/MitM/Models/poisson.mmt#2785.82.1:2831.82.47</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PoissonEquation</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/poisson?Charge]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">?Charge</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1600.46.1:1616.46.17">http://mathhub.info/MitM/Models/poisson.mmt#1600.46.1:1616.46.17</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Displacement">Displacement</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/poisson?Displacement]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement">?Displacement</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1619.47.1:1641.47.23">http://mathhub.info/MitM/Models/poisson.mmt#1619.47.1:1641.47.23</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Defintion of the Poisson equation with total charge <br/>       as right hand side.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonEquation?poisson_equation">poisson_equation</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?poisson_equation" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1752.51.20:1760.51.28" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1752.51.20:1760.51.28" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1756.51.24" data-mmt-position="2_3_3">D</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1756.51.24" data-mmt-position="2_3_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1756.51.24" data-mmt-position="2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">[</mo><mi data-mmt-position="2_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">]</mo><mrow data-mmt-position="2_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="2_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">[</mo><mi data-mmt-position="2_2_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">]</mo><mrow data-mmt-position="2_2_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_2_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_2_1_2_2_0"></mspace><mi data-mmt-varref="2_2_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_2_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_4">Q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1733.51.1:1762.51.30">http://mathhub.info/MitM/Models/poisson.mmt#1733.51.1:1762.51.30</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PoissonParameters</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The relative dielelectric permitivity constant denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-position="">ε_r</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity">relative_dielectric_permitivity</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ε_r (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#323.8.1:368.8.46">http://mathhub.info/MitM/Models/poisson.mmt#323.8.1:368.8.46</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The static dielelectric permitivity constant denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-position="">ε_s</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity">dielectric_permitivity</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="2">ε_r</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="3">ε_0</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ε_s (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#439.10.1:489.10.51">http://mathhub.info/MitM/Models/poisson.mmt#439.10.1:489.10.51</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ThermodynamicEquilibrium</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/poisson?Charge]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">?Charge</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1906.59.1:1922.59.17">http://mathhub.info/MitM/Models/poisson.mmt#1906.59.1:1922.59.17</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Value of build-in potential ψ_0 at top contact guranteeing <br/>       local charge neutrality.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top">equilibrium_potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_0_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2026.63.1:2067.63.42">http://mathhub.info/MitM/Models/poisson.mmt#2026.63.1:2067.63.42</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Value of build-in potential ψ_0 at bottom contact guranteeing <br/>       local charge neutrality. <br/>       N.B. the build-in potential is given as U_b = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2236.-1.11" data-mmt-position="2">ψ_0_2</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2236.-1.11" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2236.-1.11" data-mmt-position="3">ψ_0_1</mo></mrow></math> (Check!)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom">equilibrium_potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_0_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2257.69.1:2301.69.45">http://mathhub.info/MitM/Models/poisson.mmt#2257.69.1:2301.69.45</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Charge.html">http://mathhub.info/MitM/Models/poisson?Charge</a></div><div class="submodule"><a href="$Displacement.html">http://mathhub.info/MitM/Models/poisson?Displacement</a></div><div class="submodule"><a href="$Poisson$Boundary$Conditions.html">http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions</a></div><div class="submodule"><a href="$Poisson$Equation.html">http://mathhub.info/MitM/Models/poisson?PoissonEquation</a></div><div class="submodule"><a href="$Poisson$Parameters.html">http://mathhub.info/MitM/Models/poisson?PoissonParameters</a></div><div class="submodule"><a href="$Thermodynamic$Equilibrium.html">http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Recombination</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#236.7.2:272.7.38">http://mathhub.info/MitM/Models/recombination.mmt#236.7.2:272.7.38</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#276.8.1:311.8.36">http://mathhub.info/MitM/Models/recombination.mmt#276.8.1:311.8.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#314.9.1:345.9.32">http://mathhub.info/MitM/Models/recombination.mmt#314.9.1:345.9.32</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The kernel of the recombination rate depending <br/>     on electron and hole densities.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient">recombination_coefficient</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>r (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#442.13.1:487.13.46">http://mathhub.info/MitM/Models/recombination.mmt#442.13.1:487.13.46</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Recombination rate for right hand side of continuity equations.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate">recombination_rate</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="3">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="4">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="5">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#608.17.6:609.17.7" data-mmt-position="1">xn</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#608.17.6:609.17.7" data-mmt-position="1_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#612.17.10:613.17.11" data-mmt-position="2">xp</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#612.17.10:613.17.11" data-mmt-position="2_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#616.17.14:619.17.17" data-mmt-position="3">xφ_n</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#616.17.14:619.17.17" data-mmt-position="3_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#622.17.20:625.17.23" data-mmt-position="4">xφ_p</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#622.17.20:625.17.23" data-mmt-position="4_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="5"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:647.17.45" data-mmt-position="5_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:641.17.39" data-mmt-position="5_2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_1">r</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#631.17.29:632.17.30" data-mmt-position="5_2_2_2_2">xn</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_0"></mspace><mi data-mmt-varref="2" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#634.17.32:635.17.33" data-mmt-position="5_2_2_2_3">xp</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:641.17.39" data-mmt-position="5_2_2_1">⋅</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#640.17.38:641.17.39" data-mmt-position="5_2_2_3">xn</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:647.17.45" data-mmt-position="5_2_1">⋅</mo><mi data-mmt-varref="2" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#646.17.44:647.17.45" data-mmt-position="5_2_3">xp</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_3"><mo class="operator brackets">(</mo><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?pos_lit" data-mmt-position="5_3_2">1</mn><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#651.17.49:690.17.88" data-mmt-position="5_3_1">-</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#651.17.49:690.17.88" data-mmt-position="5_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:658.17.56" data-mmt-position="5_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:689.17.87" data-mmt-position="5_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:689.17.87" data-mmt-position="5_3_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mfrac><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_2">q</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="3" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#666.17.64:669.17.67" data-mmt-position="5_3_3_2_2_3_2">xφ_n</mi><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#665.17.63:677.17.75" data-mmt-position="5_3_3_2_2_3_1">-</mo><mi data-mmt-varref="4" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#673.17.71:676.17.74" data-mmt-position="5_3_3_2_2_3_3">xφ_p</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mfrac><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf" data-mmt-position="5_3_3_2_4">prf</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>R (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#562.16.1:701.18.7">http://mathhub.info/MitM/Models/recombination.mmt#562.16.1:701.18.7</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">SpontaneousRecombination</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#816.23.1:839.23.24">http://mathhub.info/MitM/Models/recombination.mmt#816.23.1:839.23.24</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">The coefficient for the sponanteous recombination rate is denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-position="">B</mo></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient">spontaneous_recombination_coefficient</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>B (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#923.26.1:971.26.49">http://mathhub.info/MitM/Models/recombination.mmt#923.26.1:971.26.49</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formula for sponanteous recombination <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-position="">r</mo></math>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-position="">n</mo></math>,<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-position="">p</mo></math>) = <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-position="">B</mo></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?axiom_spontaneous">axiom_spontaneous</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?axiom_spontaneous" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1056.28.21:1070.28.35" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1056.28.21:1070.28.35" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_3">r</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_3">ℝ</mo><mo class="operator brackets">)</mo></mrow></mrow></mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_4"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1064.28.29:1064.28.29" data-mmt-position="2_4_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1064.28.29:1064.28.29" data-mmt-position="2_4_1_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1066.28.31:1066.28.31" data-mmt-position="2_4_2">y</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1066.28.31:1066.28.31" data-mmt-position="2_4_2_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_0">]</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_3">B</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#1036.28.1:1089.28.54">http://mathhub.info/MitM/Models/recombination.mmt#1036.28.1:1089.28.54</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Recombination.html">http://mathhub.info/MitM/Models/recombination?Recombination</a></div><div class="submodule"><a href="$Spontaneous$Recombination.html">http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Models</span></div><div class="document-body"><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc">http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/constants.omdoc">http://mathhub.info/MitM/Models/constants.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/continuity.omdoc">http://mathhub.info/MitM/Models/continuity.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/densities.omdoc">http://mathhub.info/MitM/Models/densities.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/device.omdoc">http://mathhub.info/MitM/Models/device.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/poisson.omdoc">http://mathhub.info/MitM/Models/poisson.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/recombination.omdoc">http://mathhub.info/MitM/Models/recombination.omdoc</span></div></div></div></div></body></html>
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diff --git a/export/html/narration/VanRoosbroeck.html b/export/html/narration/VanRoosbroeck.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">VanRoosbroeck.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing the stationary van Roosbroeck system <br/>     describung the charge transport of electrons and holes<br/>     in a one-dimensional (layered) semiconductor device. <br/>     The model includes electron and hole <br/>     densities according the Boltzmann approximation and <br/>     spontaneous radiative recombination processes only. <br/>     Furthermore the material properties such as band edges, <br/>     density of states, mobilties are assumed to be<br/>     homogenous (spatially constant). Also a homogenous device<br/>     temperature is assumed.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck">http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck</span></div></div></div></div></body></html>
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diff --git a/export/html/narration/constants.html b/export/html/narration/constants.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">constants.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing general physical constants</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models?PhysicalConstants">http://mathhub.info/MitM/Models?PhysicalConstants</span></div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models?Base">http://mathhub.info/MitM/Models?Base</span></div></div></div></div></body></html>
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diff --git a/export/html/narration/continuity.html b/export/html/narration/continuity.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">continuity.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing the mobilitiy parameters of <br/>     the semiconductor.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/continuity?Mobilities">http://mathhub.info/MitM/Models/continuity?Mobilities</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing the expression for the electron current.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">http://mathhub.info/MitM/Models/continuity?CurrentElectrons</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing the expression for the hole current.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/continuity?CurrentHoles">http://mathhub.info/MitM/Models/continuity?CurrentHoles</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing the continuity equation for the electrons.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons">http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing the continuity equation for the holes.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles">http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing the boundary conditions for the<br/>     electron continuity equation modeling Ohmic contacts.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons">http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing the boundary conditions for the<br/>     holes continuity equation modeling Ohmic contacts.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles">http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles</span></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">densities.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing the bandstructure parameters of <br/>     the semiconductor.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/densities?BandstructureParameters">http://mathhub.info/MitM/Models/densities?BandstructureParameters</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing spatial variation of the <br/>     quasi-Fermi potential for the electrons. <br/>     This is a basic variable of the system</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing spatial variation of the <br/>     quasi-Fermi potential for the holes. <br/>     This is a basic variable (unknown) of the system.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">http://mathhub.info/MitM/Models/densities?FermiPotentialHoles</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing spatial variation of the <br/>     electrostatic potential. <br/>     This is a basic variable (unknown) of the system.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">http://mathhub.info/MitM/Models/densities?ElectrostaticPotential</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing state equation for the <br/>	   electron density for the Boltzmann approximation (exp).</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/densities?DensityElectrons">http://mathhub.info/MitM/Models/densities?DensityElectrons</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing state equation for the <br/>	   hole density for the Boltzmann approximation (exp).</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/densities?DensityHoles">http://mathhub.info/MitM/Models/densities?DensityHoles</span></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">device.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This theory intentionally left empty. It has a narrative in sTeX</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/device?Device">http://mathhub.info/MitM/Models/device?Device</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing description of device geometry.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/device?DeviceGeometry">http://mathhub.info/MitM/Models/device?DeviceGeometry</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing description of the doping profile.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/device?DopingProfile">http://mathhub.info/MitM/Models/device?DopingProfile</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing a description the the operating state,<br/>     that means applied voltages and device temperature.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/device?DeviceOperationState">http://mathhub.info/MitM/Models/device?DeviceOperationState</span></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">poisson.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing the static dielectric permitivity constant<br/>     of the semiconductor.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/poisson?PoissonParameters">http://mathhub.info/MitM/Models/poisson?PoissonParameters</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing the total charge entering <br/>     the right side of Poisson's equation.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/poisson?Charge">http://mathhub.info/MitM/Models/poisson?Charge</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing the electric displacement.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/poisson?Displacement">http://mathhub.info/MitM/Models/poisson?Displacement</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing Poissons equation.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/poisson?PoissonEquation">http://mathhub.info/MitM/Models/poisson?PoissonEquation</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing build-in potential in <br/>     thermodynamic equilibrium.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium</span></div><div class="opaque-text inlineBoxSibling">This is a theory containing the boundary values for the Poisson eqauation.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions">http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions</span></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">recombination.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing the general structure for <br/>     a recombination rate.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/recombination?Recombination">http://mathhub.info/MitM/Models/recombination?Recombination</span></div><div class="opaque-text inlineBoxSibling">Kernel for spontaneous recombination with coefficient B.</div><div class="document-mref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination">http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination</span></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Base</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#574.15.1:601.15.28">http://mathhub.info/MitM/Models/constants.mmt#574.15.1:601.15.28</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma">LFSigma</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma">?LFSigma</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#604.16.1:631.16.28">http://mathhub.info/MitM/Models/constants.mmt#604.16.1:631.16.28</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://gl.mathhub.info/MMT/LFX/Sigma?TypedSigma">TypedSigma</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://gl.mathhub.info/MMT/LFX/Sigma?TypedSigma]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?TypedSigma">?TypedSigma</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols">Symbols</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://gl.mathhub.info/MMT/LFX/Sigma?Symbols]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols">?Symbols</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://gl.mathhub.info/MMT/LFX/Sigma?Rules">Rules</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://gl.mathhub.info/MMT/LFX/Sigma?Rules]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Rules">?Rules</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?LF">LF</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?LF]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LF">?LF</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?TermsTypesKinds">TermsTypesKinds</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?TermsTypesKinds]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?TermsTypesKinds">?TermsTypesKinds</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/mmt?Errors">Errors</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/mmt?Errors]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/mmt?Errors">?Errors</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/mmt?ModExp">ModExp</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/mmt?ModExp]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/mmt?ModExp">?ModExp</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/mmt?mmt">mmt</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/mmt?mmt]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/mmt?mmt">?mmt</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?Typed">Typed</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?Typed]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed">?Typed</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?Kinded">Kinded</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?Kinded]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Kinded">?Kinded</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?TypedConstants">TypedConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?TypedConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?TypedConstants">?TypedConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?KindedConstants">KindedConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?KindedConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?KindedConstants">?KindedConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?LambdaPi">LambdaPi</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?LambdaPi]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi">?LambdaPi</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://cds.omdoc.org/urtheories?LFRules">LFRules</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://cds.omdoc.org/urtheories?LFRules]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LFRules">?LFRules</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?exp">exp</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?exp" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#640.17.7:644.17.11" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#640.17.7:644.17.11" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#640.17.7:644.17.11" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#634.17.1:647.17.14">http://mathhub.info/MitM/Models/constants.mmt#634.17.1:647.17.14</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?der">der</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?der" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#655.18.7:696.18.48" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#656.18.8:656.18.8" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#656.18.8:656.18.8" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#660.18.12:667.18.19" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#660.18.12:667.18.19" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#664.18.16:667.18.19" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#655.18.7:696.18.48" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#655.18.7:696.18.48" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:696.18.48" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:681.18.33" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#671.18.23:676.18.28" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#676.18.28:676.18.28" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:681.18.33" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:681.18.33" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:696.18.48" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:696.18.48" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#685.18.37:696.18.48" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#691.18.43:691.18.43" data-mmt-position="2_2_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#685.18.37:696.18.48" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#685.18.37:696.18.48" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>b ' (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#649.18.1:707.18.59">http://mathhub.info/MitM/Models/constants.mmt#649.18.1:707.18.59</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?Real_vec_space2">Real_vec_space2</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#793.21.19:796.21.22">type</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ℝ2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#775.21.1:816.21.42">http://mathhub.info/MitM/Models/constants.mmt#775.21.1:816.21.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?Real_vec_space3">Real_vec_space3</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#836.22.19:839.22.22">type</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ℝ3 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#818.22.1:863.22.46">http://mathhub.info/MitM/Models/constants.mmt#818.22.1:863.22.46</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?comp1">comp1</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#875.24.9:880.24.14" data-mmt-position="1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#875.24.9:880.24.14" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#875.24.9:880.24.14" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#887.24.21:887.24.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#887.24.21:887.24.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#890.24.24:893.24.27" data-mmt-position="2_0">πl</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#893.24.27:893.24.27" data-mmt-position="2_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#867.24.1:896.24.30">http://mathhub.info/MitM/Models/constants.mmt#867.24.1:896.24.30</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?comp2">comp2</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#906.25.9:911.25.14" data-mmt-position="1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#906.25.9:911.25.14" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#906.25.9:911.25.14" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#918.25.21:918.25.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#918.25.21:918.25.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#921.25.24:929.25.32" data-mmt-position="2_0">πl</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#921.25.24:929.25.32" data-mmt-position="2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#924.25.27:929.25.32" data-mmt-position="2_1_0">πr</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#928.25.31:928.25.31" data-mmt-position="2_1_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#898.25.1:932.25.35">http://mathhub.info/MitM/Models/constants.mmt#898.25.1:932.25.35</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?comp3">comp3</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#942.26.9:947.26.14" data-mmt-position="1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#942.26.9:947.26.14" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#942.26.9:947.26.14" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#954.26.21:954.26.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#954.26.21:954.26.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#957.26.24:965.26.32" data-mmt-position="2_0">πr</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#957.26.24:965.26.32" data-mmt-position="2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#960.26.27:965.26.32" data-mmt-position="2_1_0">πr</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#964.26.31:964.26.31" data-mmt-position="2_1_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#934.26.1:968.26.35">http://mathhub.info/MitM/Models/constants.mmt#934.26.1:968.26.35</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?pred_as_sub2">pred_as_sub2</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#987.28.16:1004.28.33" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#993.28.22:996.28.25" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#987.28.16:1004.28.33" data-mmt-position="0">→</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1001.28.30:1004.28.33" data-mmt-position="2">type</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1011.28.40:1011.28.40" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1011.28.40:1011.28.40" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#993.28.22:996.28.25" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">⟨</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_1">ℝ2</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">|</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52" data-mmt-position="2_2_1">z</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52" data-mmt-position="2_2_1_1">ℝ2</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59" data-mmt-position="2_2_2_1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59" data-mmt-position="2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1028.28.57" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1030.28.59" data-mmt-position="2_2_2_2_0"></mspace><mi data-mmt-varref="2_2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1030.28.59:1030.28.59" data-mmt-position="2_2_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">⟩</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>pred2 a (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#972.28.1:1048.28.77">http://mathhub.info/MitM/Models/constants.mmt#972.28.1:1048.28.77</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?pred_as_sub3">pred_as_sub3</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1065.29.16:1082.29.33" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-position="1_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1071.29.22:1074.29.25" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1065.29.16:1082.29.33" data-mmt-position="0">→</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1079.29.30:1082.29.33" data-mmt-position="2">type</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-position="1_1_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1071.29.22:1074.29.25" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">⟨</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">|</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52" data-mmt-position="2_2_1">z</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52" data-mmt-position="2_2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59" data-mmt-position="2_2_2_1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59" data-mmt-position="2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1106.29.57" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1108.29.59" data-mmt-position="2_2_2_2_0"></mspace><mi data-mmt-varref="2_2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1108.29.59:1108.29.59" data-mmt-position="2_2_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">⟩</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>pred3 a (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1050.29.1:1126.29.77">http://mathhub.info/MitM/Models/constants.mmt#1050.29.1:1126.29.77</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three">lift_type_one_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1155.31.26:1178.31.49" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1160.31.31:1163.31.34" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1155.31.26:1178.31.49" data-mmt-position="0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1155.31.26:1178.31.49" data-mmt-position="2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1168.31.39:1178.31.49" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1168.31.39:1178.31.49" data-mmt-position="2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1174.31.45:1177.31.48" data-mmt-position="2_2">bool</mo><mo class="operator brackets">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1160.31.31:1163.31.34" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9" data-mmt-position="2_1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9" data-mmt-position="2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1195.32.13:1195.32.13" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24" data-mmt-position="2_2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24" data-mmt-position="2_2_2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1198.32.16:1202.32.20" data-mmt-position="2_2_2_2_2_1">comp1</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1197.32.15:1205.32.23" data-mmt-position="2_2_2_2_2_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1204.32.22:1204.32.22" data-mmt-position="2_2_2_2_2_2">v</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_1">∧</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1215.32.33" data-mmt-position="2_2_2_3_3_1">comp2</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1217.32.35" data-mmt-position="2_2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1217.32.35:1217.32.35" data-mmt-position="2_2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_2_3_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_1">∧</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1231.32.49" data-mmt-position="2_2_3_3_1">comp3</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1233.32.51" data-mmt-position="2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1233.32.51:1233.32.51" data-mmt-position="2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_3_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>t1↑ a (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1130.31.1:1252.32.70">http://mathhub.info/MitM/Models/constants.mmt#1130.31.1:1252.32.70</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three">lift_type_two_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1279.33.26:1303.33.50" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1285.33.32:1288.33.35" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1279.33.26:1303.33.50" data-mmt-position="0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1279.33.26:1303.33.50" data-mmt-position="2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1293.33.40:1303.33.50" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1293.33.40:1303.33.50" data-mmt-position="2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1299.33.46:1302.33.49" data-mmt-position="2_2">bool</mo><mo class="operator brackets">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1285.33.32:1288.33.35" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9" data-mmt-position="2_1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9" data-mmt-position="2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1320.34.13:1320.34.13" data-mmt-position="2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35" data-mmt-position="2_2_2_2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">⟨</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1328.34.21" data-mmt-position="2_2_2_2_1_1">comp1</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1330.34.23" data-mmt-position="2_2_2_2_1_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1330.34.23:1330.34.23" data-mmt-position="2_2_2_2_1_2">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">,</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1337.34.30" data-mmt-position="2_2_2_2_2_1">comp2</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1339.34.32" data-mmt-position="2_2_2_2_2_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1339.34.32:1339.34.32" data-mmt-position="2_2_2_2_2_2">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">⟩</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_1">∧</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1351.34.44" data-mmt-position="2_2_3_3_1">comp3</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1353.34.46" data-mmt-position="2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1353.34.46:1353.34.46" data-mmt-position="2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_3_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>t2↑ a (precedence -1)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1254.33.1:1380.34.73">http://mathhub.info/MitM/Models/constants.mmt#1254.33.1:1380.34.73</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_function_one_to_three">lift_function_one_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_function_one_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1414.36.30:1461.36.77" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1415.36.31:1415.36.31" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1415.36.31:1415.36.31" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1419.36.35:1426.36.42" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1419.36.35:1426.36.42" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1423.36.39:1426.36.42" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1414.36.30:1461.36.77" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1414.36.30:1461.36.77" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1461.36.77" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1439.36.55" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1429.36.45:1434.36.50" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1434.36.50:1434.36.50" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1439.36.55" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1439.36.55" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1461.36.77" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1461.36.77" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1443.36.59:1461.36.77" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1444.36.60:1456.36.72" data-mmt-position="2_2_1_1">pred3</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1444.36.60:1456.36.72" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1450.36.66:1456.36.72" data-mmt-position="2_2_1_2_1">t1↑</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1455.36.71:1455.36.71" data-mmt-position="2_2_1_2_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1443.36.59:1461.36.77" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1443.36.59:1461.36.77" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>f1↑ b (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1385.36.1:1510.37.45">http://mathhub.info/MitM/Models/constants.mmt#1385.36.1:1510.37.45</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_function_two_to_three">lift_function_two_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_function_two_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1541.38.30:1590.38.79" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1542.38.31:1542.38.31" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1542.38.31:1542.38.31" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1546.38.35:1554.38.43" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1546.38.35:1554.38.43" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1551.38.40:1554.38.43" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1541.38.30:1590.38.79" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1541.38.30:1590.38.79" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1590.38.79" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1568.38.57" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1557.38.46:1563.38.52" data-mmt-position="2_1_1_1">pred2</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1563.38.52:1563.38.52" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1568.38.57" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1568.38.57" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1590.38.79" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1590.38.79" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1572.38.61:1590.38.79" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1573.38.62:1585.38.74" data-mmt-position="2_2_1_1">pred3</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1573.38.62:1585.38.74" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1579.38.68:1585.38.74" data-mmt-position="2_2_1_2_1">t2↑</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1584.38.73:1584.38.73" data-mmt-position="2_2_1_2_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1572.38.61:1590.38.79" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1572.38.61:1590.38.79" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>f2↑ b (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1512.38.1:1650.39.56">http://mathhub.info/MitM/Models/constants.mmt#1512.38.1:1650.39.56</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PhysicalConstants</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The vaccuum dielectric permitivity constant (usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-position="">ε_0</mo></math>)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity">vacuum_dielectric_permitivity</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ε_0 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#326.7.1:369.7.44">http://mathhub.info/MitM/Models/constants.mmt#326.7.1:369.7.44</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The elementary charge (denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-position="">q</mo></math>)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge">elementary_charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>q (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#417.9.1:446.9.30">http://mathhub.info/MitM/Models/constants.mmt#417.9.1:446.9.30</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The Boltzmann constant (usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-position="">k_B</mo></math>)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant">Boltzmann_constant</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>k_B (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#506.11.1:538.11.33">http://mathhub.info/MitM/Models/constants.mmt#506.11.1:538.11.33</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../html.js"></script></head><body><div class="namespace"><div class="subnamespace"><a href="VanRoosbroeck/.html">http://mathhub.info/MitM/Models/VanRoosbroeck</a></div><div class="subnamespace"><a href="continuity/.html">http://mathhub.info/MitM/Models/continuity</a></div><div class="subnamespace"><a href="densities/.html">http://mathhub.info/MitM/Models/densities</a></div><div class="subnamespace"><a href="device/.html">http://mathhub.info/MitM/Models/device</a></div><div class="subnamespace"><a href="poisson/.html">http://mathhub.info/MitM/Models/poisson</a></div><div class="subnamespace"><a href="recombination/.html">http://mathhub.info/MitM/Models/recombination</a></div><div class="submodule"><a href="$Base.html">http://mathhub.info/MitM/Models?Base</a></div><div class="submodule"><a href="$Physical$Constants.html">http://mathhub.info/MitM/Models?PhysicalConstants</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">VanRoosbroeck</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonEquation">PoissonEquation</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?PoissonEquation]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonEquation">?PoissonEquation</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#702.15.1:734.15.33">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#702.15.1:734.15.33</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?Charge]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">?Charge</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Displacement">Displacement</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?Displacement]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement">?Displacement</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions">PoissonBoundaryConditions</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions">?PoissonBoundaryConditions</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#737.16.1:779.16.43">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#737.16.1:779.16.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">ThermodynamicEquilibrium</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">?ThermodynamicEquilibrium</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons">ContinuityEquationElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons">?ContinuityEquationElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#782.17.1:829.17.48">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#782.17.1:829.17.48</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">CurrentElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?CurrentElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">?CurrentElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles">ContinuityEquationHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles">?ContinuityEquationHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#832.18.1:875.18.44">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#832.18.1:875.18.44</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentHoles">CurrentHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?CurrentHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles">?CurrentHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons">ContinuityBoundaryConditionsElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons">?ContinuityBoundaryConditionsElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#878.19.1:935.19.58">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#878.19.1:935.19.58</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles">ContinuityBoundaryConditionsHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles">?ContinuityBoundaryConditionsHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#938.20.1:991.20.54">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#938.20.1:991.20.54</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination">SpontaneousRecombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination">?SpontaneousRecombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#994.21.1:1041.21.48">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#994.21.1:1041.21.48</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Van$Roosbroeck.html">http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck</a></div></div></body></html>
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diff --git a/export/mh-html/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Electrons.html b/export/mh-html/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Electrons.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityBoundaryConditionsElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2985.81.1:3021.81.37">http://mathhub.info/MitM/Models/continuity.mmt#2985.81.1:3021.81.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the top contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top">potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_n_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3071.83.1:3108.83.38">http://mathhub.info/MitM/Models/continuity.mmt#3071.83.1:3108.83.38</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the bottom contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom">potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_n_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3160.85.1:3200.85.41">http://mathhub.info/MitM/Models/continuity.mmt#3160.85.1:3200.85.41</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityBoundaryConditionsHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3386.92.1:3422.92.37">http://mathhub.info/MitM/Models/continuity.mmt#3386.92.1:3422.92.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the top contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top">potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_p_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3471.94.1:3508.94.38">http://mathhub.info/MitM/Models/continuity.mmt#3471.94.1:3508.94.38</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the bottom contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom">potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_p_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3559.96.1:3599.96.41">http://mathhub.info/MitM/Models/continuity.mmt#3559.96.1:3599.96.41</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityEquationElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">CurrentElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/continuity?CurrentElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">?CurrentElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1879.50.1:1905.50.27">http://mathhub.info/MitM/Models/continuity.mmt#1879.50.1:1905.50.27</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1908.51.1:1939.51.32">http://mathhub.info/MitM/Models/continuity.mmt#1908.51.1:1939.51.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1942.52.1:1980.52.39">http://mathhub.info/MitM/Models/continuity.mmt#1942.52.1:1980.52.39</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1983.53.1:2019.53.37">http://mathhub.info/MitM/Models/continuity.mmt#1983.53.1:2019.53.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2022.54.1:2063.54.42">http://mathhub.info/MitM/Models/continuity.mmt#2022.54.1:2063.54.42</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formulation of the continuity equation for electrons in divergence form.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation_electrons">continuity_equation_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation_electrons" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2188.59.2:2272.59.86" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2188.59.2:2272.59.86" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2272.59.86" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2202.59.16" data-mmt-position="2_3_3"><mo class="operator brackets">(</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_1">j_n</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">[</mo><mi data-mmt-position="2_3_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">]</mo><mrow data-mmt-position="2_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_3_2_2_0"></mspace><mi data-mmt-varref="2_3_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_3">ψ</mo><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_4">φ_n</mo><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2202.59.16" data-mmt-position="2_3_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2202.59.16" data-mmt-position="2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">[</mo><mi data-mmt-position="2_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_1_1">ℝ</mo><mo 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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" 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class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentHoles">CurrentHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/continuity?CurrentHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles">?CurrentHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2403.65.1:2425.65.23">http://mathhub.info/MitM/Models/continuity.mmt#2403.65.1:2425.65.23</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2428.66.1:2463.66.36">http://mathhub.info/MitM/Models/continuity.mmt#2428.66.1:2463.66.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2466.67.1:2508.67.43">http://mathhub.info/MitM/Models/continuity.mmt#2466.67.1:2508.67.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2511.68.1:2547.68.37">http://mathhub.info/MitM/Models/continuity.mmt#2511.68.1:2547.68.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2550.69.1:2591.69.42">http://mathhub.info/MitM/Models/continuity.mmt#2550.69.1:2591.69.42</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formulation of the continuity equation for holes in divergence form.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes">continuity_equation_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2703.74.2:2788.74.87" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2703.74.2:2788.74.87" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2717.74.16" data-mmt-position="2_3_3"><mo class="operator brackets">(</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_1">j_p</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">[</mo><mi data-mmt-position="2_3_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">]</mo><mrow data-mmt-position="2_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_3_2_2_0"></mspace><mi data-mmt-varref="2_3_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_3">ψ</mo><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_4">φ_p</mo><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2717.74.16" data-mmt-position="2_3_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2717.74.16" data-mmt-position="2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">[</mo><mi data-mmt-position="2_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">]</mo><mrow data-mmt-position="2_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="2_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">[</mo><mi data-mmt-position="2_2_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">]</mo><mrow data-mmt-position="2_2_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_2_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_2_1_2_2_0"></mspace><mi data-mmt-varref="2_2_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_2_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow></mrow></mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_4"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2721.74.20:2788.74.87" data-mmt-position="2_4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2722.74.21:2722.74.21" data-mmt-position="2_4_1">x</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2722.74.21:2722.74.21" data-mmt-position="2_4_1_1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2721.74.20:2788.74.87" data-mmt-position="2_4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2721.74.20:2788.74.87" data-mmt-position="2_4_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2788.74.87" data-mmt-position="2_4_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2730.74.29" data-mmt-position="2_4_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" 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data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_1">n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2740.74.39:2744.74.43" data-mmt-position="2_4_2_3_2_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2740.74.39:2744.74.43" data-mmt-position="2_4_2_3_2_2_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2743.74.42:2743.74.42" data-mmt-position="2_4_2_3_2_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2746.74.45:2752.74.51" data-mmt-position="2_4_2_3_2_3_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2746.74.45:2752.74.51" data-mmt-position="2_4_2_3_2_3_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2751.74.50:2751.74.50" data-mmt-position="2_4_2_3_2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" 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data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2761.74.60:2761.74.60" data-mmt-position="2_4_2_3_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2764.74.63:2770.74.69" data-mmt-position="2_4_2_3_3_3_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2764.74.63:2770.74.69" data-mmt-position="2_4_2_3_3_3_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2769.74.68:2769.74.68" data-mmt-position="2_4_2_3_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_4"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2773.74.72:2779.74.78" data-mmt-position="2_4_2_3_4_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2773.74.72:2779.74.78" data-mmt-position="2_4_2_3_4_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2778.74.77:2778.74.77" data-mmt-position="2_4_2_3_4_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_5"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2781.74.80:2787.74.86" data-mmt-position="2_4_2_3_5_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2781.74.80:2787.74.86" data-mmt-position="2_4_2_3_5_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2786.74.85:2786.74.85" data-mmt-position="2_4_2_3_5_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2672.73.1:2791.74.90">http://mathhub.info/MitM/Models/continuity.mmt#2672.73.1:2791.74.90</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">CurrentElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#531.16.1:573.16.43">http://mathhub.info/MitM/Models/continuity.mmt#531.16.1:573.16.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo 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class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#576.17.1:617.17.42">http://mathhub.info/MitM/Models/continuity.mmt#576.17.1:617.17.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#620.18.1:655.18.36">http://mathhub.info/MitM/Models/continuity.mmt#620.18.1:655.18.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#658.19.1:678.19.21">http://mathhub.info/MitM/Models/continuity.mmt#658.19.1:678.19.21</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Definition of the electron current in gradient form. <br/>     The driving force of the current are the negative gradients of <br/>     the quasi-Fermi potential, here denoted by j_n.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons">current_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#966.26.21:1021.26.76" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#967.26.22:967.26.22" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#967.26.22:967.26.22" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#974.26.29:977.26.32" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#966.26.21:1021.26.76" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#966.26.21:1021.26.76" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:991.26.46" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#981.26.36:986.26.41" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#986.26.41:986.26.41" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:991.26.46" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:991.26.46" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#995.26.50:1006.26.61" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#996.26.51:1001.26.56" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1001.26.56:1001.26.56" data-mmt-position="2_2_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#995.26.50:1006.26.61" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#995.26.50:1006.26.61" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1010.26.65:1021.26.76" data-mmt-position="2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1011.26.66:1016.26.71" data-mmt-position="2_3_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1016.26.71:1016.26.71" data-mmt-position="2_3_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1010.26.65:1021.26.76" data-mmt-position="2_3_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1010.26.65:1021.26.76" data-mmt-position="2_3_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1030.27.5:1030.27.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1030.27.5:1030.27.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#974.26.29:977.26.32" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">]</mo><mrow data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1033.27.8:1033.27.8" data-mmt-position="2_1">f</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1033.27.8:1033.27.8" data-mmt-position="2_1_1"><mrow data-mmt-position="2_1_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#981.26.36:986.26.41" data-mmt-position="2_1_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#986.26.41:986.26.41" data-mmt-position="2_1_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_1_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1035.27.10:1035.27.10" data-mmt-position="2_2">g</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1035.27.10:1035.27.10" data-mmt-position="2_2_1"><mrow data-mmt-position="2_2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#996.26.51:1001.26.56" data-mmt-position="2_2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1001.26.56:1001.26.56" data-mmt-position="2_2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1037.27.12:1075.27.50" data-mmt-position="2_3_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1038.27.13:1038.27.13" data-mmt-position="2_3_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1038.27.13:1038.27.13" data-mmt-position="2_3_1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_3_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1016.26.71:1016.26.71" data-mmt-position="2_3_1_1_2">P</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1037.27.12:1075.27.50" data-mmt-position="2_3_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1037.27.12:1075.27.50" data-mmt-position="2_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1075.27.50" data-mmt-position="2_3_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1066.27.41" data-mmt-position="2_3_2_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1048.27.23" data-mmt-position="2_3_2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1042.27.17" data-mmt-position="2_3_2_2_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1042.27.17" data-mmt-position="2_3_2_2_2_2_2">q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1048.27.23" data-mmt-position="2_3_2_2_2_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1048.27.23" data-mmt-position="2_3_2_2_2_3">μ_n</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1066.27.41" data-mmt-position="2_3_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1066.27.41" data-mmt-position="2_3_2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_1">n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1056.27.31:1056.27.31" data-mmt-position="2_3_2_2_3_2_1">f</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1055.27.30:1059.27.34" data-mmt-position="2_3_2_2_3_2_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1058.27.33:1058.27.33" data-mmt-position="2_3_2_2_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1062.27.37:1062.27.37" data-mmt-position="2_3_2_2_3_3_1">g</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1061.27.36:1065.27.40" data-mmt-position="2_3_2_2_3_3_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1064.27.39:1064.27.39" data-mmt-position="2_3_2_2_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1075.27.50" data-mmt-position="2_3_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1075.27.50" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1070.27.45:1075.27.50" data-mmt-position="2_3_2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1071.27.46:1071.27.46" data-mmt-position="2_3_2_3_1_3">g</mi><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1071.27.46:1072.27.47" data-mmt-position="2_3_2_3_1_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1071.27.46:1072.27.47" data-mmt-position="2_3_2_3_1_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">[</mo><mi data-mmt-position="2_3_2_3_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_3_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">]</mo><mrow data-mmt-position="2_3_2_3_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7824.214.54" data-mmt-position="2_3_2_3_1_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_0"></mspace><mi data-mmt-varref="2_3_2_3_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1070.27.45:1075.27.50" data-mmt-position="2_3_2_3_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1074.27.49:1074.27.49" data-mmt-position="2_3_2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>j_n b c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#946.26.1:1089.27.64">http://mathhub.info/MitM/Models/continuity.mmt#946.26.1:1089.27.64</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">CurrentHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1201.33.1:1239.33.39">http://mathhub.info/MitM/Models/continuity.mmt#1201.33.1:1239.33.39</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1242.34.1:1283.34.42">http://mathhub.info/MitM/Models/continuity.mmt#1242.34.1:1283.34.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1286.35.1:1317.35.32">http://mathhub.info/MitM/Models/continuity.mmt#1286.35.1:1317.35.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1320.36.1:1340.36.21">http://mathhub.info/MitM/Models/continuity.mmt#1320.36.1:1340.36.21</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Defintion of the hole current in gradient form. <br/>     The driving force of the current are the negative gradient of <br/>     the quasi-Fermi potential, here denoted by j_p.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes">current_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1622.43.17:1677.43.72" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1623.43.18:1623.43.18" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1623.43.18:1623.43.18" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1630.43.25:1633.43.28" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1622.43.17:1677.43.72" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1622.43.17:1677.43.72" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1647.43.42" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1637.43.32:1642.43.37" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1642.43.37:1642.43.37" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1647.43.42" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1647.43.42" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1651.43.46:1662.43.57" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1652.43.47:1657.43.52" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1657.43.52:1657.43.52" data-mmt-position="2_2_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1651.43.46:1662.43.57" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1651.43.46:1662.43.57" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1666.43.61:1677.43.72" data-mmt-position="2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1667.43.62:1672.43.67" data-mmt-position="2_3_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1672.43.67:1672.43.67" data-mmt-position="2_3_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1666.43.61:1677.43.72" data-mmt-position="2_3_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1666.43.61:1677.43.72" data-mmt-position="2_3_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1686.44.5:1686.44.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1686.44.5:1686.44.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1630.43.25:1633.43.28" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">]</mo><mrow data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1689.44.8:1689.44.8" data-mmt-position="2_1">f</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1689.44.8:1689.44.8" data-mmt-position="2_1_1"><mrow data-mmt-position="2_1_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1637.43.32:1642.43.37" data-mmt-position="2_1_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1642.43.37:1642.43.37" data-mmt-position="2_1_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_1_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1691.44.10:1691.44.10" data-mmt-position="2_2">g</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1691.44.10:1691.44.10" data-mmt-position="2_2_1"><mrow data-mmt-position="2_2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1652.43.47:1657.43.52" data-mmt-position="2_2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1657.43.52:1657.43.52" data-mmt-position="2_2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1694.44.13:1694.44.13" data-mmt-position="2_3_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1694.44.13:1694.44.13" data-mmt-position="2_3_1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_3_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1672.43.67:1672.43.67" data-mmt-position="2_3_1_1_2">P</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1698.44.17" data-mmt-position="2_3_2_2_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1698.44.17" data-mmt-position="2_3_2_2_2_2_2">q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_3">μ_p</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1712.44.31:1712.44.31" data-mmt-position="2_3_2_2_3_2_1">f</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1711.44.30:1715.44.34" data-mmt-position="2_3_2_2_3_2_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1714.44.33:1714.44.33" data-mmt-position="2_3_2_2_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1718.44.37:1718.44.37" data-mmt-position="2_3_2_2_3_3_1">g</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1717.44.36:1721.44.40" data-mmt-position="2_3_2_2_3_3_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1720.44.39:1720.44.39" data-mmt-position="2_3_2_2_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1726.44.45:1731.44.50" data-mmt-position="2_3_2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1727.44.46:1727.44.46" data-mmt-position="2_3_2_3_1_3">g</mi><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1727.44.46:1728.44.47" data-mmt-position="2_3_2_3_1_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1727.44.46:1728.44.47" data-mmt-position="2_3_2_3_1_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">[</mo><mi data-mmt-position="2_3_2_3_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_3_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">]</mo><mrow data-mmt-position="2_3_2_3_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7824.214.54" data-mmt-position="2_3_2_3_1_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_0"></mspace><mi data-mmt-varref="2_3_2_3_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1726.44.45:1731.44.50" data-mmt-position="2_3_2_3_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1730.44.49:1730.44.49" data-mmt-position="2_3_2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>j_p b c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1606.43.1:1745.44.64">http://mathhub.info/MitM/Models/continuity.mmt#1606.43.1:1745.44.64</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Mobilities</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The electron mobility parameter usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-position="">μ_n</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons">mobility_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>μ_n (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#287.8.1:319.8.33">http://mathhub.info/MitM/Models/continuity.mmt#287.8.1:319.8.33</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The hole mobility parameter usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-position="">μ_p</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes">mobility_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>μ_p (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#381.10.1:409.10.29">http://mathhub.info/MitM/Models/continuity.mmt#381.10.1:409.10.29</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Continuity$Boundary$Conditions$Electrons.html">http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons</a></div><div class="submodule"><a href="$Continuity$Boundary$Conditions$Holes.html">http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles</a></div><div class="submodule"><a href="$Continuity$Equation$Electrons.html">http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons</a></div><div class="submodule"><a href="$Continuity$Equation$Holes.html">http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles</a></div><div class="submodule"><a href="$Current$Electrons.html">http://mathhub.info/MitM/Models/continuity?CurrentElectrons</a></div><div class="submodule"><a href="$Current$Holes.html">http://mathhub.info/MitM/Models/continuity?CurrentHoles</a></div><div class="submodule"><a href="$Mobilities.html">http://mathhub.info/MitM/Models/continuity?Mobilities</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">BandstructureParameters</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The effective density of states for the conduction bands <br/>     usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-position="">N_c</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands">effective_density_of_states_conduction_bands</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>N_c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#340.9.1:398.9.59">http://mathhub.info/MitM/Models/densities.mmt#340.9.1:398.9.59</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The effective density of states for the valence bands <br/>     usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-position="">N_v</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands">effective_density_of_states_valence_bands</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>N_v (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#493.12.1:548.12.56">http://mathhub.info/MitM/Models/densities.mmt#493.12.1:548.12.56</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The conduction band edge usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-position="">E_c</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge">conduction_band_edge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>E_c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#608.14.1:642.14.35">http://mathhub.info/MitM/Models/densities.mmt#608.14.1:642.14.35</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The valence band edge usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-position="">E_v</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge">valence_band_edge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>E_v (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#699.16.1:730.16.32">http://mathhub.info/MitM/Models/densities.mmt#699.16.1:730.16.32</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">N.B.: The band gap of the semiconductor is given by Eg = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:800.-1.5" data-mmt-position="2">E_c</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:800.-1.5" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:800.-1.5" data-mmt-position="3">E_v</mo></mrow></math>.</div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DensityElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2092.58.1:2128.58.37">http://mathhub.info/MitM/Models/densities.mmt#2092.58.1:2128.58.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2131.59.1:2162.59.32">http://mathhub.info/MitM/Models/densities.mmt#2131.59.1:2162.59.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2166.60.1:2199.60.34">http://mathhub.info/MitM/Models/densities.mmt#2166.60.1:2199.60.34</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formula for the electron density for the Boltzmann approximation.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons">density_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/mmt?mmt?unknown">unknown</mo><mspace width=".2em"></mspace><mo>[</mo><mi data-mmt-position="1">y/2</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="2">x/1</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="3">I/0</mi><mo>]</mo><mspace width=".2em"></mspace><mrow data-mmt-position="4"><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2319.64.5:2319.64.5" data-mmt-position="4_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mi data-mmt-position="4_1_1">x/1</mi></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2321.64.7:2321.64.7" data-mmt-position="4_2">y</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2321.64.7:2321.64.7" data-mmt-position="4_2_1"><mi data-mmt-position="4_2_1_1">y/2</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_2_1_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_2_1_2">x</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_2">N_c</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2332.64.18" data-mmt-position="4_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2364.64.50" data-mmt-position="4_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2364.64.50" data-mmt-position="4_3_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mfrac><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2334.64.20:2364.64.50" data-mmt-position="4_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2335.64.21:2353.64.39" data-mmt-position="4_3_3_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2346.64.32" data-mmt-position="4_3_3_2_2_2_2">q</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2346.64.32" data-mmt-position="4_3_3_2_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2346.64.32" data-mmt-position="4_3_3_2_2_2_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="4_1" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2341.64.27:2341.64.27" data-mmt-position="4_3_3_2_2_2_3_2">x</mi><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2340.64.26:2346.64.32" data-mmt-position="4_3_3_2_2_2_3_1">-</mo><mi data-mmt-varref="4_2" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2345.64.31:2345.64.31" data-mmt-position="4_3_3_2_2_2_3_3">y</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2335.64.21:2353.64.39" data-mmt-position="4_3_3_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2335.64.21:2353.64.39" data-mmt-position="4_3_3_2_2_3">E_c</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2334.64.20:2364.64.50" data-mmt-position="4_3_3_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2363.64.49" data-mmt-position="4_3_3_2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2363.64.49" data-mmt-position="4_3_3_2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2363.64.49" data-mmt-position="4_3_3_2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mfrac><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2334.64.20:2364.64.50" data-mmt-position="4_3_3_2_4"><mo class="operator brackets">(</mo><mi data-mmt-position="4_3_3_2_4_1">I/0</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_3_3_2_4_2">x</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_2" data-mmt-position="4_3_3_2_4_3">y</mi><mo class="operator brackets">)</mo></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mo class="operator brackets">)</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>n (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2276.63.1:2366.64.52">http://mathhub.info/MitM/Models/densities.mmt#2276.63.1:2366.64.52</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DensityHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2531.72.1:2567.72.37">http://mathhub.info/MitM/Models/densities.mmt#2531.72.1:2567.72.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2570.73.1:2601.73.32">http://mathhub.info/MitM/Models/densities.mmt#2570.73.1:2601.73.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2605.74.1:2638.74.34">http://mathhub.info/MitM/Models/densities.mmt#2605.74.1:2638.74.34</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formula for the hole density for the Boltzmann approximation.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes">density_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/mmt?mmt?unknown">unknown</mo><mspace width=".2em"></mspace><mo>[</mo><mi data-mmt-position="1">y/2</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="2">x/1</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="3">I/0</mi><mo>]</mo><mspace width=".2em"></mspace><mrow data-mmt-position="4"><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2748.77.5:2748.77.5" data-mmt-position="4_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mi data-mmt-position="4_1_1">x/1</mi></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2750.77.7:2750.77.7" data-mmt-position="4_2">y</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2750.77.7:2750.77.7" data-mmt-position="4_2_1"><mi data-mmt-position="4_2_1_1">y/2</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_2_1_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_2_1_2">x</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2793.77.50" data-mmt-position="4_3_2">N_v</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2793.77.50" data-mmt-position="4_3_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2793.77.50" data-mmt-position="4_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2761.77.18" data-mmt-position="4_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2793.77.50" data-mmt-position="4_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2793.77.50" data-mmt-position="4_3_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mfrac><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2763.77.20:2793.77.50" data-mmt-position="4_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2764.77.21:2782.77.39" data-mmt-position="4_3_3_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2775.77.32" data-mmt-position="4_3_3_2_2_2_2">q</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2775.77.32" data-mmt-position="4_3_3_2_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2775.77.32" data-mmt-position="4_3_3_2_2_2_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="4_2" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2770.77.27:2770.77.27" data-mmt-position="4_3_3_2_2_2_3_2">y</mi><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2769.77.26:2775.77.32" data-mmt-position="4_3_3_2_2_2_3_1">-</mo><mi data-mmt-varref="4_1" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2774.77.31:2774.77.31" data-mmt-position="4_3_3_2_2_2_3_3">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2764.77.21:2782.77.39" data-mmt-position="4_3_3_2_2_1">+</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2764.77.21:2782.77.39" data-mmt-position="4_3_3_2_2_3">E_v</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2763.77.20:2793.77.50" data-mmt-position="4_3_3_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2792.77.49" data-mmt-position="4_3_3_2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2792.77.49" data-mmt-position="4_3_3_2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2792.77.49" data-mmt-position="4_3_3_2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mfrac><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2763.77.20:2793.77.50" data-mmt-position="4_3_3_2_4"><mo class="operator brackets">(</mo><mi data-mmt-position="4_3_3_2_4_1">I/0</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_3_3_2_4_2">x</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_2" data-mmt-position="4_3_3_2_4_3">y</mi><mo class="operator brackets">)</mo></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mo class="operator brackets">)</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>p (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2709.76.1:2795.77.52">http://mathhub.info/MitM/Models/densities.mmt#2709.76.1:2795.77.52</a></td></tr></table></div></div></div></div></body></html>
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diff --git a/export/mh-html/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.html b/export/mh-html/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ElectrostaticPotential</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1766.47.1:1796.47.31">http://mathhub.info/MitM/Models/densities.mmt#1766.47.1:1796.47.31</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Spatial variation of the electrostatic potential,<br/>	   usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-position="">ψ</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential">electrostatic_potential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1884.51.1:1923.51.40">http://mathhub.info/MitM/Models/densities.mmt#1884.51.1:1923.51.40</a></td></tr></table></div></div></div></div></body></html>
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diff --git a/export/mh-html/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.html b/export/mh-html/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">FermiPotentialElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1011.25.1:1041.25.31">http://mathhub.info/MitM/Models/densities.mmt#1011.25.1:1041.25.31</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Spatial variation of the quasi-Fermi potential for the electrons,<br/>	   usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-position="">φ_n</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential">quasi_Fermi_potential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_n (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1147.28.1:1186.28.40">http://mathhub.info/MitM/Models/densities.mmt#1147.28.1:1186.28.40</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">FermiPotentialHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1397.36.1:1427.36.31">http://mathhub.info/MitM/Models/densities.mmt#1397.36.1:1427.36.31</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Spatial variation of the quasi-Fermi potential for the holes,<br/>	   usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-position="">φ_p</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential">quasi_Fermi_potential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_p (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1528.39.1:1567.39.40">http://mathhub.info/MitM/Models/densities.mmt#1528.39.1:1567.39.40</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Bandstructure$Parameters.html">http://mathhub.info/MitM/Models/densities?BandstructureParameters</a></div><div class="submodule"><a href="$Density$Electrons.html">http://mathhub.info/MitM/Models/densities?DensityElectrons</a></div><div class="submodule"><a href="$Density$Holes.html">http://mathhub.info/MitM/Models/densities?DensityHoles</a></div><div class="submodule"><a href="$Electrostatic$Potential.html">http://mathhub.info/MitM/Models/densities?ElectrostaticPotential</a></div><div class="submodule"><a href="$Fermi$Potential$Electrons.html">http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons</a></div><div class="submodule"><a href="$Fermi$Potential$Holes.html">http://mathhub.info/MitM/Models/densities?FermiPotentialHoles</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DeviceGeometry</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#292.8.1:308.8.17">http://mathhub.info/MitM/Models/device.mmt#292.8.1:308.8.17</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop">domain_prop</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#355.10.15:362.10.22" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#355.10.15:362.10.22" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#359.10.19:362.10.22" data-mmt-position="2">bool</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#341.10.1:365.10.25">http://mathhub.info/MitM/Models/device.mmt#341.10.1:365.10.25</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The one-dimensional spatial domain of the device (denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="">Ω</mo></math>).</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain">domain</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type">type</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#506.13.19:521.13.34" data-mmt-position="1">pred</mo><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#511.13.24:521.13.34" data-mmt-position="2">domain_prop</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>Ω (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#488.13.1:530.13.43">http://mathhub.info/MitM/Models/device.mmt#488.13.1:530.13.43</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DeviceOperationState</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1410.49.1:1434.49.25">http://mathhub.info/MitM/Models/device.mmt#1410.49.1:1434.49.25</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">The global temperature of the device denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-position="">T</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur">temperatur</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>T (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1528.52.1:1550.52.23">http://mathhub.info/MitM/Models/device.mmt#1528.52.1:1550.52.23</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The applied voltage at the bottom contact denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom">voltage_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>U_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1618.54.1:1646.54.29">http://mathhub.info/MitM/Models/device.mmt#1618.54.1:1646.54.29</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The applied voltage at the top contact denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top">voltage_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>U_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1711.56.1:1736.56.26">http://mathhub.info/MitM/Models/device.mmt#1711.56.1:1736.56.26</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf">prf</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1780.59.7:1792.59.19" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1780.59.7:1792.59.19" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1792.59.19" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1788.59.15" data-mmt-position="2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1788.59.15" data-mmt-position="2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1788.59.15" data-mmt-position="2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?neq" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1792.59.19" data-mmt-position="2_1">≠</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1792.59.19" data-mmt-position="2_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1774.59.1:1795.59.22">http://mathhub.info/MitM/Models/device.mmt#1774.59.1:1795.59.22</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Device</span></div><div class="document-body"></div></div></div></body></html>
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diff --git a/export/mh-html/content/http..mathhub.info/MitM/Models/device/$Doping$Profile.html b/export/mh-html/content/http..mathhub.info/MitM/Models/device/$Doping$Profile.html
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DopingProfile</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DopingProfile?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1128.39.1:1152.39.25">http://mathhub.info/MitM/Models/device.mmt#1128.39.1:1152.39.25</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DopingProfile?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">The doping profile, denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-position="">C</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile">doping_profile</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>C (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1198.41.1:1229.41.32">http://mathhub.info/MitM/Models/device.mmt#1198.41.1:1229.41.32</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Device$Geometry.html">http://mathhub.info/MitM/Models/device?DeviceGeometry</a></div><div class="submodule"><a href="$Device$Operation$State.html">http://mathhub.info/MitM/Models/device?DeviceOperationState</a></div><div class="submodule"><a href="$Device.html">http://mathhub.info/MitM/Models/device?Device</a></div><div class="submodule"><a href="$Doping$Profile.html">http://mathhub.info/MitM/Models/device?DopingProfile</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Charge</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#628.16.1:658.16.31">http://mathhub.info/MitM/Models/poisson.mmt#628.16.1:658.16.31</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#661.17.1:690.17.30">http://mathhub.info/MitM/Models/poisson.mmt#661.17.1:690.17.30</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#693.18.1:720.18.28">http://mathhub.info/MitM/Models/poisson.mmt#693.18.1:720.18.28</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#723.19.1:758.19.36">http://mathhub.info/MitM/Models/poisson.mmt#723.19.1:758.19.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#761.20.1:803.20.43">http://mathhub.info/MitM/Models/poisson.mmt#761.20.1:803.20.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#806.21.1:847.21.42">http://mathhub.info/MitM/Models/poisson.mmt#806.21.1:847.21.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#850.22.1:881.22.32">http://mathhub.info/MitM/Models/poisson.mmt#850.22.1:881.22.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#884.23.1:922.23.39">http://mathhub.info/MitM/Models/poisson.mmt#884.23.1:922.23.39</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The total charge denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-position="">Q</mo></math> composed of doping profile <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-position="">C</mo></math> and <br/>     electron and hole densities <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-position="">n</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-position="">p</mo></math>, defined by<br/>     <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-position="">Q</mo></math> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-position="">q</mo></math>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-position="">C</mo></math>+<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-position="">p</mo></math> - <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-position="">n</mo></math>).</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge?total_charge">total_charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1123.29.5:1123.29.5" data-mmt-position="1">x</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1123.29.5:1123.29.5" data-mmt-position="1_1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1131.29.13" data-mmt-position="2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1131.29.13" data-mmt-position="2_2_2">q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1140.29.22" data-mmt-position="2_3_2_2_1">C</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1140.29.22" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1139.29.21:1139.29.21" data-mmt-position="2_3_2_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_1">+</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1147.29.29:1151.29.33" data-mmt-position="2_3_2_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1147.29.29:1151.29.33" data-mmt-position="2_3_2_3_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1150.29.32:1150.29.32" data-mmt-position="2_3_2_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1153.29.35:1159.29.41" data-mmt-position="2_3_2_3_3_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1153.29.35:1159.29.41" data-mmt-position="2_3_2_3_3_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1158.29.40:1158.29.40" data-mmt-position="2_3_2_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_1">-</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_1">n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1167.29.49:1171.29.53" data-mmt-position="2_3_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1167.29.49:1171.29.53" data-mmt-position="2_3_3_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1170.29.52:1170.29.52" data-mmt-position="2_3_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1173.29.55:1179.29.61" data-mmt-position="2_3_3_3_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1173.29.55:1179.29.61" data-mmt-position="2_3_3_3_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1178.29.60:1178.29.60" data-mmt-position="2_3_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>Q (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1089.28.1:1183.29.65">http://mathhub.info/MitM/Models/poisson.mmt#1089.28.1:1183.29.65</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Displacement</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1287.35.1:1328.35.42">http://mathhub.info/MitM/Models/poisson.mmt#1287.35.1:1328.35.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1331.36.1:1358.36.28">http://mathhub.info/MitM/Models/poisson.mmt#1331.36.1:1358.36.28</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Expression for electric displacement denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-position="">D</mo></math> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1421.-1.-1:1425.-1.3" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1421.-1.-1:1425.-1.3" data-mmt-position="2">ε_s</mo></mrow></math> d/dx <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-position="">ψ</mo></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement">electric_displacement</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1478.40.5:1478.40.5" data-mmt-position="1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1478.40.5:1478.40.5" data-mmt-position="1_1">Ω</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1494.40.21" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1484.40.11" data-mmt-position="2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1484.40.11" data-mmt-position="2_2_2">ε_s</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1494.40.21" data-mmt-position="2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1494.40.21" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1488.40.15:1494.40.21" data-mmt-position="2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1491.40.18" data-mmt-position="2_3_1_3">ψ</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1491.40.18" data-mmt-position="2_3_1_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1491.40.18" data-mmt-position="2_3_1_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_1_2_0">[</mo><mi data-mmt-position="2_3_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_1_2_0">]</mo><mrow data-mmt-position="2_3_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_1_2_2_0"></mspace><mi data-mmt-varref="2_3_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1488.40.15:1494.40.21" data-mmt-position="2_3_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1493.40.20:1493.40.20" data-mmt-position="2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>D (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1441.39.1:1503.40.30">http://mathhub.info/MitM/Models/poisson.mmt#1441.39.1:1503.40.30</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PoissonBoundaryConditions</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">ThermodynamicEquilibrium</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">?ThermodynamicEquilibrium</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2439.75.1:2473.75.35">http://mathhub.info/MitM/Models/poisson.mmt#2439.75.1:2473.75.35</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/poisson?Charge]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">?Charge</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary value for electrostatic potential at top contact <br/>	     for an applied voltage <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top">potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2609.78.33" data-mmt-position="2">ψ_0_1</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2609.78.33" data-mmt-position="1">+</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2609.78.33" data-mmt-position="3">U_1</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2577.78.1:2620.78.44">http://mathhub.info/MitM/Models/poisson.mmt#2577.78.1:2620.78.44</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary value for electrostatic potential at bottom contact <br/>	     for an applied voltage <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math>.<br/>	     N.B.: the applied bias voltage is U_bias = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2779.-1.5" data-mmt-position="2">U_2</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2779.-1.5" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2779.-1.5" data-mmt-position="3">U_1</mo></mrow></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom">potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36" data-mmt-position="2">ψ_0_2</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36" data-mmt-position="1">+</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36" data-mmt-position="3">U_2</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2785.82.1:2831.82.47">http://mathhub.info/MitM/Models/poisson.mmt#2785.82.1:2831.82.47</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PoissonEquation</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/poisson?Charge]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">?Charge</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1600.46.1:1616.46.17">http://mathhub.info/MitM/Models/poisson.mmt#1600.46.1:1616.46.17</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Displacement">Displacement</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/poisson?Displacement]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement">?Displacement</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1619.47.1:1641.47.23">http://mathhub.info/MitM/Models/poisson.mmt#1619.47.1:1641.47.23</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Defintion of the Poisson equation with total charge <br/>       as right hand side.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonEquation?poisson_equation">poisson_equation</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?poisson_equation" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1752.51.20:1760.51.28" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1752.51.20:1760.51.28" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1756.51.24" data-mmt-position="2_3_3">D</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1756.51.24" data-mmt-position="2_3_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1756.51.24" data-mmt-position="2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">[</mo><mi data-mmt-position="2_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">]</mo><mrow data-mmt-position="2_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="2_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">[</mo><mi data-mmt-position="2_2_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">]</mo><mrow data-mmt-position="2_2_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_2_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_2_1_2_2_0"></mspace><mi data-mmt-varref="2_2_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_2_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_4">Q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1733.51.1:1762.51.30">http://mathhub.info/MitM/Models/poisson.mmt#1733.51.1:1762.51.30</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PoissonParameters</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The relative dielelectric permitivity constant denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-position="">ε_r</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity">relative_dielectric_permitivity</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ε_r (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#323.8.1:368.8.46">http://mathhub.info/MitM/Models/poisson.mmt#323.8.1:368.8.46</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The static dielelectric permitivity constant denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-position="">ε_s</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity">dielectric_permitivity</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="2">ε_r</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="3">ε_0</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ε_s (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#439.10.1:489.10.51">http://mathhub.info/MitM/Models/poisson.mmt#439.10.1:489.10.51</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ThermodynamicEquilibrium</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/poisson?Charge]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">?Charge</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1906.59.1:1922.59.17">http://mathhub.info/MitM/Models/poisson.mmt#1906.59.1:1922.59.17</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">Value of build-in potential ψ_0 at top contact guranteeing <br/>       local charge neutrality.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top">equilibrium_potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_0_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2026.63.1:2067.63.42">http://mathhub.info/MitM/Models/poisson.mmt#2026.63.1:2067.63.42</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Value of build-in potential ψ_0 at bottom contact guranteeing <br/>       local charge neutrality. <br/>       N.B. the build-in potential is given as U_b = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2236.-1.11" data-mmt-position="2">ψ_0_2</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2236.-1.11" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2236.-1.11" data-mmt-position="3">ψ_0_1</mo></mrow></math> (Check!)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom">equilibrium_potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_0_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2257.69.1:2301.69.45">http://mathhub.info/MitM/Models/poisson.mmt#2257.69.1:2301.69.45</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Charge.html">http://mathhub.info/MitM/Models/poisson?Charge</a></div><div class="submodule"><a href="$Displacement.html">http://mathhub.info/MitM/Models/poisson?Displacement</a></div><div class="submodule"><a href="$Poisson$Boundary$Conditions.html">http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions</a></div><div class="submodule"><a href="$Poisson$Equation.html">http://mathhub.info/MitM/Models/poisson?PoissonEquation</a></div><div class="submodule"><a href="$Poisson$Parameters.html">http://mathhub.info/MitM/Models/poisson?PoissonParameters</a></div><div class="submodule"><a href="$Thermodynamic$Equilibrium.html">http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Recombination</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#236.7.2:272.7.38">http://mathhub.info/MitM/Models/recombination.mmt#236.7.2:272.7.38</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#276.8.1:311.8.36">http://mathhub.info/MitM/Models/recombination.mmt#276.8.1:311.8.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#314.9.1:345.9.32">http://mathhub.info/MitM/Models/recombination.mmt#314.9.1:345.9.32</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The kernel of the recombination rate depending <br/>     on electron and hole densities.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient">recombination_coefficient</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>r (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#442.13.1:487.13.46">http://mathhub.info/MitM/Models/recombination.mmt#442.13.1:487.13.46</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Recombination rate for right hand side of continuity equations.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate">recombination_rate</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="3">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="4">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="5">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#608.17.6:609.17.7" data-mmt-position="1">xn</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#608.17.6:609.17.7" data-mmt-position="1_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#612.17.10:613.17.11" data-mmt-position="2">xp</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#612.17.10:613.17.11" data-mmt-position="2_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#616.17.14:619.17.17" data-mmt-position="3">xφ_n</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#616.17.14:619.17.17" data-mmt-position="3_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#622.17.20:625.17.23" data-mmt-position="4">xφ_p</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#622.17.20:625.17.23" data-mmt-position="4_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="5"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:647.17.45" data-mmt-position="5_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:641.17.39" data-mmt-position="5_2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_1">r</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#631.17.29:632.17.30" data-mmt-position="5_2_2_2_2">xn</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_0"></mspace><mi data-mmt-varref="2" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#634.17.32:635.17.33" data-mmt-position="5_2_2_2_3">xp</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:641.17.39" data-mmt-position="5_2_2_1">⋅</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#640.17.38:641.17.39" data-mmt-position="5_2_2_3">xn</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:647.17.45" data-mmt-position="5_2_1">⋅</mo><mi data-mmt-varref="2" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#646.17.44:647.17.45" data-mmt-position="5_2_3">xp</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_3"><mo class="operator brackets">(</mo><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?pos_lit" data-mmt-position="5_3_2">1</mn><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#651.17.49:690.17.88" data-mmt-position="5_3_1">-</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#651.17.49:690.17.88" data-mmt-position="5_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:658.17.56" data-mmt-position="5_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:689.17.87" data-mmt-position="5_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:689.17.87" data-mmt-position="5_3_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mfrac><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_2">q</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="3" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#666.17.64:669.17.67" data-mmt-position="5_3_3_2_2_3_2">xφ_n</mi><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#665.17.63:677.17.75" data-mmt-position="5_3_3_2_2_3_1">-</mo><mi data-mmt-varref="4" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#673.17.71:676.17.74" data-mmt-position="5_3_3_2_2_3_3">xφ_p</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mfrac><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf" data-mmt-position="5_3_3_2_4">prf</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>R (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#562.16.1:701.18.7">http://mathhub.info/MitM/Models/recombination.mmt#562.16.1:701.18.7</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">SpontaneousRecombination</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#816.23.1:839.23.24">http://mathhub.info/MitM/Models/recombination.mmt#816.23.1:839.23.24</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr></table></div><div class="opaque-text inlineBoxSibling">The coefficient for the sponanteous recombination rate is denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-position="">B</mo></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient">spontaneous_recombination_coefficient</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>B (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#923.26.1:971.26.49">http://mathhub.info/MitM/Models/recombination.mmt#923.26.1:971.26.49</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formula for sponanteous recombination <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-position="">r</mo></math>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-position="">n</mo></math>,<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-position="">p</mo></math>) = <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-position="">B</mo></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?axiom_spontaneous">axiom_spontaneous</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?axiom_spontaneous" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1056.28.21:1070.28.35" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1056.28.21:1070.28.35" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_3">r</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_3">ℝ</mo><mo class="operator brackets">)</mo></mrow></mrow></mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_4"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1064.28.29:1064.28.29" data-mmt-position="2_4_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1064.28.29:1064.28.29" data-mmt-position="2_4_1_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1066.28.31:1066.28.31" data-mmt-position="2_4_2">y</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1066.28.31:1066.28.31" data-mmt-position="2_4_2_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_0">]</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_3">B</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#1036.28.1:1089.28.54">http://mathhub.info/MitM/Models/recombination.mmt#1036.28.1:1089.28.54</a></td></tr></table></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div class="namespace"><div class="submodule"><a href="$Recombination.html">http://mathhub.info/MitM/Models/recombination?Recombination</a></div><div class="submodule"><a href="$Spontaneous$Recombination.html">http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination</a></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Models</span></div><div class="document-body"><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc">http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/constants.omdoc">http://mathhub.info/MitM/Models/constants.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/continuity.omdoc">http://mathhub.info/MitM/Models/continuity.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/densities.omdoc">http://mathhub.info/MitM/Models/densities.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/device.omdoc">http://mathhub.info/MitM/Models/device.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/poisson.omdoc">http://mathhub.info/MitM/Models/poisson.omdoc</span></div><div class="document-dref inlineBoxSibling"><span class="name mmturi loadable" data-mmt-load="http://mathhub.info/MitM/Models/recombination.omdoc">http://mathhub.info/MitM/Models/recombination.omdoc</span></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">VanRoosbroeck.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing the stationary van Roosbroeck system <br/>     describung the charge transport of electrons and holes<br/>     in a one-dimensional (layered) semiconductor device. <br/>     The model includes electron and hole <br/>     densities according the Boltzmann approximation and <br/>     spontaneous radiative recombination processes only. <br/>     Furthermore the material properties such as band edges, <br/>     density of states, mobilties are assumed to be<br/>     homogenous (spatially constant). Also a homogenous device<br/>     temperature is assumed.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">VanRoosbroeck</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonEquation">PoissonEquation</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?PoissonEquation]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonEquation">?PoissonEquation</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#702.15.1:734.15.33">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#702.15.1:734.15.33</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions">PoissonBoundaryConditions</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions">?PoissonBoundaryConditions</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#737.16.1:779.16.43">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#737.16.1:779.16.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons">ContinuityEquationElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons">?ContinuityEquationElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#782.17.1:829.17.48">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#782.17.1:829.17.48</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles">ContinuityEquationHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles">?ContinuityEquationHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#832.18.1:875.18.44">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#832.18.1:875.18.44</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons">ContinuityBoundaryConditionsElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons">?ContinuityBoundaryConditionsElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#878.19.1:935.19.58">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#878.19.1:935.19.58</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles">ContinuityBoundaryConditionsHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles">?ContinuityBoundaryConditionsHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#938.20.1:991.20.54">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#938.20.1:991.20.54</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination">SpontaneousRecombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck?[http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination">?SpontaneousRecombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#994.21.1:1041.21.48">http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#994.21.1:1041.21.48</a></td></tr></table></div></div></div></div></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">constants.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing general physical constants</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PhysicalConstants</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The vaccuum dielectric permitivity constant (usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-position="">ε_0</mo></math>)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity">vacuum_dielectric_permitivity</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ε_0 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#326.7.1:369.7.44">http://mathhub.info/MitM/Models/constants.mmt#326.7.1:369.7.44</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The elementary charge (denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-position="">q</mo></math>)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge">elementary_charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>q (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#417.9.1:446.9.30">http://mathhub.info/MitM/Models/constants.mmt#417.9.1:446.9.30</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The Boltzmann constant (usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-position="">k_B</mo></math>)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant">Boltzmann_constant</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>k_B (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#506.11.1:538.11.33">http://mathhub.info/MitM/Models/constants.mmt#506.11.1:538.11.33</a></td></tr></table></div></div></div></div></div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Base</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#574.15.1:601.15.28">http://mathhub.info/MitM/Models/constants.mmt#574.15.1:601.15.28</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma">LFSigma</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?[http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma">?LFSigma</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#604.16.1:631.16.28">http://mathhub.info/MitM/Models/constants.mmt#604.16.1:631.16.28</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?exp">exp</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?exp" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#640.17.7:644.17.11" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#640.17.7:644.17.11" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#640.17.7:644.17.11" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#634.17.1:647.17.14">http://mathhub.info/MitM/Models/constants.mmt#634.17.1:647.17.14</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?der">der</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?der" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#655.18.7:696.18.48" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#656.18.8:656.18.8" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#656.18.8:656.18.8" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#660.18.12:667.18.19" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#660.18.12:667.18.19" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#664.18.16:667.18.19" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#655.18.7:696.18.48" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#655.18.7:696.18.48" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:696.18.48" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:681.18.33" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#671.18.23:676.18.28" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#676.18.28:676.18.28" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:681.18.33" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:681.18.33" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:696.18.48" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#670.18.22:696.18.48" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#685.18.37:696.18.48" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#691.18.43:691.18.43" data-mmt-position="2_2_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#685.18.37:696.18.48" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#685.18.37:696.18.48" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>b ' (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#649.18.1:707.18.59">http://mathhub.info/MitM/Models/constants.mmt#649.18.1:707.18.59</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?Real_vec_space2">Real_vec_space2</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#793.21.19:796.21.22">type</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ℝ2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#775.21.1:816.21.42">http://mathhub.info/MitM/Models/constants.mmt#775.21.1:816.21.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?Real_vec_space3">Real_vec_space3</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#836.22.19:839.22.22">type</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ℝ3 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#818.22.1:863.22.46">http://mathhub.info/MitM/Models/constants.mmt#818.22.1:863.22.46</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?comp1">comp1</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#875.24.9:880.24.14" data-mmt-position="1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#875.24.9:880.24.14" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#875.24.9:880.24.14" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#887.24.21:887.24.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#887.24.21:887.24.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#890.24.24:893.24.27" data-mmt-position="2_0">πl</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#893.24.27:893.24.27" data-mmt-position="2_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#867.24.1:896.24.30">http://mathhub.info/MitM/Models/constants.mmt#867.24.1:896.24.30</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?comp2">comp2</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#906.25.9:911.25.14" data-mmt-position="1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#906.25.9:911.25.14" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#906.25.9:911.25.14" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#918.25.21:918.25.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#918.25.21:918.25.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#921.25.24:929.25.32" data-mmt-position="2_0">πl</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#921.25.24:929.25.32" data-mmt-position="2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#924.25.27:929.25.32" data-mmt-position="2_1_0">πr</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#928.25.31:928.25.31" data-mmt-position="2_1_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#898.25.1:932.25.35">http://mathhub.info/MitM/Models/constants.mmt#898.25.1:932.25.35</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?comp3">comp3</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#942.26.9:947.26.14" data-mmt-position="1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#942.26.9:947.26.14" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#942.26.9:947.26.14" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#954.26.21:954.26.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#954.26.21:954.26.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#957.26.24:965.26.32" data-mmt-position="2_0">πr</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#957.26.24:965.26.32" data-mmt-position="2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#960.26.27:965.26.32" data-mmt-position="2_1_0">πr</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#964.26.31:964.26.31" data-mmt-position="2_1_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#934.26.1:968.26.35">http://mathhub.info/MitM/Models/constants.mmt#934.26.1:968.26.35</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?pred_as_sub2">pred_as_sub2</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#987.28.16:1004.28.33" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#993.28.22:996.28.25" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#987.28.16:1004.28.33" data-mmt-position="0">→</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1001.28.30:1004.28.33" data-mmt-position="2">type</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1011.28.40:1011.28.40" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1011.28.40:1011.28.40" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#993.28.22:996.28.25" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">⟨</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_1">ℝ2</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">|</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52" data-mmt-position="2_2_1">z</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52" data-mmt-position="2_2_1_1">ℝ2</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59" data-mmt-position="2_2_2_1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59" data-mmt-position="2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1028.28.57" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1030.28.59" data-mmt-position="2_2_2_2_0"></mspace><mi data-mmt-varref="2_2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1030.28.59:1030.28.59" data-mmt-position="2_2_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">⟩</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>pred2 a (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#972.28.1:1048.28.77">http://mathhub.info/MitM/Models/constants.mmt#972.28.1:1048.28.77</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?pred_as_sub3">pred_as_sub3</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1065.29.16:1082.29.33" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-position="1_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1071.29.22:1074.29.25" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1065.29.16:1082.29.33" data-mmt-position="0">→</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1079.29.30:1082.29.33" data-mmt-position="2">type</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-position="1_1_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1071.29.22:1074.29.25" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">⟨</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">|</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52" data-mmt-position="2_2_1">z</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52" data-mmt-position="2_2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59" data-mmt-position="2_2_2_1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59" data-mmt-position="2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1106.29.57" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1108.29.59" data-mmt-position="2_2_2_2_0"></mspace><mi data-mmt-varref="2_2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1108.29.59:1108.29.59" data-mmt-position="2_2_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">⟩</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>pred3 a (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1050.29.1:1126.29.77">http://mathhub.info/MitM/Models/constants.mmt#1050.29.1:1126.29.77</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three">lift_type_one_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1155.31.26:1178.31.49" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1160.31.31:1163.31.34" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1155.31.26:1178.31.49" data-mmt-position="0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1155.31.26:1178.31.49" data-mmt-position="2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1168.31.39:1178.31.49" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1168.31.39:1178.31.49" data-mmt-position="2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1174.31.45:1177.31.48" data-mmt-position="2_2">bool</mo><mo class="operator brackets">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1160.31.31:1163.31.34" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9" data-mmt-position="2_1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9" data-mmt-position="2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1195.32.13:1195.32.13" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24" data-mmt-position="2_2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24" data-mmt-position="2_2_2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1198.32.16:1202.32.20" data-mmt-position="2_2_2_2_2_1">comp1</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1197.32.15:1205.32.23" data-mmt-position="2_2_2_2_2_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1204.32.22:1204.32.22" data-mmt-position="2_2_2_2_2_2">v</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_1">∧</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1215.32.33" data-mmt-position="2_2_2_3_3_1">comp2</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1217.32.35" data-mmt-position="2_2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1217.32.35:1217.32.35" data-mmt-position="2_2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_2_3_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_1">∧</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1231.32.49" data-mmt-position="2_2_3_3_1">comp3</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1233.32.51" data-mmt-position="2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1233.32.51:1233.32.51" data-mmt-position="2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_3_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>t1↑ a (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1130.31.1:1252.32.70">http://mathhub.info/MitM/Models/constants.mmt#1130.31.1:1252.32.70</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three">lift_type_two_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1279.33.26:1303.33.50" data-mmt-position="1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1285.33.32:1288.33.35" data-mmt-position="1_2">bool</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1279.33.26:1303.33.50" data-mmt-position="0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1279.33.26:1303.33.50" data-mmt-position="2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1293.33.40:1303.33.50" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1293.33.40:1303.33.50" data-mmt-position="2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1299.33.46:1302.33.49" data-mmt-position="2_2">bool</mo><mo class="operator brackets">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1285.33.32:1288.33.35" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9" data-mmt-position="2_1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9" data-mmt-position="2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1320.34.13:1320.34.13" data-mmt-position="2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35" data-mmt-position="2_2_2_2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">⟨</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1328.34.21" data-mmt-position="2_2_2_2_1_1">comp1</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1330.34.23" data-mmt-position="2_2_2_2_1_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1330.34.23:1330.34.23" data-mmt-position="2_2_2_2_1_2">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">,</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1337.34.30" data-mmt-position="2_2_2_2_2_1">comp2</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1339.34.32" data-mmt-position="2_2_2_2_2_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1339.34.32:1339.34.32" data-mmt-position="2_2_2_2_2_2">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">⟩</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_1">∧</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1351.34.44" data-mmt-position="2_2_3_3_1">comp3</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1353.34.46" data-mmt-position="2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1353.34.46:1353.34.46" data-mmt-position="2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_3_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>t2↑ a (precedence -1)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1254.33.1:1380.34.73">http://mathhub.info/MitM/Models/constants.mmt#1254.33.1:1380.34.73</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_function_one_to_three">lift_function_one_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_function_one_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1414.36.30:1461.36.77" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1415.36.31:1415.36.31" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1415.36.31:1415.36.31" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1419.36.35:1426.36.42" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1419.36.35:1426.36.42" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1423.36.39:1426.36.42" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1414.36.30:1461.36.77" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1414.36.30:1461.36.77" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1461.36.77" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1439.36.55" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1429.36.45:1434.36.50" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1434.36.50:1434.36.50" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1439.36.55" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1439.36.55" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1461.36.77" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1461.36.77" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1443.36.59:1461.36.77" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1444.36.60:1456.36.72" data-mmt-position="2_2_1_1">pred3</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1444.36.60:1456.36.72" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1450.36.66:1456.36.72" data-mmt-position="2_2_1_2_1">t1↑</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1455.36.71:1455.36.71" data-mmt-position="2_2_1_2_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1443.36.59:1461.36.77" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1443.36.59:1461.36.77" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>f1↑ b (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1385.36.1:1510.37.45">http://mathhub.info/MitM/Models/constants.mmt#1385.36.1:1510.37.45</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?Base?lift_function_two_to_three">lift_function_two_to_three</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models?Base?lift_function_two_to_three" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1541.38.30:1590.38.79" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1542.38.31:1542.38.31" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1542.38.31:1542.38.31" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1546.38.35:1554.38.43" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1546.38.35:1554.38.43" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1551.38.40:1554.38.43" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1541.38.30:1590.38.79" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1541.38.30:1590.38.79" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1590.38.79" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1568.38.57" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1557.38.46:1563.38.52" data-mmt-position="2_1_1_1">pred2</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1563.38.52:1563.38.52" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1568.38.57" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1568.38.57" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1590.38.79" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1590.38.79" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1572.38.61:1590.38.79" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1573.38.62:1585.38.74" data-mmt-position="2_2_1_1">pred3</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1573.38.62:1585.38.74" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1579.38.68:1585.38.74" data-mmt-position="2_2_1_2_1">t2↑</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1584.38.73:1584.38.73" data-mmt-position="2_2_1_2_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1572.38.61:1590.38.79" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1572.38.61:1590.38.79" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>f2↑ b (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/constants.mmt#1512.38.1:1650.39.56">http://mathhub.info/MitM/Models/constants.mmt#1512.38.1:1650.39.56</a></td></tr></table></div></div></div></div></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">continuity.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing the mobilitiy parameters of <br/>     the semiconductor.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Mobilities</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The electron mobility parameter usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-position="">μ_n</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons">mobility_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>μ_n (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#287.8.1:319.8.33">http://mathhub.info/MitM/Models/continuity.mmt#287.8.1:319.8.33</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The hole mobility parameter usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-position="">μ_p</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes">mobility_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>μ_p (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#381.10.1:409.10.29">http://mathhub.info/MitM/Models/continuity.mmt#381.10.1:409.10.29</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing the expression for the electron current.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">CurrentElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#531.16.1:573.16.43">http://mathhub.info/MitM/Models/continuity.mmt#531.16.1:573.16.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#576.17.1:617.17.42">http://mathhub.info/MitM/Models/continuity.mmt#576.17.1:617.17.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#620.18.1:655.18.36">http://mathhub.info/MitM/Models/continuity.mmt#620.18.1:655.18.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#658.19.1:678.19.21">http://mathhub.info/MitM/Models/continuity.mmt#658.19.1:678.19.21</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Definition of the electron current in gradient form. <br/>     The driving force of the current are the negative gradients of <br/>     the quasi-Fermi potential, here denoted by j_n.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons">current_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#966.26.21:1021.26.76" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#967.26.22:967.26.22" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#967.26.22:967.26.22" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#974.26.29:977.26.32" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#966.26.21:1021.26.76" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#966.26.21:1021.26.76" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:991.26.46" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#981.26.36:986.26.41" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#986.26.41:986.26.41" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:991.26.46" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:991.26.46" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#995.26.50:1006.26.61" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#996.26.51:1001.26.56" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1001.26.56:1001.26.56" data-mmt-position="2_2_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#995.26.50:1006.26.61" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#995.26.50:1006.26.61" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#980.26.35:1021.26.76" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1010.26.65:1021.26.76" data-mmt-position="2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1011.26.66:1016.26.71" data-mmt-position="2_3_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1016.26.71:1016.26.71" data-mmt-position="2_3_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1010.26.65:1021.26.76" data-mmt-position="2_3_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1010.26.65:1021.26.76" data-mmt-position="2_3_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1030.27.5:1030.27.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1030.27.5:1030.27.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#974.26.29:977.26.32" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">]</mo><mrow data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1033.27.8:1033.27.8" data-mmt-position="2_1">f</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1033.27.8:1033.27.8" data-mmt-position="2_1_1"><mrow data-mmt-position="2_1_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#981.26.36:986.26.41" data-mmt-position="2_1_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#986.26.41:986.26.41" data-mmt-position="2_1_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_1_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1035.27.10:1035.27.10" data-mmt-position="2_2">g</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1035.27.10:1035.27.10" data-mmt-position="2_2_1"><mrow data-mmt-position="2_2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#996.26.51:1001.26.56" data-mmt-position="2_2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1001.26.56:1001.26.56" data-mmt-position="2_2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1037.27.12:1075.27.50" data-mmt-position="2_3_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1038.27.13:1038.27.13" data-mmt-position="2_3_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1038.27.13:1038.27.13" data-mmt-position="2_3_1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_3_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1016.26.71:1016.26.71" data-mmt-position="2_3_1_1_2">P</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1037.27.12:1075.27.50" data-mmt-position="2_3_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1037.27.12:1075.27.50" data-mmt-position="2_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1075.27.50" data-mmt-position="2_3_2_2"><mo class="operator brackets">(</mo><mrow 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data-mmt-position="2_3_2_2_2_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1048.27.23" data-mmt-position="2_3_2_2_2_3">μ_n</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1066.27.41" data-mmt-position="2_3_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1066.27.41" data-mmt-position="2_3_2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1052.27.27:1066.27.41" data-mmt-position="2_3_2_2_3_1">n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" 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data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1075.27.50" data-mmt-position="2_3_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1041.27.16:1075.27.50" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1070.27.45:1075.27.50" data-mmt-position="2_3_2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1071.27.46:1071.27.46" data-mmt-position="2_3_2_3_1_3">g</mi><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1071.27.46:1072.27.47" data-mmt-position="2_3_2_3_1_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1071.27.46:1072.27.47" data-mmt-position="2_3_2_3_1_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">[</mo><mi data-mmt-position="2_3_2_3_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_3_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">]</mo><mrow data-mmt-position="2_3_2_3_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7824.214.54" data-mmt-position="2_3_2_3_1_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_0"></mspace><mi data-mmt-varref="2_3_2_3_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1070.27.45:1075.27.50" data-mmt-position="2_3_2_3_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1074.27.49:1074.27.49" data-mmt-position="2_3_2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>j_n b c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#946.26.1:1089.27.64">http://mathhub.info/MitM/Models/continuity.mmt#946.26.1:1089.27.64</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing the expression for the hole current.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">CurrentHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1201.33.1:1239.33.39">http://mathhub.info/MitM/Models/continuity.mmt#1201.33.1:1239.33.39</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1242.34.1:1283.34.42">http://mathhub.info/MitM/Models/continuity.mmt#1242.34.1:1283.34.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1286.35.1:1317.35.32">http://mathhub.info/MitM/Models/continuity.mmt#1286.35.1:1317.35.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?[http://mathhub.info/MitM/Models/continuity?Mobilities]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">?Mobilities</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1320.36.1:1340.36.21">http://mathhub.info/MitM/Models/continuity.mmt#1320.36.1:1340.36.21</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Defintion of the hole current in gradient form. <br/>     The driving force of the current are the negative gradient of <br/>     the quasi-Fermi potential, here denoted by j_p.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes">current_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1622.43.17:1677.43.72" data-mmt-position="0">{</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1623.43.18:1623.43.18" data-mmt-position="1">P</mi><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1623.43.18:1623.43.18" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1630.43.25:1633.43.28" data-mmt-position="1_1_2">bool</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?Pi" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1622.43.17:1677.43.72" data-mmt-position="0">}</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1622.43.17:1677.43.72" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_1"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1647.43.42" data-mmt-position="2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1637.43.32:1642.43.37" data-mmt-position="2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1642.43.37:1642.43.37" data-mmt-position="2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1647.43.42" data-mmt-position="2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1647.43.42" data-mmt-position="2_1_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1651.43.46:1662.43.57" data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1652.43.47:1657.43.52" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1657.43.52:1657.43.52" data-mmt-position="2_2_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1651.43.46:1662.43.57" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1651.43.46:1662.43.57" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_0">→</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1636.43.31:1677.43.72" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1666.43.61:1677.43.72" data-mmt-position="2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1667.43.62:1672.43.67" data-mmt-position="2_3_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1672.43.67:1672.43.67" data-mmt-position="2_3_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1666.43.61:1677.43.72" data-mmt-position="2_3_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1666.43.61:1677.43.72" data-mmt-position="2_3_2">ℝ</mo><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1686.44.5:1686.44.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1686.44.5:1686.44.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1630.43.25:1633.43.28" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">]</mo><mrow data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1689.44.8:1689.44.8" data-mmt-position="2_1">f</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1689.44.8:1689.44.8" data-mmt-position="2_1_1"><mrow data-mmt-position="2_1_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1637.43.32:1642.43.37" data-mmt-position="2_1_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1642.43.37:1642.43.37" data-mmt-position="2_1_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_1_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1691.44.10:1691.44.10" data-mmt-position="2_2">g</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1691.44.10:1691.44.10" data-mmt-position="2_2_1"><mrow data-mmt-position="2_2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1652.43.47:1657.43.52" data-mmt-position="2_2_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1657.43.52:1657.43.52" data-mmt-position="2_2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1694.44.13:1694.44.13" data-mmt-position="2_3_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1694.44.13:1694.44.13" data-mmt-position="2_3_1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_3_1_1_1">pred</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1672.43.67:1672.43.67" data-mmt-position="2_3_1_1_2">P</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1698.44.17" data-mmt-position="2_3_2_2_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1698.44.17" data-mmt-position="2_3_2_2_2_2_2">q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_3">μ_p</mo><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1712.44.31:1712.44.31" data-mmt-position="2_3_2_2_3_2_1">f</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1711.44.30:1715.44.34" data-mmt-position="2_3_2_2_3_2_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1714.44.33:1714.44.33" data-mmt-position="2_3_2_2_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1718.44.37:1718.44.37" data-mmt-position="2_3_2_2_3_3_1">g</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1717.44.36:1721.44.40" data-mmt-position="2_3_2_2_3_3_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1720.44.39:1720.44.39" data-mmt-position="2_3_2_2_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1726.44.45:1731.44.50" data-mmt-position="2_3_2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="2_2" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1727.44.46:1727.44.46" data-mmt-position="2_3_2_3_1_3">g</mi><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1727.44.46:1728.44.47" data-mmt-position="2_3_2_3_1_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1727.44.46:1728.44.47" data-mmt-position="2_3_2_3_1_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">[</mo><mi data-mmt-position="2_3_2_3_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_3_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_3_1_2_0">]</mo><mrow data-mmt-position="2_3_2_3_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7824.214.54" data-mmt-position="2_3_2_3_1_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_0"></mspace><mi data-mmt-varref="2_3_2_3_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_3_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1726.44.45:1731.44.50" data-mmt-position="2_3_2_3_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1730.44.49:1730.44.49" data-mmt-position="2_3_2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>j_p b c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1606.43.1:1745.44.64">http://mathhub.info/MitM/Models/continuity.mmt#1606.43.1:1745.44.64</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing the continuity equation for the electrons.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityEquationElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">CurrentElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/continuity?CurrentElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">?CurrentElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1879.50.1:1905.50.27">http://mathhub.info/MitM/Models/continuity.mmt#1879.50.1:1905.50.27</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1908.51.1:1939.51.32">http://mathhub.info/MitM/Models/continuity.mmt#1908.51.1:1939.51.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1942.52.1:1980.52.39">http://mathhub.info/MitM/Models/continuity.mmt#1942.52.1:1980.52.39</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#1983.53.1:2019.53.37">http://mathhub.info/MitM/Models/continuity.mmt#1983.53.1:2019.53.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2022.54.1:2063.54.42">http://mathhub.info/MitM/Models/continuity.mmt#2022.54.1:2063.54.42</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formulation of the continuity equation for electrons in divergence form.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation_electrons">continuity_equation_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation_electrons" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2188.59.2:2272.59.86" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2188.59.2:2272.59.86" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2272.59.86" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2202.59.16" data-mmt-position="2_3_3"><mo class="operator brackets">(</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_1">j_n</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">[</mo><mi data-mmt-position="2_3_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">]</mo><mrow data-mmt-position="2_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_3_2_2_0"></mspace><mi data-mmt-varref="2_3_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_3">ψ</mo><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2200.59.14" data-mmt-position="2_3_3_4">φ_n</mo><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2202.59.16" data-mmt-position="2_3_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2202.59.16" data-mmt-position="2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">[</mo><mi data-mmt-position="2_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">]</mo><mrow data-mmt-position="2_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="2_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2272.59.86" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2272.59.86" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">[</mo><mi data-mmt-position="2_2_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">]</mo><mrow data-mmt-position="2_2_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_2_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_2_1_2_2_0"></mspace><mi data-mmt-varref="2_2_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_2_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow></mrow></mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2190.59.4:2272.59.86" data-mmt-position="2_4"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2206.59.20:2272.59.86" data-mmt-position="2_4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2207.59.21:2207.59.21" data-mmt-position="2_4_1">x</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2207.59.21:2207.59.21" data-mmt-position="2_4_1_1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2206.59.20:2272.59.86" data-mmt-position="2_4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2206.59.20:2272.59.86" data-mmt-position="2_4_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2214.59.28:2272.59.86" data-mmt-position="2_4_2_2">q</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2214.59.28:2272.59.86" data-mmt-position="2_4_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2214.59.28:2272.59.86" data-mmt-position="2_4_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2218.59.32:2272.59.86" data-mmt-position="2_4_2_3_1">R</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2218.59.32:2272.59.86" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2218.59.32:2272.59.86" data-mmt-position="2_4_2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2221.59.35:2237.59.51" data-mmt-position="2_4_2_3_2_1">n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2221.59.35:2237.59.51" data-mmt-position="2_4_2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2221.59.35:2237.59.51" data-mmt-position="2_4_2_3_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2224.59.38:2228.59.42" data-mmt-position="2_4_2_3_2_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2224.59.38:2228.59.42" data-mmt-position="2_4_2_3_2_2_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2227.59.41:2227.59.41" data-mmt-position="2_4_2_3_2_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2221.59.35:2237.59.51" data-mmt-position="2_4_2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2221.59.35:2237.59.51" data-mmt-position="2_4_2_3_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2230.59.44:2236.59.50" data-mmt-position="2_4_2_3_2_3_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2230.59.44:2236.59.50" data-mmt-position="2_4_2_3_2_3_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2235.59.49:2235.59.49" data-mmt-position="2_4_2_3_2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2218.59.32:2272.59.86" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2218.59.32:2272.59.86" data-mmt-position="2_4_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2239.59.53:2255.59.69" data-mmt-position="2_4_2_3_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2239.59.53:2255.59.69" data-mmt-position="2_4_2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2239.59.53:2255.59.69" data-mmt-position="2_4_2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2242.59.56:2246.59.60" data-mmt-position="2_4_2_3_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2242.59.56:2246.59.60" data-mmt-position="2_4_2_3_3_2_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2245.59.59:2245.59.59" data-mmt-position="2_4_2_3_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2239.59.53:2255.59.69" data-mmt-position="2_4_2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2239.59.53:2255.59.69" data-mmt-position="2_4_2_3_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2248.59.62:2254.59.68" data-mmt-position="2_4_2_3_3_3_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2248.59.62:2254.59.68" data-mmt-position="2_4_2_3_3_3_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2253.59.67:2253.59.67" data-mmt-position="2_4_2_3_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2218.59.32:2272.59.86" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2218.59.32:2272.59.86" data-mmt-position="2_4_2_3_4"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2257.59.71:2263.59.77" data-mmt-position="2_4_2_3_4_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2257.59.71:2263.59.77" data-mmt-position="2_4_2_3_4_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2262.59.76:2262.59.76" data-mmt-position="2_4_2_3_4_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2218.59.32:2272.59.86" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2218.59.32:2272.59.86" data-mmt-position="2_4_2_3_5"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2265.59.79:2271.59.85" data-mmt-position="2_4_2_3_5_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2265.59.79:2271.59.85" data-mmt-position="2_4_2_3_5_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2270.59.84:2270.59.84" data-mmt-position="2_4_2_3_5_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2153.58.1:2275.59.89">http://mathhub.info/MitM/Models/continuity.mmt#2153.58.1:2275.59.89</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing the continuity equation for the holes.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityEquationHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?CurrentHoles">CurrentHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/continuity?CurrentHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles">?CurrentHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2403.65.1:2425.65.23">http://mathhub.info/MitM/Models/continuity.mmt#2403.65.1:2425.65.23</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2428.66.1:2463.66.36">http://mathhub.info/MitM/Models/continuity.mmt#2428.66.1:2463.66.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2466.67.1:2508.67.43">http://mathhub.info/MitM/Models/continuity.mmt#2466.67.1:2508.67.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2511.68.1:2547.68.37">http://mathhub.info/MitM/Models/continuity.mmt#2511.68.1:2547.68.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2550.69.1:2591.69.42">http://mathhub.info/MitM/Models/continuity.mmt#2550.69.1:2591.69.42</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formulation of the continuity equation for holes in divergence form.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes">continuity_equation_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2703.74.2:2788.74.87" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2703.74.2:2788.74.87" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2717.74.16" data-mmt-position="2_3_3"><mo class="operator brackets">(</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_1">j_p</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">[</mo><mi data-mmt-position="2_3_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_3_2_0">]</mo><mrow data-mmt-position="2_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_3_2_2_0"></mspace><mi data-mmt-varref="2_3_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_3">ψ</mo><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2715.74.14" data-mmt-position="2_3_3_4">φ_p</mo><mo class="operator brackets">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2717.74.16" data-mmt-position="2_3_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2717.74.16" data-mmt-position="2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">[</mo><mi data-mmt-position="2_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">]</mo><mrow data-mmt-position="2_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="2_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">[</mo><mi data-mmt-position="2_2_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">]</mo><mrow data-mmt-position="2_2_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_2_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_2_1_2_2_0"></mspace><mi data-mmt-varref="2_2_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_2_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow></mrow></mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2705.74.4:2788.74.87" data-mmt-position="2_4"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2721.74.20:2788.74.87" data-mmt-position="2_4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2722.74.21:2722.74.21" data-mmt-position="2_4_1">x</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2722.74.21:2722.74.21" data-mmt-position="2_4_1_1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2721.74.20:2788.74.87" data-mmt-position="2_4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2721.74.20:2788.74.87" data-mmt-position="2_4_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2788.74.87" data-mmt-position="2_4_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2730.74.29" data-mmt-position="2_4_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2730.74.29" data-mmt-position="2_4_2_2_2">q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2788.74.87" data-mmt-position="2_4_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2729.74.28:2788.74.87" data-mmt-position="2_4_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_1">R</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_1">n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2740.74.39:2744.74.43" data-mmt-position="2_4_2_3_2_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2740.74.39:2744.74.43" data-mmt-position="2_4_2_3_2_2_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2743.74.42:2743.74.42" data-mmt-position="2_4_2_3_2_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52" data-mmt-position="2_4_2_3_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2746.74.45:2752.74.51" data-mmt-position="2_4_2_3_2_3_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2746.74.45:2752.74.51" data-mmt-position="2_4_2_3_2_3_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2751.74.50:2751.74.50" data-mmt-position="2_4_2_3_2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2758.74.57:2762.74.61" data-mmt-position="2_4_2_3_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2758.74.57:2762.74.61" data-mmt-position="2_4_2_3_3_2_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2761.74.60:2761.74.60" data-mmt-position="2_4_2_3_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2755.74.54:2771.74.70" data-mmt-position="2_4_2_3_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2764.74.63:2770.74.69" data-mmt-position="2_4_2_3_3_3_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2764.74.63:2770.74.69" data-mmt-position="2_4_2_3_3_3_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2769.74.68:2769.74.68" data-mmt-position="2_4_2_3_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_4"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2773.74.72:2779.74.78" data-mmt-position="2_4_2_3_4_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2773.74.72:2779.74.78" data-mmt-position="2_4_2_3_4_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2778.74.77:2778.74.77" data-mmt-position="2_4_2_3_4_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2734.74.33:2788.74.87" data-mmt-position="2_4_2_3_5"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2781.74.80:2787.74.86" data-mmt-position="2_4_2_3_5_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2781.74.80:2787.74.86" data-mmt-position="2_4_2_3_5_0"></mspace><mi data-mmt-varref="2_4_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#2786.74.85:2786.74.85" data-mmt-position="2_4_2_3_5_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2672.73.1:2791.74.90">http://mathhub.info/MitM/Models/continuity.mmt#2672.73.1:2791.74.90</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing the boundary conditions for the<br/>     electron continuity equation modeling Ohmic contacts.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityBoundaryConditionsElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#2985.81.1:3021.81.37">http://mathhub.info/MitM/Models/continuity.mmt#2985.81.1:3021.81.37</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the top contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top">potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_n_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3071.83.1:3108.83.38">http://mathhub.info/MitM/Models/continuity.mmt#3071.83.1:3108.83.38</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the bottom contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom">potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_n_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3160.85.1:3200.85.41">http://mathhub.info/MitM/Models/continuity.mmt#3160.85.1:3200.85.41</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing the boundary conditions for the<br/>     holes continuity equation modeling Ohmic contacts.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ContinuityBoundaryConditionsHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3386.92.1:3422.92.37">http://mathhub.info/MitM/Models/continuity.mmt#3386.92.1:3422.92.37</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the top contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top">potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_p_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3471.94.1:3508.94.38">http://mathhub.info/MitM/Models/continuity.mmt#3471.94.1:3508.94.38</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary condition for the bottom contact.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom">potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom" data-mmt-component="definition" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_p_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/continuity.mmt#3559.96.1:3599.96.41">http://mathhub.info/MitM/Models/continuity.mmt#3559.96.1:3599.96.41</a></td></tr></table></div></div></div></div></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">densities.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing the bandstructure parameters of <br/>     the semiconductor.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">BandstructureParameters</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The effective density of states for the conduction bands <br/>     usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-position="">N_c</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands">effective_density_of_states_conduction_bands</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>N_c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#340.9.1:398.9.59">http://mathhub.info/MitM/Models/densities.mmt#340.9.1:398.9.59</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The effective density of states for the valence bands <br/>     usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-position="">N_v</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands">effective_density_of_states_valence_bands</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>N_v (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#493.12.1:548.12.56">http://mathhub.info/MitM/Models/densities.mmt#493.12.1:548.12.56</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The conduction band edge usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-position="">E_c</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge">conduction_band_edge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>E_c (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#608.14.1:642.14.35">http://mathhub.info/MitM/Models/densities.mmt#608.14.1:642.14.35</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The valence band edge usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-position="">E_v</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge">valence_band_edge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>E_v (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#699.16.1:730.16.32">http://mathhub.info/MitM/Models/densities.mmt#699.16.1:730.16.32</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">N.B.: The band gap of the semiconductor is given by Eg = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:800.-1.5" data-mmt-position="2">E_c</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:800.-1.5" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:800.-1.5" data-mmt-position="3">E_v</mo></mrow></math>.</div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing spatial variation of the <br/>     quasi-Fermi potential for the electrons. <br/>     This is a basic variable of the system</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">FermiPotentialElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1011.25.1:1041.25.31">http://mathhub.info/MitM/Models/densities.mmt#1011.25.1:1041.25.31</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Spatial variation of the quasi-Fermi potential for the electrons,<br/>	   usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-position="">φ_n</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential">quasi_Fermi_potential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_n (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1147.28.1:1186.28.40">http://mathhub.info/MitM/Models/densities.mmt#1147.28.1:1186.28.40</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing spatial variation of the <br/>     quasi-Fermi potential for the holes. <br/>     This is a basic variable (unknown) of the system.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">FermiPotentialHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1397.36.1:1427.36.31">http://mathhub.info/MitM/Models/densities.mmt#1397.36.1:1427.36.31</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Spatial variation of the quasi-Fermi potential for the holes,<br/>	   usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-position="">φ_p</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential">quasi_Fermi_potential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>φ_p (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1528.39.1:1567.39.40">http://mathhub.info/MitM/Models/densities.mmt#1528.39.1:1567.39.40</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing spatial variation of the <br/>     electrostatic potential. <br/>     This is a basic variable (unknown) of the system.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ElectrostaticPotential</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1766.47.1:1796.47.31">http://mathhub.info/MitM/Models/densities.mmt#1766.47.1:1796.47.31</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Spatial variation of the electrostatic potential,<br/>	   usually denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-position="">ψ</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential">electrostatic_potential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#1884.51.1:1923.51.40">http://mathhub.info/MitM/Models/densities.mmt#1884.51.1:1923.51.40</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing state equation for the <br/>	   electron density for the Boltzmann approximation (exp).</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DensityElectrons</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2092.58.1:2128.58.37">http://mathhub.info/MitM/Models/densities.mmt#2092.58.1:2128.58.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2131.59.1:2162.59.32">http://mathhub.info/MitM/Models/densities.mmt#2131.59.1:2162.59.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2166.60.1:2199.60.34">http://mathhub.info/MitM/Models/densities.mmt#2166.60.1:2199.60.34</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formula for the electron density for the Boltzmann approximation.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons">density_electrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2296.63.21:2304.63.29" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/mmt?mmt?unknown">unknown</mo><mspace width=".2em"></mspace><mo>[</mo><mi data-mmt-position="1">y/2</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="2">x/1</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="3">I/0</mi><mo>]</mo><mspace width=".2em"></mspace><mrow data-mmt-position="4"><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2319.64.5:2319.64.5" data-mmt-position="4_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mi data-mmt-position="4_1_1">x/1</mi></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2321.64.7:2321.64.7" data-mmt-position="4_2">y</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2321.64.7:2321.64.7" data-mmt-position="4_2_1"><mi data-mmt-position="4_2_1_1">y/2</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_2_1_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_2_1_2">x</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_2">N_c</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2332.64.18" data-mmt-position="4_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2364.64.50" data-mmt-position="4_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2364.64.50" data-mmt-position="4_3_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mfrac><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2334.64.20:2364.64.50" data-mmt-position="4_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2335.64.21:2353.64.39" data-mmt-position="4_3_3_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2346.64.32" data-mmt-position="4_3_3_2_2_2_2">q</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2346.64.32" data-mmt-position="4_3_3_2_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2336.64.22:2346.64.32" data-mmt-position="4_3_3_2_2_2_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="4_1" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2341.64.27:2341.64.27" data-mmt-position="4_3_3_2_2_2_3_2">x</mi><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2340.64.26:2346.64.32" data-mmt-position="4_3_3_2_2_2_3_1">-</mo><mi data-mmt-varref="4_2" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2345.64.31:2345.64.31" data-mmt-position="4_3_3_2_2_2_3_3">y</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2335.64.21:2353.64.39" data-mmt-position="4_3_3_2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2335.64.21:2353.64.39" data-mmt-position="4_3_3_2_2_3">E_c</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2334.64.20:2364.64.50" data-mmt-position="4_3_3_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2363.64.49" data-mmt-position="4_3_3_2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2363.64.49" data-mmt-position="4_3_3_2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2357.64.43:2363.64.49" data-mmt-position="4_3_3_2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mfrac><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2334.64.20:2364.64.50" data-mmt-position="4_3_3_2_4"><mo class="operator brackets">(</mo><mi data-mmt-position="4_3_3_2_4_1">I/0</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_3_3_2_4_2">x</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_2" data-mmt-position="4_3_3_2_4_3">y</mi><mo class="operator brackets">)</mo></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mo class="operator brackets">)</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>n (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2276.63.1:2366.64.52">http://mathhub.info/MitM/Models/densities.mmt#2276.63.1:2366.64.52</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing state equation for the <br/>	   hole density for the Boltzmann approximation (exp).</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DensityHoles</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2531.72.1:2567.72.37">http://mathhub.info/MitM/Models/densities.mmt#2531.72.1:2567.72.37</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models?PhysicalConstants]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">?PhysicalConstants</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2570.73.1:2601.73.32">http://mathhub.info/MitM/Models/densities.mmt#2570.73.1:2601.73.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">?BandstructureParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2605.74.1:2638.74.34">http://mathhub.info/MitM/Models/densities.mmt#2605.74.1:2638.74.34</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formula for the hole density for the Boltzmann approximation.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes">density_holes</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2725.76.17:2733.76.25" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/mmt?mmt?unknown">unknown</mo><mspace width=".2em"></mspace><mo>[</mo><mi data-mmt-position="1">y/2</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="2">x/1</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="3">I/0</mi><mo>]</mo><mspace width=".2em"></mspace><mrow data-mmt-position="4"><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2748.77.5:2748.77.5" data-mmt-position="4_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mi data-mmt-position="4_1_1">x/1</mi></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2750.77.7:2750.77.7" data-mmt-position="4_2">y</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2750.77.7:2750.77.7" data-mmt-position="4_2_1"><mi data-mmt-position="4_2_1_1">y/2</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_2_1_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_2_1_2">x</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2747.77.4:2793.77.50" data-mmt-position="4_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2793.77.50" data-mmt-position="4_3_2">N_v</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2793.77.50" data-mmt-position="4_3_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2753.77.10:2793.77.50" data-mmt-position="4_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2761.77.18" data-mmt-position="4_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2793.77.50" data-mmt-position="4_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2759.77.16:2793.77.50" data-mmt-position="4_3_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mfrac><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2763.77.20:2793.77.50" data-mmt-position="4_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2764.77.21:2782.77.39" data-mmt-position="4_3_3_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2775.77.32" data-mmt-position="4_3_3_2_2_2_2">q</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2775.77.32" data-mmt-position="4_3_3_2_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2765.77.22:2775.77.32" data-mmt-position="4_3_3_2_2_2_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="4_2" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2770.77.27:2770.77.27" data-mmt-position="4_3_3_2_2_2_3_2">y</mi><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2769.77.26:2775.77.32" data-mmt-position="4_3_3_2_2_2_3_1">-</mo><mi data-mmt-varref="4_1" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2774.77.31:2774.77.31" data-mmt-position="4_3_3_2_2_2_3_3">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2764.77.21:2782.77.39" data-mmt-position="4_3_3_2_2_1">+</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2764.77.21:2782.77.39" data-mmt-position="4_3_3_2_2_3">E_v</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2763.77.20:2793.77.50" data-mmt-position="4_3_3_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2792.77.49" data-mmt-position="4_3_3_2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2792.77.49" data-mmt-position="4_3_3_2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2786.77.43:2792.77.49" data-mmt-position="4_3_3_2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mfrac><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2763.77.20:2793.77.50" data-mmt-position="4_3_3_2_4"><mo class="operator brackets">(</mo><mi data-mmt-position="4_3_3_2_4_1">I/0</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_3_3_2_4_2">x</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_3_3_2_4_0"></mspace><mi data-mmt-varref="4_2" data-mmt-position="4_3_3_2_4_3">y</mi><mo class="operator brackets">)</mo></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mo class="operator brackets">)</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>p (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/densities.mmt#2709.76.1:2795.77.52">http://mathhub.info/MitM/Models/densities.mmt#2709.76.1:2795.77.52</a></td></tr></table></div></div></div></div></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">device.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This theory intentionally left empty. It has a narrative in sTeX</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Device</span></div><div class="document-body"></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing description of device geometry.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DeviceGeometry</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?Device">Device</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?[http://mathhub.info/MitM/Models/device?Device]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">?Device</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#292.8.1:308.8.17">http://mathhub.info/MitM/Models/device.mmt#292.8.1:308.8.17</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop">domain_prop</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#355.10.15:362.10.22" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#355.10.15:362.10.22" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#359.10.19:362.10.22" data-mmt-position="2">bool</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#341.10.1:365.10.25">http://mathhub.info/MitM/Models/device.mmt#341.10.1:365.10.25</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The one-dimensional spatial domain of the device (denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="">Ω</mo></math>).</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain">domain</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?Typed?type">type</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#506.13.19:521.13.34" data-mmt-position="1">pred</mo><mspace width=".2em"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#511.13.24:521.13.34" data-mmt-position="2">domain_prop</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>Ω (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#488.13.1:530.13.43">http://mathhub.info/MitM/Models/device.mmt#488.13.1:530.13.43</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing description of the doping profile.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DopingProfile</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DopingProfile?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1128.39.1:1152.39.25">http://mathhub.info/MitM/Models/device.mmt#1128.39.1:1152.39.25</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The doping profile, denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-position="">C</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile">doping_profile</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>C (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1198.41.1:1229.41.32">http://mathhub.info/MitM/Models/device.mmt#1198.41.1:1229.41.32</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing a description the the operating state,<br/>     that means applied voltages and device temperature.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">DeviceOperationState</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1410.49.1:1434.49.25">http://mathhub.info/MitM/Models/device.mmt#1410.49.1:1434.49.25</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The global temperature of the device denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-position="">T</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur">temperatur</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>T (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1528.52.1:1550.52.23">http://mathhub.info/MitM/Models/device.mmt#1528.52.1:1550.52.23</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The applied voltage at the bottom contact denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom">voltage_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>U_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1618.54.1:1646.54.29">http://mathhub.info/MitM/Models/device.mmt#1618.54.1:1646.54.29</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The applied voltage at the top contact denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top">voltage_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>U_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1711.56.1:1736.56.26">http://mathhub.info/MitM/Models/device.mmt#1711.56.1:1736.56.26</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf">prf</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1780.59.7:1792.59.19" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1780.59.7:1792.59.19" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1792.59.19" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1788.59.15" data-mmt-position="2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1788.59.15" data-mmt-position="2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1788.59.15" data-mmt-position="2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?neq" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1792.59.19" data-mmt-position="2_1">≠</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1792.59.19" data-mmt-position="2_2">ℝ</mo></mrow></mrow><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_4">0</mn><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/device.mmt#1774.59.1:1795.59.22">http://mathhub.info/MitM/Models/device.mmt#1774.59.1:1795.59.22</a></td></tr></table></div></div></div></div></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">poisson.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing the static dielectric permitivity constant<br/>     of the semiconductor.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PoissonParameters</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">The relative dielelectric permitivity constant denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-position="">ε_r</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity">relative_dielectric_permitivity</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ε_r (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#323.8.1:368.8.46">http://mathhub.info/MitM/Models/poisson.mmt#323.8.1:368.8.46</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The static dielelectric permitivity constant denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-position="">ε_s</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity">dielectric_permitivity</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="2">ε_r</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="3">ε_0</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ε_s (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#439.10.1:489.10.51">http://mathhub.info/MitM/Models/poisson.mmt#439.10.1:489.10.51</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing the total charge entering <br/>     the right side of Poisson's equation.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Charge</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/device?DeviceGeometry]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">?DeviceGeometry</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#628.16.1:658.16.31">http://mathhub.info/MitM/Models/poisson.mmt#628.16.1:658.16.31</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/device?DopingProfile]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">?DopingProfile</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#661.17.1:690.17.30">http://mathhub.info/MitM/Models/poisson.mmt#661.17.1:690.17.30</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#693.18.1:720.18.28">http://mathhub.info/MitM/Models/poisson.mmt#693.18.1:720.18.28</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#723.19.1:758.19.36">http://mathhub.info/MitM/Models/poisson.mmt#723.19.1:758.19.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">?FermiPotentialElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#761.20.1:803.20.43">http://mathhub.info/MitM/Models/poisson.mmt#761.20.1:803.20.43</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#806.21.1:847.21.42">http://mathhub.info/MitM/Models/poisson.mmt#806.21.1:847.21.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#850.22.1:881.22.32">http://mathhub.info/MitM/Models/poisson.mmt#850.22.1:881.22.32</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">?FermiPotentialHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#884.23.1:922.23.39">http://mathhub.info/MitM/Models/poisson.mmt#884.23.1:922.23.39</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The total charge denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-position="">Q</mo></math> composed of doping profile <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-position="">C</mo></math> and <br/>     electron and hole densities <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-position="">n</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-position="">p</mo></math>, defined by<br/>     <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-position="">Q</mo></math> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-position="">q</mo></math>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-position="">C</mo></math>+<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-position="">p</mo></math> - <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-position="">n</mo></math>).</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge?total_charge">total_charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1123.29.5:1123.29.5" data-mmt-position="1">x</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1123.29.5:1123.29.5" data-mmt-position="1_1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1131.29.13" data-mmt-position="2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1131.29.13" data-mmt-position="2_2_2">q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1140.29.22" data-mmt-position="2_3_2_2_1">C</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1140.29.22" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1139.29.21:1139.29.21" data-mmt-position="2_3_2_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_1">+</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1147.29.29:1151.29.33" data-mmt-position="2_3_2_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1147.29.29:1151.29.33" data-mmt-position="2_3_2_3_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1150.29.32:1150.29.32" data-mmt-position="2_3_2_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1153.29.35:1159.29.41" data-mmt-position="2_3_2_3_3_1">φ_p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1153.29.35:1159.29.41" data-mmt-position="2_3_2_3_3_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1158.29.40:1158.29.40" data-mmt-position="2_3_2_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_1">-</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_1">n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1167.29.49:1171.29.53" data-mmt-position="2_3_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1167.29.49:1171.29.53" data-mmt-position="2_3_3_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1170.29.52:1170.29.52" data-mmt-position="2_3_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1164.29.46:1180.29.62" data-mmt-position="2_3_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1173.29.55:1179.29.61" data-mmt-position="2_3_3_3_1">φ_n</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1173.29.55:1179.29.61" data-mmt-position="2_3_3_3_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1178.29.60:1178.29.60" data-mmt-position="2_3_3_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>Q (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1089.28.1:1183.29.65">http://mathhub.info/MitM/Models/poisson.mmt#1089.28.1:1183.29.65</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing the electric displacement.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Displacement</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">?ElectrostaticPotential</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1287.35.1:1328.35.42">http://mathhub.info/MitM/Models/poisson.mmt#1287.35.1:1328.35.42</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">?PoissonParameters</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1331.36.1:1358.36.28">http://mathhub.info/MitM/Models/poisson.mmt#1331.36.1:1358.36.28</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Expression for electric displacement denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-position="">D</mo></math> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1421.-1.-1:1425.-1.3" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1421.-1.-1:1425.-1.3" data-mmt-position="2">ε_s</mo></mrow></math> d/dx <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-position="">ψ</mo></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement">electric_displacement</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1478.40.5:1478.40.5" data-mmt-position="1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1478.40.5:1478.40.5" data-mmt-position="1_1">Ω</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1494.40.21" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1484.40.11" data-mmt-position="2_2_1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1484.40.11" data-mmt-position="2_2_2">ε_s</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1494.40.21" data-mmt-position="2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1481.40.8:1494.40.21" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1488.40.15:1494.40.21" data-mmt-position="2_3_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1491.40.18" data-mmt-position="2_3_1_3">ψ</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1491.40.18" data-mmt-position="2_3_1_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1489.40.16:1491.40.18" data-mmt-position="2_3_1_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_1_2_0">[</mo><mi data-mmt-position="2_3_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_1_2_0">]</mo><mrow data-mmt-position="2_3_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_1_2_2_0"></mspace><mi data-mmt-varref="2_3_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1488.40.15:1494.40.21" data-mmt-position="2_3_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1493.40.20:1493.40.20" data-mmt-position="2_3_2">x</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>D (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1441.39.1:1503.40.30">http://mathhub.info/MitM/Models/poisson.mmt#1441.39.1:1503.40.30</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing Poissons equation.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PoissonEquation</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/poisson?Charge]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">?Charge</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1600.46.1:1616.46.17">http://mathhub.info/MitM/Models/poisson.mmt#1600.46.1:1616.46.17</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Displacement">Displacement</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?[http://mathhub.info/MitM/Models/poisson?Displacement]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement">?Displacement</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1619.47.1:1641.47.23">http://mathhub.info/MitM/Models/poisson.mmt#1619.47.1:1641.47.23</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Defintion of the Poisson equation with total charge <br/>       as right hand side.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonEquation?poisson_equation">poisson_equation</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonEquation?poisson_equation" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1752.51.20:1760.51.28" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1752.51.20:1760.51.28" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1756.51.24" data-mmt-position="2_3_3">D</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1756.51.24" data-mmt-position="2_3_1">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1756.51.24" data-mmt-position="2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">[</mo><mi data-mmt-position="2_3_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_3_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_3_2_0">]</mo><mrow data-mmt-position="2_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_3_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="2_3_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_3_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mrow data-mmt-position="2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_1">pred</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43" data-mmt-position="2_2_1_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">[</mo><mi data-mmt-position="2_2_1_2_1">z</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="2_2_1_2_0">]</mo><mrow data-mmt-position="2_2_1_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-position="2_2_1_2_2_1">domain_prop</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56" data-mmt-position="2_2_1_2_2_0"></mspace><mi data-mmt-varref="2_2_1_2_1" data-mmt-source="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56" data-mmt-position="2_2_1_2_2_2">z</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_2">ℝ</mo><mo class="operator brackets">)</mo></mrow></mrow></mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28" data-mmt-position="2_4">Q</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1733.51.1:1762.51.30">http://mathhub.info/MitM/Models/poisson.mmt#1733.51.1:1762.51.30</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing build-in potential in <br/>     thermodynamic equilibrium.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">ThermodynamicEquilibrium</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?[http://mathhub.info/MitM/Models/poisson?Charge]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">?Charge</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#1906.59.1:1922.59.17">http://mathhub.info/MitM/Models/poisson.mmt#1906.59.1:1922.59.17</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Value of build-in potential ψ_0 at top contact guranteeing <br/>       local charge neutrality.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top">equilibrium_potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_0_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2026.63.1:2067.63.42">http://mathhub.info/MitM/Models/poisson.mmt#2026.63.1:2067.63.42</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Value of build-in potential ψ_0 at bottom contact guranteeing <br/>       local charge neutrality. <br/>       N.B. the build-in potential is given as U_b = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2236.-1.11" data-mmt-position="2">ψ_0_2</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2236.-1.11" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2236.-1.11" data-mmt-position="3">ψ_0_1</mo></mrow></math> (Check!)</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom">equilibrium_potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_0_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2257.69.1:2301.69.45">http://mathhub.info/MitM/Models/poisson.mmt#2257.69.1:2301.69.45</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">This is a theory containing the boundary values for the Poisson eqauation.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">PoissonBoundaryConditions</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">ThermodynamicEquilibrium</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?[http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">?ThermodynamicEquilibrium</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2439.75.1:2473.75.35">http://mathhub.info/MitM/Models/poisson.mmt#2439.75.1:2473.75.35</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary value for electrostatic potential at top contact <br/>	     for an applied voltage <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math>.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top">potential_top</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2609.78.33" data-mmt-position="2">ψ_0_1</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2609.78.33" data-mmt-position="1">+</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2609.78.33" data-mmt-position="3">U_1</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_1 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2577.78.1:2620.78.44">http://mathhub.info/MitM/Models/poisson.mmt#2577.78.1:2620.78.44</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Boundary value for electrostatic potential at bottom contact <br/>	     for an applied voltage <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math>.<br/>	     N.B.: the applied bias voltage is U_bias = <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2779.-1.5" data-mmt-position="2">U_2</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2779.-1.5" data-mmt-position="1">-</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2779.-1.5" data-mmt-position="3">U_1</mo></mrow></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom">potential_bottom</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36" data-mmt-position="2">ψ_0_2</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36" data-mmt-position="1">+</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36" data-mmt-position="3">U_2</mo></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>ψ_2 (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/poisson.mmt#2785.82.1:2831.82.47">http://mathhub.info/MitM/Models/poisson.mmt#2785.82.1:2831.82.47</a></td></tr></table></div></div></div></div></div></div></div></div></body></html>
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-<html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/mmt.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/JOBAD.css"></link><link rel="stylesheet" type="text/css" href="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/css/jquery/jquery-ui.css"></link><link rel="stylesheet" type="text/css" href="../../../../../html.css"></link><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jquery/jquery-ui.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/mmt-js-api.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/mmt/browser.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/deps/underscore-min.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/JOBAD.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/hovering.js"></script><script type="text/javascript" src="https://svn.kwarc.info/repos/MMT/src/mmt-api/trunk/resources/mmt-web/script/jobad/modules/interactive-viewing.js"></script><script type="text/javascript" src="../../../../../html.js"></script></head><body><div><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">recombination.omdoc</span></div><div class="document-body"><div class="opaque-text inlineBoxSibling">This is a theory containing the general structure for <br/>     a recombination rate.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">Recombination</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/device?DeviceOperationState]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">?DeviceOperationState</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#236.7.2:272.7.38">http://mathhub.info/MitM/Models/recombination.mmt#236.7.2:272.7.38</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/densities?DensityElectrons]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">?DensityElectrons</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#276.8.1:311.8.36">http://mathhub.info/MitM/Models/recombination.mmt#276.8.1:311.8.36</a></td></tr></table></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?[http://mathhub.info/MitM/Models/densities?DensityHoles]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">?DensityHoles</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#314.9.1:345.9.32">http://mathhub.info/MitM/Models/recombination.mmt#314.9.1:345.9.32</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The kernel of the recombination rate depending <br/>     on electron and hole densities.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient">recombination_coefficient</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="3">ℝ</mo></mrow></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>r (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#442.13.1:487.13.46">http://mathhub.info/MitM/Models/recombination.mmt#442.13.1:487.13.46</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Recombination rate for right hand side of continuity equations.</div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate">recombination_rate</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-definition">definition</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="3">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="4">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#583.16.22:599.16.38" data-mmt-position="5">ℝ</mo></mrow></math></td></tr><tr class="component-definition"><td><span class="constant-component-label">definition</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-component="definition" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#608.17.6:609.17.7" data-mmt-position="1">xn</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#608.17.6:609.17.7" data-mmt-position="1_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#612.17.10:613.17.11" data-mmt-position="2">xp</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#612.17.10:613.17.11" data-mmt-position="2_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#616.17.14:619.17.17" data-mmt-position="3">xφ_n</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#616.17.14:619.17.17" data-mmt-position="3_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#622.17.20:625.17.23" data-mmt-position="4">xφ_p</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#622.17.20:625.17.23" data-mmt-position="4_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="5"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:647.17.45" data-mmt-position="5_2_2"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:641.17.39" data-mmt-position="5_2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_1">r</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#631.17.29:632.17.30" data-mmt-position="5_2_2_2_2">xn</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_0"></mspace><mi data-mmt-varref="2" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#634.17.32:635.17.33" data-mmt-position="5_2_2_2_3">xp</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:641.17.39" data-mmt-position="5_2_2_1">⋅</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#640.17.38:641.17.39" data-mmt-position="5_2_2_3">xn</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:647.17.45" data-mmt-position="5_2_1">⋅</mo><mi data-mmt-varref="2" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#646.17.44:647.17.45" data-mmt-position="5_2_3">xp</mi><mo class="operator brackets">)</mo></mrow><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_3"><mo class="operator brackets">(</mo><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?pos_lit" data-mmt-position="5_3_2">1</mn><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#651.17.49:690.17.88" data-mmt-position="5_3_1">-</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#651.17.49:690.17.88" data-mmt-position="5_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:658.17.56" data-mmt-position="5_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:689.17.87" data-mmt-position="5_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:689.17.87" data-mmt-position="5_3_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mfrac><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_2">q</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_1">⋅</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_3"><mo class="operator brackets">(</mo><mi data-mmt-varref="3" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#666.17.64:669.17.67" data-mmt-position="5_3_3_2_2_3_2">xφ_n</mi><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#665.17.63:677.17.75" data-mmt-position="5_3_3_2_2_3_1">-</mo><mi data-mmt-varref="4" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#673.17.71:676.17.74" data-mmt-position="5_3_3_2_2_3_3">xφ_p</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow><mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_2">k_B</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_1">⋅</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_3">T</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mfrac><mrow class="implicit-arg implicit-arg-hidden"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf" data-mmt-position="5_3_3_2_4">prf</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>R (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#562.16.1:701.18.7">http://mathhub.info/MitM/Models/recombination.mmt#562.16.1:701.18.7</a></td></tr></table></div></div></div></div></div><div class="opaque-text inlineBoxSibling">Kernel for spontaneous recombination with coefficient B.</div><div><div class="theory"><div class="document toggle-root inlineBoxSibling"><div class="document-header" data-mmt-toggle="document-body"><span class="name">SpontaneousRecombination</span></div><div class="document-body"><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>structure </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-domain">domain</button></div><table class="constant-body "><tr class="component-domain"><td><span class="constant-component-label">domain</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?[http://mathhub.info/MitM/Models/recombination?Recombination]" data-mmt-component="domain" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">?Recombination</mo></math></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#816.23.1:839.23.24">http://mathhub.info/MitM/Models/recombination.mmt#816.23.1:839.23.24</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">The coefficient for the sponanteous recombination rate is denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-position="">B</mo></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient">spontaneous_recombination_coefficient</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-parsing-notation">parsing notation</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-component="type" data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="">ℝ</mo></math></td></tr><tr class="component-definition"></tr><tr class="component-parsing-notation"><td><span class="constant-component-label">parsing-notation</span></td><td><span>B (precedence 0)</span></td></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#923.26.1:971.26.49">http://mathhub.info/MitM/Models/recombination.mmt#923.26.1:971.26.49</a></td></tr></table></div><div class="opaque-text inlineBoxSibling">Formula for sponanteous recombination <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-position="">r</mo></math>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-position="">n</mo></math>,<math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-position="">p</mo></math>) = <math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-position="">B</mo></math></div><div class="constant toggle-root inlineBoxSibling"><div class="constant-header"><span>constant </span><span><span class="name" data-mmt-href="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?axiom_spontaneous">axiom_spontaneous</span></span><button class="component-toggle" data-mmt-toggle="metadata">metadata</button><button class="component-toggle" data-mmt-toggle="component-type">type</button></div><table class="constant-body "><tr class="component-type"><td><span class="constant-component-label">type</span></td><td><math xmlns="http://www.w3.org/1998/Math/MathML" data-mmt-owner="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?axiom_spontaneous" data-mmt-component="type" data-mmt-position=""><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1056.28.21:1070.28.35" data-mmt-position="1">⊦</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1056.28.21:1070.28.35" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_3">r</mo><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_1">≐</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_2">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_3">ℝ</mo><mo class="operator brackets">)</mo></mrow></mrow></mrow><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35" data-mmt-position="2_4"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1064.28.29:1064.28.29" data-mmt-position="2_4_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1064.28.29:1064.28.29" data-mmt-position="2_4_1_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1066.28.31:1066.28.31" data-mmt-position="2_4_2">y</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1066.28.31:1066.28.31" data-mmt-position="2_4_2_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_0">]</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35" data-mmt-position="2_4_3">B</mo><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></math></td></tr><tr class="component-definition"></tr><tr class="link metadata"><td><span class="key constant-component-label" title="http://cds.omdoc.org/mmt?metadata?sourceRef">http://cds.omdoc.org/mmt?metadata?sourceRef</span></td><td><a href="http://mathhub.info/MitM/Models/recombination.mmt#1036.28.1:1089.28.54">http://mathhub.info/MitM/Models/recombination.mmt#1036.28.1:1089.28.54</a></td></tr></table></div></div></div></div></div></div></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models?Base"></meta><title> Base </title><meta name="url" content="http://mathhub.info/MitM/Models"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base" id="Base">Base</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma">LFSigma</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" id="Base?exp">exp</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" id="Base?der">der</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_der_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_der_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>2</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mi style="color:red;" data-mmt-position="2">b</mi><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-position="0">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mi style="color:red;" data-mmt-position="1">a</mi></mrow></mrow></mrow></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" id="Base?Real_vec_space2">Real_vec_space2</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_Real_vec_space2_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_Real_vec_space2_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="">ℝ2</mo></math></td></tr></tbody></table><math id="-877742477" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="2">ℝ</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" id="Base?Real_vec_space3">Real_vec_space3</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_Real_vec_space3_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_Real_vec_space3_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-position="">ℝ3</mo></math></td></tr></tbody></table><math id="1711602100" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="3">ℝ</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" id="Base?comp1">comp1</span><math id="999305725" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#887.24.21:887.24.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#887.24.21:887.24.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#890.24.24:893.24.27" data-mmt-position="2_0">πl</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#893.24.27:893.24.27" data-mmt-position="2_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>v</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl</csymbol><ci>v</ci></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" id="Base?comp2">comp2</span><math id="-1254170805" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#918.25.21:918.25.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#918.25.21:918.25.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#921.25.24:929.25.32" data-mmt-position="2_0">πl</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#921.25.24:929.25.32" data-mmt-position="2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#924.25.27:929.25.32" data-mmt-position="2_1_0">πr</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#928.25.31:928.25.31" data-mmt-position="2_1_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>v</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl</csymbol><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr</csymbol><ci>v</ci></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" id="Base?comp3">comp3</span><math id="1142432552" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#954.26.21:954.26.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#954.26.21:954.26.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#957.26.24:965.26.32" data-mmt-position="2_0">πr</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#957.26.24:965.26.32" data-mmt-position="2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#960.26.27:965.26.32" data-mmt-position="2_1_0">πr</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#964.26.31:964.26.31" data-mmt-position="2_1_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>v</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr</csymbol><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr</csymbol><ci>v</ci></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub2" id="Base?pred_as_sub2">pred_as_sub2</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_pred_as_sub2_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_pred_as_sub2_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>1</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-position="0">pred2</mo><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="1">a</mi></mrow></math></td></tr></tbody></table><math id="46770261" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1011.28.40:1011.28.40" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1011.28.40:1011.28.40" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#993.28.22:996.28.25" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">⟨</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_1">ℝ2</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">|</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52" data-mmt-position="2_2_1">z</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52" data-mmt-position="2_2_1_1">ℝ2</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-position="2_2_2_1">ded</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59" data-mmt-position="2_2_2_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1028.28.57" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1030.28.59" data-mmt-position="2_2_2_2_0"></mspace><mi data-mmt-varref="2_2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1030.28.59:1030.28.59" data-mmt-position="2_2_2_2_2">z</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">⟩</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>P</ci><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?arrow</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space2</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?bool</csymbol></apply></bvar><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space2</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>z</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space2</csymbol></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?ded</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><ci>P</ci><ci>z</ci></apply></apply></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub3" id="Base?pred_as_sub3">pred_as_sub3</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_pred_as_sub3_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_pred_as_sub3_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>1</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-position="0">pred3</mo><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="1">a</mi></mrow></math></td></tr></tbody></table><math id="-720277543" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-position="1_1_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1071.29.22:1074.29.25" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">⟨</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">|</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52" data-mmt-position="2_2_1">z</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52" data-mmt-position="2_2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-position="2_2_2_1">ded</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59" data-mmt-position="2_2_2_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1106.29.57" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1108.29.59" data-mmt-position="2_2_2_2_0"></mspace><mi data-mmt-varref="2_2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1108.29.59:1108.29.59" data-mmt-position="2_2_2_2_2">z</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">⟩</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>P</ci><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?arrow</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?bool</csymbol></apply></bvar><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>z</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?ded</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><ci>P</ci><ci>z</ci></apply></apply></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" id="Base?lift_type_one_to_three">lift_type_one_to_three</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_lift_type_one_to_three_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_lift_type_one_to_three_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>1</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-position="0">t1↑</mo><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="1">a</mi></mrow></math></td></tr></tbody></table><math id="-637953129" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1160.31.31:1163.31.34" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9" data-mmt-position="2_1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9" data-mmt-position="2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-position="2_2_1">and</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-position="2_2_2_1">and</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1195.32.13:1195.32.13" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24" data-mmt-position="2_2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24" data-mmt-position="2_2_2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1198.32.16:1202.32.20" data-mmt-position="2_2_2_2_2_1">comp1</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1197.32.15:1205.32.23" data-mmt-position="2_2_2_2_2_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1204.32.22:1204.32.22" data-mmt-position="2_2_2_2_2_2">v</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-position="2_2_2_3_1">eq</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_2">ℝ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1215.32.33" data-mmt-position="2_2_2_3_3_1">comp2</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1217.32.35" data-mmt-position="2_2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1217.32.35:1217.32.35" data-mmt-position="2_2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_0"></mspace><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_2_3_4">0</mn><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-position="2_2_3_1">eq</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_2">ℝ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1231.32.49" data-mmt-position="2_2_3_3_1">comp3</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1233.32.51" data-mmt-position="2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1233.32.51:1233.32.51" data-mmt-position="2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_0"></mspace><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_3_4">0</mn><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>P</ci><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?arrow</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?bool</csymbol></apply></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>v</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?and</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?and</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><ci>P</ci><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp1</csymbol><ci>v</ci></apply></apply><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?eq</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp2</csymbol><ci>v</ci></apply><cn definitionURL="http://mathhub.info/MitM/Foundation?Literals?nat_lit" encoding="mmt-literal">0</cn></apply></apply><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?eq</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp3</csymbol><ci>v</ci></apply><cn definitionURL="http://mathhub.info/MitM/Foundation?Literals?nat_lit" encoding="mmt-literal">0</cn></apply></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" id="Base?lift_type_two_to_three">lift_type_two_to_three</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_lift_type_two_to_three_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_lift_type_two_to_three_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>1</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-position="0">t2↑</mo><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="1">a</mi></mrow></math></td></tr></tbody></table><math id="1582316142" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1285.33.32:1288.33.35" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9" data-mmt-position="2_1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9" data-mmt-position="2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-position="2_2_1">and</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1320.34.13:1320.34.13" data-mmt-position="2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35" data-mmt-position="2_2_2_2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">⟨</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1328.34.21" data-mmt-position="2_2_2_2_1_1">comp1</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1330.34.23" data-mmt-position="2_2_2_2_1_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1330.34.23:1330.34.23" data-mmt-position="2_2_2_2_1_2">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">,</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1337.34.30" data-mmt-position="2_2_2_2_2_1">comp2</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1339.34.32" data-mmt-position="2_2_2_2_2_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1339.34.32:1339.34.32" data-mmt-position="2_2_2_2_2_2">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">⟩</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-position="2_2_3_1">eq</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_2">ℝ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1351.34.44" data-mmt-position="2_2_3_3_1">comp3</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1353.34.46" data-mmt-position="2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1353.34.46:1353.34.46" data-mmt-position="2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_0"></mspace><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_3_4">0</mn><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>P</ci><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?arrow</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space2</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?bool</csymbol></apply></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>v</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?and</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><ci>P</ci><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp1</csymbol><ci>v</ci></apply><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp2</csymbol><ci>v</ci></apply></apply></apply><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?eq</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp3</csymbol><ci>v</ci></apply><cn definitionURL="http://mathhub.info/MitM/Foundation?Literals?nat_lit" encoding="mmt-literal">0</cn></apply></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_function_one_to_three" id="Base?lift_function_one_to_three">lift_function_one_to_three</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_lift_function_one_to_three_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_lift_function_one_to_three_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>2</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_function_one_to_three" data-mmt-position="0">f1↑</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mi style="color:red;" data-mmt-position="1">a</mi></mrow></mrow><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="2">b</mi></mrow></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_function_two_to_three" id="Base?lift_function_two_to_three">lift_function_two_to_three</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_lift_function_two_to_three_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_lift_function_two_to_three_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>2</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_function_two_to_three" data-mmt-position="0">f2↑</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mi style="color:red;" data-mmt-position="1">a</mi></mrow></mrow><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="2">b</mi></mrow></math></td></tr></tbody></table></div></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models?PhysicalConstants"></meta><title> PhysicalConstants </title><meta name="url" content="http://mathhub.info/MitM/Models"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants" id="PhysicalConstants">PhysicalConstants</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" id="PhysicalConstants?vacuum_dielectric_permitivity">vacuum_dielectric_permitivity</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_PhysicalConstants_vacuum_dielectric_permitivity_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_PhysicalConstants_vacuum_dielectric_permitivity_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-position="">ε_0</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" id="PhysicalConstants?elementary_charge">elementary_charge</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_PhysicalConstants_elementary_charge_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_PhysicalConstants_elementary_charge_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-position="">q</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" id="PhysicalConstants?Boltzmann_constant">Boltzmann_constant</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_PhysicalConstants_Boltzmann_constant_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_PhysicalConstants_Boltzmann_constant_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-position="">k_B</mo></math></td></tr></tbody></table></div></div></div></body></html>
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-<div class="namespace"><div class="subnamespace"><a href="VanRoosbroeck/.html">http://mathhub.info/MitM/Models/VanRoosbroeck</a></div><div class="subnamespace"><a href="continuity/.html">http://mathhub.info/MitM/Models/continuity</a></div><div class="subnamespace"><a href="densities/.html">http://mathhub.info/MitM/Models/densities</a></div><div class="subnamespace"><a href="device/.html">http://mathhub.info/MitM/Models/device</a></div><div class="subnamespace"><a href="poisson/.html">http://mathhub.info/MitM/Models/poisson</a></div><div class="subnamespace"><a href="recombination/.html">http://mathhub.info/MitM/Models/recombination</a></div><div class="submodule"><a href="$Base.html">http://mathhub.info/MitM/Models?Base</a></div><div class="submodule"><a href="$Physical$Constants.html">http://mathhub.info/MitM/Models?PhysicalConstants</a></div></div>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck"></meta><title> VanRoosbroeck </title><meta name="url" content="http://mathhub.info/MitM/Models/VanRoosbroeck"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck" id="VanRoosbroeck">VanRoosbroeck</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonEquation">PoissonEquation</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions">PoissonBoundaryConditions</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons">ContinuityEquationElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles">ContinuityEquationHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons">ContinuityBoundaryConditionsElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles">ContinuityBoundaryConditionsHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination">SpontaneousRecombination</span></div></div></div></body></html>
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-<div class="namespace"><div class="submodule"><a href="$Van$Roosbroeck.html">http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck</a></div></div>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons"></meta><title> ContinuityBoundaryConditionsElectrons </title><meta name="url" content="http://mathhub.info/MitM/Models/continuity"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons" id="ContinuityBoundaryConditionsElectrons">ContinuityBoundaryConditionsElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top" id="ContinuityBoundaryConditionsElectrons?potential_top">potential_top</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ContinuityBoundaryConditionsElectrons_potential_top_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ContinuityBoundaryConditionsElectrons_potential_top_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top" data-mmt-position="">φ_n_1</mo></math></td></tr></tbody></table><math id="-588024757" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></mrow><annotation-xml encoding="MathML-Content"><csymbol>http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom</csymbol></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom" id="ContinuityBoundaryConditionsElectrons?potential_bottom">potential_bottom</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ContinuityBoundaryConditionsElectrons_potential_bottom_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ContinuityBoundaryConditionsElectrons_potential_bottom_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom" data-mmt-position="">φ_n_2</mo></math></td></tr></tbody></table><math id="300820980" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></mrow><annotation-xml encoding="MathML-Content"><csymbol>http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top</csymbol></annotation-xml></semantics></math></div></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles"></meta><title> ContinuityBoundaryConditionsHoles </title><meta name="url" content="http://mathhub.info/MitM/Models/continuity"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles" id="ContinuityBoundaryConditionsHoles">ContinuityBoundaryConditionsHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top" id="ContinuityBoundaryConditionsHoles?potential_top">potential_top</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ContinuityBoundaryConditionsHoles_potential_top_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ContinuityBoundaryConditionsHoles_potential_top_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top" data-mmt-position="">φ_p_1</mo></math></td></tr></tbody></table><math id="-588024757" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></mrow><annotation-xml encoding="MathML-Content"><csymbol>http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom</csymbol></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom" id="ContinuityBoundaryConditionsHoles?potential_bottom">potential_bottom</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ContinuityBoundaryConditionsHoles_potential_bottom_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ContinuityBoundaryConditionsHoles_potential_bottom_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom" data-mmt-position="">φ_p_2</mo></math></td></tr></tbody></table><math id="300820980" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></mrow><annotation-xml encoding="MathML-Content"><csymbol>http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top</csymbol></annotation-xml></semantics></math></div></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons"></meta><title> ContinuityEquationElectrons </title><meta name="url" content="http://mathhub.info/MitM/Models/continuity"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" id="ContinuityEquationElectrons">ContinuityEquationElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">CurrentElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation_electrons" id="ContinuityEquationElectrons?continuity_equation_electrons">continuity_equation_electrons</span></div></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles"></meta><title> ContinuityEquationHoles </title><meta name="url" content="http://mathhub.info/MitM/Models/continuity"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles" id="ContinuityEquationHoles">ContinuityEquationHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles">CurrentHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes" id="ContinuityEquationHoles?continuity_equation_holes">continuity_equation_holes</span></div></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/continuity?CurrentElectrons"></meta><title> CurrentElectrons </title><meta name="url" content="http://mathhub.info/MitM/Models/continuity"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons" id="CurrentElectrons">CurrentElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" id="CurrentElectrons?current_electrons">current_electrons</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_CurrentElectrons_current_electrons_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_CurrentElectrons_current_electrons_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>3</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" data-mmt-position="0">j_n</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mi style="color:red;" data-mmt-position="1">a</mi></mrow></mrow><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="2">b</mi><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="3">c</mi></mrow></math></td></tr></tbody></table><math id="-34722689" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1030.27.5:1030.27.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1030.27.5:1030.27.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#974.26.29:977.26.32" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">]</mo><mrow data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1033.27.8:1033.27.8" data-mmt-position="2_1">f</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1033.27.8:1033.27.8" data-mmt-position="2_1_1"><mrow data-mmt-position="2_1_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_1_1_1_1">pred_as_sub</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#981.26.36:986.26.41" data-mmt-position="2_1_1_1_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#986.26.41:986.26.41" data-mmt-position="2_1_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_1_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1035.27.10:1035.27.10" data-mmt-position="2_2">g</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1035.27.10:1035.27.10" data-mmt-position="2_2_1"><mrow data-mmt-position="2_2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_2_1_1_1">pred_as_sub</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#996.26.51:1001.26.56" data-mmt-position="2_2_1_1_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1001.26.56:1001.26.56" data-mmt-position="2_2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1037.27.12:1075.27.50" data-mmt-position="2_3_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1038.27.13:1038.27.13" data-mmt-position="2_3_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1038.27.13:1038.27.13" data-mmt-position="2_3_1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_3_1_1_1">pred_as_sub</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="2_3_1_1_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1016.26.71:1016.26.71" data-mmt-position="2_3_1_1_2">P</mi></mrow></mrow><mo 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diff --git a/export/planetary/content/http..mathhub.info/MitM/Models/continuity/$Current$Holes.html b/export/planetary/content/http..mathhub.info/MitM/Models/continuity/$Current$Holes.html
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/continuity?CurrentHoles"></meta><title> CurrentHoles </title><meta name="url" content="http://mathhub.info/MitM/Models/continuity"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles" id="CurrentHoles">CurrentHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" id="CurrentHoles?current_holes">current_holes</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_CurrentHoles_current_holes_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_CurrentHoles_current_holes_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>3</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mrow><mo 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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/continuity?Mobilities"></meta><title> Mobilities </title><meta name="url" content="http://mathhub.info/MitM/Models/continuity"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities" id="Mobilities">Mobilities</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" id="Mobilities?mobility_electrons">mobility_electrons</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Mobilities_mobility_electrons_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Mobilities_mobility_electrons_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-position="">μ_n</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" id="Mobilities?mobility_holes">mobility_holes</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Mobilities_mobility_holes_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Mobilities_mobility_holes_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-position="">μ_p</mo></math></td></tr></tbody></table></div></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/densities?BandstructureParameters"></meta><title> BandstructureParameters </title><meta name="url" content="http://mathhub.info/MitM/Models/densities"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters" id="BandstructureParameters">BandstructureParameters</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" id="BandstructureParameters?effective_density_of_states_conduction_bands">effective_density_of_states_conduction_bands</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_BandstructureParameters_effective_density_of_states_conduction_bands_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_BandstructureParameters_effective_density_of_states_conduction_bands_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-position="">N_c</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" id="BandstructureParameters?effective_density_of_states_valence_bands">effective_density_of_states_valence_bands</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_BandstructureParameters_effective_density_of_states_valence_bands_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_BandstructureParameters_effective_density_of_states_valence_bands_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-position="">N_v</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" id="BandstructureParameters?conduction_band_edge">conduction_band_edge</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_BandstructureParameters_conduction_band_edge_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_BandstructureParameters_conduction_band_edge_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-position="">E_c</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" id="BandstructureParameters?valence_band_edge">valence_band_edge</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_BandstructureParameters_valence_band_edge_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_BandstructureParameters_valence_band_edge_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-position="">E_v</mo></math></td></tr></tbody></table></div></div></div></body></html>
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diff --git a/export/planetary/content/http..mathhub.info/MitM/Models/densities/$Density$Electrons.html b/export/planetary/content/http..mathhub.info/MitM/Models/densities/$Density$Electrons.html
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diff --git a/export/planetary/content/http..mathhub.info/MitM/Models/densities/$Density$Holes.html b/export/planetary/content/http..mathhub.info/MitM/Models/densities/$Density$Holes.html
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/densities?DensityHoles"></meta><title> DensityHoles </title><meta name="url" content="http://mathhub.info/MitM/Models/densities"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles" id="DensityHoles">DensityHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></div><div 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diff --git a/export/planetary/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.html b/export/planetary/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.html
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"></meta><title> ElectrostaticPotential </title><meta name="url" content="http://mathhub.info/MitM/Models/densities"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential" id="ElectrostaticPotential">ElectrostaticPotential</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" id="ElectrostaticPotential?electrostatic_potential">electrostatic_potential</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ElectrostaticPotential_electrostatic_potential_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ElectrostaticPotential_electrostatic_potential_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-position="">ψ</mo></math></td></tr></tbody></table></div></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons"></meta><title> FermiPotentialElectrons </title><meta name="url" content="http://mathhub.info/MitM/Models/densities"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons" id="FermiPotentialElectrons">FermiPotentialElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" id="FermiPotentialElectrons?quasi_Fermi_potential">quasi_Fermi_potential</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_FermiPotentialElectrons_quasi_Fermi_potential_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_FermiPotentialElectrons_quasi_Fermi_potential_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-position="">φ_n</mo></math></td></tr></tbody></table></div></div></div></body></html>
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diff --git a/export/planetary/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.html b/export/planetary/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.html
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles"></meta><title> FermiPotentialHoles </title><meta name="url" content="http://mathhub.info/MitM/Models/densities"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles" id="FermiPotentialHoles">FermiPotentialHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" id="FermiPotentialHoles?quasi_Fermi_potential">quasi_Fermi_potential</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_FermiPotentialHoles_quasi_Fermi_potential_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_FermiPotentialHoles_quasi_Fermi_potential_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-position="">φ_p</mo></math></td></tr></tbody></table></div></div></div></body></html>
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-<div class="namespace"><div class="submodule"><a href="$Bandstructure$Parameters.html">http://mathhub.info/MitM/Models/densities?BandstructureParameters</a></div><div class="submodule"><a href="$Density$Electrons.html">http://mathhub.info/MitM/Models/densities?DensityElectrons</a></div><div class="submodule"><a href="$Density$Holes.html">http://mathhub.info/MitM/Models/densities?DensityHoles</a></div><div class="submodule"><a href="$Electrostatic$Potential.html">http://mathhub.info/MitM/Models/densities?ElectrostaticPotential</a></div><div class="submodule"><a href="$Fermi$Potential$Electrons.html">http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons</a></div><div class="submodule"><a href="$Fermi$Potential$Holes.html">http://mathhub.info/MitM/Models/densities?FermiPotentialHoles</a></div></div>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/device?DeviceGeometry"></meta><title> DeviceGeometry </title><meta name="url" content="http://mathhub.info/MitM/Models/device"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry" id="DeviceGeometry">DeviceGeometry</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">Device</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" id="DeviceGeometry?domain_prop">domain_prop</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" id="DeviceGeometry?domain">domain</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_DeviceGeometry_domain_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_DeviceGeometry_domain_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-position="">Ω</mo></math></td></tr></tbody></table><math id="341123573" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="1">pred_as_sub</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#506.13.19:521.13.34" data-mmt-position="0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#511.13.24:521.13.34" data-mmt-position="2">domain_prop</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realarith?pred_as_sub</csymbol><csymbol>http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop</csymbol></apply></annotation-xml></semantics></math></div></div></div></body></html>
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diff --git a/export/planetary/content/http..mathhub.info/MitM/Models/device/$Device$Operation$State.html b/export/planetary/content/http..mathhub.info/MitM/Models/device/$Device$Operation$State.html
deleted file mode 100644
index 18b7f4c..0000000
--- a/export/planetary/content/http..mathhub.info/MitM/Models/device/$Device$Operation$State.html
+++ /dev/null
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/device?DeviceOperationState"></meta><title> DeviceOperationState </title><meta name="url" content="http://mathhub.info/MitM/Models/device"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState" id="DeviceOperationState">DeviceOperationState</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" id="DeviceOperationState?temperatur">temperatur</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_DeviceOperationState_temperatur_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_DeviceOperationState_temperatur_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-position="">T</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" id="DeviceOperationState?voltage_bottom">voltage_bottom</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_DeviceOperationState_voltage_bottom_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_DeviceOperationState_voltage_bottom_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" id="DeviceOperationState?voltage_top">voltage_top</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_DeviceOperationState_voltage_top_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_DeviceOperationState_voltage_top_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf" id="DeviceOperationState?prf">prf</span></div></div></div></body></html>
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diff --git a/export/planetary/content/http..mathhub.info/MitM/Models/device/$Device.html b/export/planetary/content/http..mathhub.info/MitM/Models/device/$Device.html
deleted file mode 100644
index 54e766d..0000000
--- a/export/planetary/content/http..mathhub.info/MitM/Models/device/$Device.html
+++ /dev/null
@@ -1 +0,0 @@
-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/device?Device"></meta><title> Device </title><meta name="url" content="http://mathhub.info/MitM/Models/device"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?Device" id="Device">Device</span></div></div></div></body></html>
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diff --git a/export/planetary/content/http..mathhub.info/MitM/Models/device/$Doping$Profile.html b/export/planetary/content/http..mathhub.info/MitM/Models/device/$Doping$Profile.html
deleted file mode 100644
index d754631..0000000
--- a/export/planetary/content/http..mathhub.info/MitM/Models/device/$Doping$Profile.html
+++ /dev/null
@@ -1 +0,0 @@
-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/device?DopingProfile"></meta><title> DopingProfile </title><meta name="url" content="http://mathhub.info/MitM/Models/device"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile" id="DopingProfile">DopingProfile</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" id="DopingProfile?doping_profile">doping_profile</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_DopingProfile_doping_profile_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_DopingProfile_doping_profile_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-position="">C</mo></math></td></tr></tbody></table></div></div></div></body></html>
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diff --git a/export/planetary/content/http..mathhub.info/MitM/Models/device/.html b/export/planetary/content/http..mathhub.info/MitM/Models/device/.html
deleted file mode 100644
index cad16cb..0000000
--- a/export/planetary/content/http..mathhub.info/MitM/Models/device/.html
+++ /dev/null
@@ -1 +0,0 @@
-<div class="namespace"><div class="submodule"><a href="$Device$Geometry.html">http://mathhub.info/MitM/Models/device?DeviceGeometry</a></div><div class="submodule"><a href="$Device$Operation$State.html">http://mathhub.info/MitM/Models/device?DeviceOperationState</a></div><div class="submodule"><a href="$Device.html">http://mathhub.info/MitM/Models/device?Device</a></div><div class="submodule"><a href="$Doping$Profile.html">http://mathhub.info/MitM/Models/device?DopingProfile</a></div></div>
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diff --git a/export/planetary/content/http..mathhub.info/MitM/Models/poisson/$Charge.html b/export/planetary/content/http..mathhub.info/MitM/Models/poisson/$Charge.html
deleted file mode 100644
index d1151a2..0000000
--- a/export/planetary/content/http..mathhub.info/MitM/Models/poisson/$Charge.html
+++ /dev/null
@@ -1 +0,0 @@
-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/poisson?Charge"></meta><title> Charge </title><meta name="url" content="http://mathhub.info/MitM/Models/poisson"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge" id="Charge">Charge</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile">DopingProfile</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" id="Charge?total_charge">total_charge</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Charge_total_charge_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Charge_total_charge_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge?total_charge" data-mmt-position="">Q</mo></math></td></tr></tbody></table><math id="380019371" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1123.29.5:1123.29.5" data-mmt-position="1">x</mi><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1123.29.5:1123.29.5" data-mmt-position="1_1">Ω</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-position="2_1">multiplication</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-position="2_2_1">uminus</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1131.29.13" data-mmt-position="2_2_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1131.29.13" data-mmt-position="2_2_2">q</mo><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1130.29.12:1181.29.63" data-mmt-position="2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-position="2_3_1">bin_minus</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1135.29.17:1181.29.63" data-mmt-position="2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-position="2_3_2_1">addition</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1140.29.22" data-mmt-position="2_3_2_2_1">C</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1140.29.22" data-mmt-position="2_3_2_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1139.29.21:1139.29.21" data-mmt-position="2_3_2_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1136.29.18:1160.29.42" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1147.29.29:1151.29.33" data-mmt-position="2_3_2_3_2_1">ψ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1147.29.29:1151.29.33" data-mmt-position="2_3_2_3_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1150.29.32:1150.29.32" data-mmt-position="2_3_2_3_2_2">x</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1144.29.26:1160.29.42" data-mmt-position="2_3_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1153.29.35:1159.29.41" data-mmt-position="2_3_2_3_3_1">φ_p</mo><mspace width=".2em" 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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/poisson?PoissonParameters"></meta><title> PoissonParameters </title><meta name="url" content="http://mathhub.info/MitM/Models/poisson"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters" id="PoissonParameters">PoissonParameters</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" id="PoissonParameters?relative_dielectric_permitivity">relative_dielectric_permitivity</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_PoissonParameters_relative_dielectric_permitivity_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_PoissonParameters_relative_dielectric_permitivity_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-position="">ε_r</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" id="PoissonParameters?dielectric_permitivity">dielectric_permitivity</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_PoissonParameters_dielectric_permitivity_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_PoissonParameters_dielectric_permitivity_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity" data-mmt-position="">ε_s</mo></math></td></tr></tbody></table><math id="1131138354" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-position="1">multiplication</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="2">ε_r</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11" data-mmt-position="3">ε_0</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realarith?multiplication</csymbol><csymbol>http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity</csymbol><csymbol>http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity</csymbol></apply></annotation-xml></semantics></math></div></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium"></meta><title> ThermodynamicEquilibrium </title><meta name="url" content="http://mathhub.info/MitM/Models/poisson"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium" id="ThermodynamicEquilibrium">ThermodynamicEquilibrium</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" id="ThermodynamicEquilibrium?equilibrium_potential_top">equilibrium_potential_top</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ThermodynamicEquilibrium_equilibrium_potential_top_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ThermodynamicEquilibrium_equilibrium_potential_top_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" data-mmt-position="">ψ_0_2</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" id="ThermodynamicEquilibrium?equilibrium_potential_bottom">equilibrium_potential_bottom</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ThermodynamicEquilibrium_equilibrium_potential_bottom_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ThermodynamicEquilibrium_equilibrium_potential_bottom_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-position="">ψ_0_1</mo></math></td></tr></tbody></table></div></div></div></body></html>
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-<div class="namespace"><div class="submodule"><a href="$Charge.html">http://mathhub.info/MitM/Models/poisson?Charge</a></div><div class="submodule"><a href="$Displacement.html">http://mathhub.info/MitM/Models/poisson?Displacement</a></div><div class="submodule"><a href="$Poisson$Boundary$Conditions.html">http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions</a></div><div class="submodule"><a href="$Poisson$Equation.html">http://mathhub.info/MitM/Models/poisson?PoissonEquation</a></div><div class="submodule"><a href="$Poisson$Parameters.html">http://mathhub.info/MitM/Models/poisson?PoissonParameters</a></div><div class="submodule"><a href="$Thermodynamic$Equilibrium.html">http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium</a></div></div>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/recombination?Recombination"></meta><title> Recombination </title><meta name="url" content="http://mathhub.info/MitM/Models/recombination"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination" id="Recombination">Recombination</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></div><div 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data-mmt-position="">r</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" id="Recombination?recombination_rate">recombination_rate</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Recombination_recombination_rate_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Recombination_recombination_rate_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-position="">R</mo></math></td></tr></tbody></table><math id="-187090076" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#608.17.6:609.17.7" data-mmt-position="1">xn</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#608.17.6:609.17.7" data-mmt-position="1_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#612.17.10:613.17.11" data-mmt-position="2">xp</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#612.17.10:613.17.11" data-mmt-position="2_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#616.17.14:619.17.17" data-mmt-position="3">xφ_n</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#616.17.14:619.17.17" data-mmt-position="3_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#622.17.20:625.17.23" data-mmt-position="4">xφ_p</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#622.17.20:625.17.23" data-mmt-position="4_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="5"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-position="5_1">multiplication</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-position="5_2_1">multiplication</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:647.17.45" data-mmt-position="5_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:647.17.45" data-mmt-position="5_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-position="5_2_2_1">multiplication</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:641.17.39" data-mmt-position="5_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:641.17.39" data-mmt-position="5_2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_1">r</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#631.17.29:632.17.30" data-mmt-position="5_2_2_2_2">xn</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:636.17.34" data-mmt-position="5_2_2_2_0"></mspace><mi data-mmt-varref="2" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#634.17.32:635.17.33" data-mmt-position="5_2_2_2_3">xp</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:641.17.39" data-mmt-position="5_2_2_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#640.17.38:641.17.39" data-mmt-position="5_2_2_3">xn</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:647.17.45" data-mmt-position="5_2_0"></mspace><mi data-mmt-varref="2" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#646.17.44:647.17.45" data-mmt-position="5_2_3">xp</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#628.17.26:690.17.88" data-mmt-position="5_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-position="5_3_1">bin_minus</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" 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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination"></meta><title> SpontaneousRecombination </title><meta name="url" content="http://mathhub.info/MitM/Models/recombination"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination" id="SpontaneousRecombination">SpontaneousRecombination</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" id="SpontaneousRecombination?spontaneous_recombination_coefficient">spontaneous_recombination_coefficient</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_SpontaneousRecombination_spontaneous_recombination_coefficient_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_SpontaneousRecombination_spontaneous_recombination_coefficient_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-position="">B</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?axiom_spontaneous" id="SpontaneousRecombination?axiom_spontaneous">axiom_spontaneous</span></div></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc"></meta><title> VanRoosbroeck.omdoc </title><meta name="url" content="http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="document"><ul class="doc-body"><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck" id="VanRoosbroeck">VanRoosbroeck</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonEquation">PoissonEquation</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions">PoissonBoundaryConditions</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons">ContinuityEquationElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles">ContinuityEquationHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons">ContinuityBoundaryConditionsElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles">ContinuityBoundaryConditionsHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination">SpontaneousRecombination</span></div></div></li></ul></div></div></body></html>
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data-mmt-position="2">b</mi><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-position="0">'</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mi style="color:red;" data-mmt-position="1">a</mi></mrow></mrow></mrow></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" id="Base?Real_vec_space2">Real_vec_space2</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_Real_vec_space2_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_Real_vec_space2_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="">ℝ2</mo></math></td></tr></tbody></table><math id="-877742477" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28" data-mmt-position="2">ℝ</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" id="Base?Real_vec_space3">Real_vec_space3</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_Real_vec_space3_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_Real_vec_space3_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-position="">ℝ3</mo></math></td></tr></tbody></table><math id="1711602100" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2">ℝ</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product" data-mmt-position="0">×</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="3">ℝ</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" id="Base?comp1">comp1</span><math id="999305725" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#887.24.21:887.24.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#887.24.21:887.24.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#886.24.20:893.24.27" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#890.24.24:893.24.27" data-mmt-position="2_0">πl</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#893.24.27:893.24.27" data-mmt-position="2_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>v</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl</csymbol><ci>v</ci></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" id="Base?comp2">comp2</span><math id="-1254170805" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#918.25.21:918.25.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#918.25.21:918.25.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#917.25.20:929.25.32" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#921.25.24:929.25.32" data-mmt-position="2_0">πl</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#921.25.24:929.25.32" data-mmt-position="2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#924.25.27:929.25.32" data-mmt-position="2_1_0">πr</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#928.25.31:928.25.31" data-mmt-position="2_1_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>v</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl</csymbol><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr</csymbol><ci>v</ci></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" id="Base?comp3">comp3</span><math id="1142432552" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#954.26.21:954.26.21" data-mmt-position="1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#954.26.21:954.26.21" data-mmt-position="1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#953.26.20:965.26.32" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#957.26.24:965.26.32" data-mmt-position="2_0">πr</mo><mspace width=".2em"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#957.26.24:965.26.32" data-mmt-position="2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#960.26.27:965.26.32" data-mmt-position="2_1_0">πr</mo><mspace width=".2em"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#964.26.31:964.26.31" data-mmt-position="2_1_1">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>v</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr</csymbol><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr</csymbol><ci>v</ci></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub2" id="Base?pred_as_sub2">pred_as_sub2</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_pred_as_sub2_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_pred_as_sub2_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>1</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub2" data-mmt-position="0">pred2</mo><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="1">a</mi></mrow></math></td></tr></tbody></table><math id="46770261" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1011.28.40:1011.28.40" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1011.28.40:1011.28.40" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#993.28.22:996.28.25" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1010.28.39:1033.28.62" data-mmt-position="2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">⟨</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_1">ℝ2</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">|</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52" data-mmt-position="2_2_1">z</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52" data-mmt-position="2_2_1_1">ℝ2</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-position="2_2_2_1">ded</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59" data-mmt-position="2_2_2_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1028.28.57" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1030.28.59" data-mmt-position="2_2_2_2_0"></mspace><mi data-mmt-varref="2_2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1030.28.59:1030.28.59" data-mmt-position="2_2_2_2_2">z</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62" data-mmt-position="2_0">⟩</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>P</ci><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?arrow</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space2</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?bool</csymbol></apply></bvar><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space2</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>z</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space2</csymbol></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?ded</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><ci>P</ci><ci>z</ci></apply></apply></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub3" id="Base?pred_as_sub3">pred_as_sub3</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_pred_as_sub3_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_pred_as_sub3_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>1</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?pred_as_sub3" data-mmt-position="0">pred3</mo><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="1">a</mi></mrow></math></td></tr></tbody></table><math id="-720277543" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-position="1_1_1">ℝ3</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1071.29.22:1074.29.25" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62" data-mmt-position="2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">⟨</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_1">ℝ3</mo><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">|</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52" data-mmt-position="2_2_1">z</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52" data-mmt-position="2_2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60" data-mmt-position="2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?ded" data-mmt-position="2_2_2_1">ded</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59" data-mmt-position="2_2_2_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1106.29.57" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1108.29.59" data-mmt-position="2_2_2_2_0"></mspace><mi data-mmt-varref="2_2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1108.29.59:1108.29.59" data-mmt-position="2_2_2_2_2">z</mi><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62" data-mmt-position="2_0">⟩</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>P</ci><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?arrow</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?bool</csymbol></apply></bvar><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtp</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>z</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?ded</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><ci>P</ci><ci>z</ci></apply></apply></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" id="Base?lift_type_one_to_three">lift_type_one_to_three</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_lift_type_one_to_three_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_lift_type_one_to_three_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>1</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_one_to_three" data-mmt-position="0">t1↑</mo><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="1">a</mi></mrow></math></td></tr></tbody></table><math id="-637953129" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1160.31.31:1163.31.34" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9" data-mmt-position="2_1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9" data-mmt-position="2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-position="2_2_1">and</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-position="2_2_2_1">and</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1195.32.13:1195.32.13" data-mmt-position="2_2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24" data-mmt-position="2_2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24" data-mmt-position="2_2_2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1198.32.16:1202.32.20" data-mmt-position="2_2_2_2_2_1">comp1</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1197.32.15:1205.32.23" data-mmt-position="2_2_2_2_2_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1204.32.22:1204.32.22" data-mmt-position="2_2_2_2_2_2">v</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40" data-mmt-position="2_2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-position="2_2_2_3_1">eq</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_2">ℝ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1215.32.33" data-mmt-position="2_2_2_3_3_1">comp2</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1217.32.35" data-mmt-position="2_2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1217.32.35:1217.32.35" data-mmt-position="2_2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40" data-mmt-position="2_2_2_3_0"></mspace><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_2_3_4">0</mn><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56" data-mmt-position="2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-position="2_2_3_1">eq</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_2">ℝ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1231.32.49" data-mmt-position="2_2_3_3_1">comp3</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1233.32.51" data-mmt-position="2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1233.32.51:1233.32.51" data-mmt-position="2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56" data-mmt-position="2_2_3_0"></mspace><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_3_4">0</mn><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>P</ci><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?arrow</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?bool</csymbol></apply></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>v</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?and</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?and</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><ci>P</ci><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp1</csymbol><ci>v</ci></apply></apply><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?eq</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp2</csymbol><ci>v</ci></apply><cn definitionURL="http://mathhub.info/MitM/Foundation?Literals?nat_lit" encoding="mmt-literal">0</cn></apply></apply><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?eq</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp3</csymbol><ci>v</ci></apply><cn definitionURL="http://mathhub.info/MitM/Foundation?Literals?nat_lit" encoding="mmt-literal">0</cn></apply></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" id="Base?lift_type_two_to_three">lift_type_two_to_three</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_lift_type_two_to_three_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_lift_type_two_to_three_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>1</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_type_two_to_three" data-mmt-position="0">t2↑</mo><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="1">a</mi></mrow></math></td></tr></tbody></table><math id="1582316142" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space2" data-mmt-position="1_1_1">ℝ2</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1285.33.32:1288.33.35" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51" data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9" data-mmt-position="2_1">v</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?Real_vec_space3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9" data-mmt-position="2_1_1">ℝ3</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51" data-mmt-position="2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?and" data-mmt-position="2_2_1">and</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1320.34.13:1320.34.13" data-mmt-position="2_2_2_1">P</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35" data-mmt-position="2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35" data-mmt-position="2_2_2_2"><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">⟨</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1328.34.21" data-mmt-position="2_2_2_2_1_1">comp1</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1330.34.23" data-mmt-position="2_2_2_2_1_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1330.34.23:1330.34.23" data-mmt-position="2_2_2_2_1_2">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">,</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp2" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1337.34.30" data-mmt-position="2_2_2_2_2_1">comp2</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1339.34.32" data-mmt-position="2_2_2_2_2_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1339.34.32:1339.34.32" data-mmt-position="2_2_2_2_2_2">v</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34" data-mmt-position="2_2_2_2_0">⟩</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51" data-mmt-position="2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?eq" data-mmt-position="2_2_3_1">eq</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_2">ℝ</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?comp3" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1351.34.44" data-mmt-position="2_2_3_3_1">comp3</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1353.34.46" data-mmt-position="2_2_3_3_0"></mspace><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1353.34.46:1353.34.46" data-mmt-position="2_2_3_3_2">v</mi><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51" data-mmt-position="2_2_3_0"></mspace><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?nat_lit" data-mmt-position="2_2_3_4">0</mn><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>P</ci><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?arrow</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space2</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?bool</csymbol></apply></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>v</ci><csymbol>http://mathhub.info/MitM/Models?Base?Real_vec_space3</csymbol></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?and</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><ci>P</ci><apply><csymbol>http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp1</csymbol><ci>v</ci></apply><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp2</csymbol><ci>v</ci></apply></apply></apply><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Foundation?Logic?eq</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?comp3</csymbol><ci>v</ci></apply><cn definitionURL="http://mathhub.info/MitM/Foundation?Literals?nat_lit" encoding="mmt-literal">0</cn></apply></apply></apply></apply></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_function_one_to_three" id="Base?lift_function_one_to_three">lift_function_one_to_three</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_lift_function_one_to_three_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_lift_function_one_to_three_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>2</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_function_one_to_three" data-mmt-position="0">f1↑</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mi style="color:red;" data-mmt-position="1">a</mi></mrow></mrow><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="2">b</mi></mrow></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_function_two_to_three" id="Base?lift_function_two_to_three">lift_function_two_to_three</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Base_lift_function_two_to_three_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Base_lift_function_two_to_three_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>2</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?lift_function_two_to_three" data-mmt-position="0">f2↑</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mi style="color:red;" data-mmt-position="1">a</mi></mrow></mrow><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="2">b</mi></mrow></math></td></tr></tbody></table></div></div></li></ul></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/continuity.omdoc"></meta><title> continuity.omdoc </title><meta name="url" content="http://mathhub.info/MitM/Models/continuity.omdoc"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="document"><ul class="doc-body"><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities" id="Mobilities">Mobilities</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" id="Mobilities?mobility_electrons">mobility_electrons</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Mobilities_mobility_electrons_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Mobilities_mobility_electrons_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons" data-mmt-position="">μ_n</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" id="Mobilities?mobility_holes">mobility_holes</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Mobilities_mobility_holes_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Mobilities_mobility_holes_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-position="">μ_p</mo></math></td></tr></tbody></table></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons" id="CurrentElectrons">CurrentElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" id="CurrentElectrons?current_electrons">current_electrons</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_CurrentElectrons_current_electrons_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_CurrentElectrons_current_electrons_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>3</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons" data-mmt-position="0">j_n</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mi style="color:red;" data-mmt-position="1">a</mi></mrow></mrow><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="2">b</mi><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="3">c</mi></mrow></math></td></tr></tbody></table><math id="-34722689" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1030.27.5:1030.27.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1030.27.5:1030.27.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#974.26.29:977.26.32" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">]</mo><mrow data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1032.27.7:1075.27.50" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1033.27.8:1033.27.8" data-mmt-position="2_1">f</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1033.27.8:1033.27.8" data-mmt-position="2_1_1"><mrow data-mmt-position="2_1_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_1_1_1_1">pred_as_sub</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#981.26.36:986.26.41" data-mmt-position="2_1_1_1_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#986.26.41:986.26.41" data-mmt-position="2_1_1_1_2">P</mi><mo 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class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles" id="CurrentHoles">CurrentHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities">Mobilities</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" id="CurrentHoles?current_holes">current_holes</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_CurrentHoles_current_holes_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_CurrentHoles_current_holes_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>3</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mmt-position=""><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes" data-mmt-position="0">j_p</mo><mspace width=".2em"></mspace><mrow class="implicit-arg implicit-arg-hidden"><mi style="color:red;" data-mmt-position="1">a</mi></mrow></mrow><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="2">b</mi><mspace width=".2em"></mspace><mi style="color:red;" data-mmt-position="3">c</mi></mrow></math></td></tr></tbody></table><math id="1552792494" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1686.44.5:1686.44.5" data-mmt-position="1">P</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1686.44.5:1686.44.5" data-mmt-position="1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="1_1_1">ℝ</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/Foundation?Logic?bool" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1630.43.25:1633.43.28" data-mmt-position="1_1_2">bool</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-position="0">]</mo><mrow data-mmt-position="2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1689.44.8:1689.44.8" data-mmt-position="2_1">f</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1689.44.8:1689.44.8" data-mmt-position="2_1_1"><mrow data-mmt-position="2_1_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_1_1_1_1">pred_as_sub</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1637.43.32:1642.43.37" data-mmt-position="2_1_1_1_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1642.43.37:1642.43.37" data-mmt-position="2_1_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_1_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_1_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1691.44.10:1691.44.10" data-mmt-position="2_2">g</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1691.44.10:1691.44.10" data-mmt-position="2_2_1"><mrow data-mmt-position="2_2_1_1"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_2_1_1_1">pred_as_sub</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1652.43.47:1657.43.52" data-mmt-position="2_2_1_1_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1657.43.52:1657.43.52" data-mmt-position="2_2_1_1_2">P</mi><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?arrow" data-mmt-position="2_2_1_0">→</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-position="2_2_1_2">ℝ</mo></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1688.44.7:1731.44.50" data-mmt-position="2_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1694.44.13:1694.44.13" data-mmt-position="2_3_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1694.44.13:1694.44.13" data-mmt-position="2_3_1_1"><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="2_3_1_1_1">pred_as_sub</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="2_3_1_1_0"></mspace><mi data-mmt-varref="1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1672.43.67:1672.43.67" data-mmt-position="2_3_1_1_2">P</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1693.44.12:1731.44.50" data-mmt-position="2_3_2"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-position="2_3_2_1">multiplication</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" 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data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?uminus" data-mmt-position="2_3_2_2_2_2_1">uminus</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1698.44.17" data-mmt-position="2_3_2_2_2_2_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1698.44.17" data-mmt-position="2_3_2_2_2_2_2">q</mo><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1704.44.23" data-mmt-position="2_3_2_2_2_3">μ_p</mo><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1722.44.41" data-mmt-position="2_3_2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_1">p</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1708.44.27:1722.44.41" data-mmt-position="2_3_2_2_3_2"><mo class="operator brackets">(</mo><mi data-mmt-varref="2_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1712.44.31:1712.44.31" data-mmt-position="2_3_2_2_3_2_1">f</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1711.44.30:1715.44.34" data-mmt-position="2_3_2_2_3_2_0"></mspace><mi data-mmt-varref="2_3_1" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1714.44.33:1714.44.33" 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class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1697.44.16:1731.44.50" data-mmt-position="2_3_2_3"><mo class="operator brackets">(</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1726.44.45:1731.44.50" data-mmt-position="2_3_2_3_1"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?der" data-mmt-position="2_3_2_3_1_1">der</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/continuity.mmt#1727.44.46:1728.44.47" data-mmt-position="2_3_2_3_1_0"></mspace><mrow 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class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons" id="ContinuityEquationElectrons">ContinuityEquationElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentElectrons">CurrentElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles">DensityHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles">FermiPotentialHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation_electrons" id="ContinuityEquationElectrons?continuity_equation_electrons">continuity_equation_electrons</span></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles" id="ContinuityEquationHoles">ContinuityEquationHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/continuity?CurrentHoles">CurrentHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons">DensityElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons">FermiPotentialElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes" id="ContinuityEquationHoles?continuity_equation_holes">continuity_equation_holes</span></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons" id="ContinuityBoundaryConditionsElectrons">ContinuityBoundaryConditionsElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top" id="ContinuityBoundaryConditionsElectrons?potential_top">potential_top</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ContinuityBoundaryConditionsElectrons_potential_top_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ContinuityBoundaryConditionsElectrons_potential_top_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_top" data-mmt-position="">φ_n_1</mo></math></td></tr></tbody></table><math id="-588024757" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></mrow><annotation-xml encoding="MathML-Content"><csymbol>http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom</csymbol></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom" id="ContinuityBoundaryConditionsElectrons?potential_bottom">potential_bottom</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ContinuityBoundaryConditionsElectrons_potential_bottom_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ContinuityBoundaryConditionsElectrons_potential_bottom_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons?potential_bottom" data-mmt-position="">φ_n_2</mo></math></td></tr></tbody></table><math id="300820980" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></mrow><annotation-xml encoding="MathML-Content"><csymbol>http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top</csymbol></annotation-xml></semantics></math></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles" id="ContinuityBoundaryConditionsHoles">ContinuityBoundaryConditionsHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top" id="ContinuityBoundaryConditionsHoles?potential_top">potential_top</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ContinuityBoundaryConditionsHoles_potential_top_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ContinuityBoundaryConditionsHoles_potential_top_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_top" data-mmt-position="">φ_p_1</mo></math></td></tr></tbody></table><math id="-588024757" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom" data-mmt-position="">U_1</mo></mrow><annotation-xml encoding="MathML-Content"><csymbol>http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom</csymbol></annotation-xml></semantics></math></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom" id="ContinuityBoundaryConditionsHoles?potential_bottom">potential_bottom</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ContinuityBoundaryConditionsHoles_potential_bottom_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ContinuityBoundaryConditionsHoles_potential_bottom_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles?potential_bottom" data-mmt-position="">φ_p_2</mo></math></td></tr></tbody></table><math id="300820980" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top" data-mmt-position="">U_2</mo></mrow><annotation-xml encoding="MathML-Content"><csymbol>http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top</csymbol></annotation-xml></semantics></math></div></div></li></ul></div></div></body></html>
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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/densities.omdoc"></meta><title> densities.omdoc </title><meta name="url" content="http://mathhub.info/MitM/Models/densities.omdoc"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="document"><ul class="doc-body"><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters" id="BandstructureParameters">BandstructureParameters</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" id="BandstructureParameters?effective_density_of_states_conduction_bands">effective_density_of_states_conduction_bands</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_BandstructureParameters_effective_density_of_states_conduction_bands_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_BandstructureParameters_effective_density_of_states_conduction_bands_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-position="">N_c</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" id="BandstructureParameters?effective_density_of_states_valence_bands">effective_density_of_states_valence_bands</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_BandstructureParameters_effective_density_of_states_valence_bands_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_BandstructureParameters_effective_density_of_states_valence_bands_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands" data-mmt-position="">N_v</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" id="BandstructureParameters?conduction_band_edge">conduction_band_edge</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_BandstructureParameters_conduction_band_edge_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_BandstructureParameters_conduction_band_edge_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge" data-mmt-position="">E_c</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" id="BandstructureParameters?valence_band_edge">valence_band_edge</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_BandstructureParameters_valence_band_edge_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_BandstructureParameters_valence_band_edge_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge" data-mmt-position="">E_v</mo></math></td></tr></tbody></table></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons" id="FermiPotentialElectrons">FermiPotentialElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" id="FermiPotentialElectrons?quasi_Fermi_potential">quasi_Fermi_potential</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_FermiPotentialElectrons_quasi_Fermi_potential_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_FermiPotentialElectrons_quasi_Fermi_potential_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential" data-mmt-position="">φ_n</mo></math></td></tr></tbody></table></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles" id="FermiPotentialHoles">FermiPotentialHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" id="FermiPotentialHoles?quasi_Fermi_potential">quasi_Fermi_potential</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_FermiPotentialHoles_quasi_Fermi_potential_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_FermiPotentialHoles_quasi_Fermi_potential_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential" data-mmt-position="">φ_p</mo></math></td></tr></tbody></table></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential" id="ElectrostaticPotential">ElectrostaticPotential</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry">DeviceGeometry</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" id="ElectrostaticPotential?electrostatic_potential">electrostatic_potential</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ElectrostaticPotential_electrostatic_potential_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ElectrostaticPotential_electrostatic_potential_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential" data-mmt-position="">ψ</mo></math></td></tr></tbody></table></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons" id="DensityElectrons">DensityElectrons</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" id="DensityElectrons?density_electrons">density_electrons</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_DensityElectrons_density_electrons_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_DensityElectrons_density_electrons_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons" data-mmt-position="">n</mo></math></td></tr></tbody></table><math id="719413975" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo class="operator brackets">(</mo><mo data-mmt-symref="http://cds.omdoc.org/mmt?mmt?unknown">unknown</mo><mspace width=".2em"></mspace><mo>[</mo><mi data-mmt-position="1">y/2</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="2">x/1</mi><mo>,</mo><mspace width=".2em"></mspace><mi data-mmt-position="3">I/0</mi><mo>]</mo><mspace width=".2em"></mspace><mrow data-mmt-position="4"><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2319.64.5:2319.64.5" data-mmt-position="4_1">x</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mi data-mmt-position="4_1_1">x/1</mi></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2321.64.7:2321.64.7" data-mmt-position="4_2">y</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2321.64.7:2321.64.7" data-mmt-position="4_2_1"><mi data-mmt-position="4_2_1_1">y/2</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-position="4_2_1_0"></mspace><mi data-mmt-varref="4_1" data-mmt-position="4_2_1_2">x</mi></mrow></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2318.64.4:2364.64.50" data-mmt-position="4_3"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-position="4_3_1">multiplication</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_2">N_c</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2324.64.10:2364.64.50" data-mmt-position="4_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2332.64.18" data-mmt-position="4_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/densities.mmt#2330.64.16:2364.64.50" 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class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles" id="DensityHoles">DensityHoles</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState">DeviceOperationState</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants">PhysicalConstants</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?BandstructureParameters">BandstructureParameters</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes" id="DensityHoles?density_holes">density_holes</span> <small><a style="cursor:pointer;" onclick="if 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-<!DOCTYPE html><html><head><meta name="mmturi" content="http://mathhub.info/MitM/Models/device.omdoc"></meta><title> device.omdoc </title><meta name="url" content="http://mathhub.info/MitM/Models/device.omdoc"></meta></head><body><div xmlns="http://www.w3.org/1999/xhtml"><div class="document"><ul class="doc-body"><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?Device" id="Device">Device</span></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry" id="DeviceGeometry">DeviceGeometry</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/device?Device">Device</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" 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data-mmt-position="">Ω</mo></math></td></tr></tbody></table><math id="341123573" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?pred_as_sub" data-mmt-position="1">pred_as_sub</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#506.13.19:521.13.34" data-mmt-position="0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceGeometry?domain_prop" data-mmt-source="http://mathhub.info/MitM/Models/device.mmt#511.13.24:521.13.34" data-mmt-position="2">domain_prop</mo></mrow></mrow><annotation-xml 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diff --git a/export/planetary/narration/poisson.html b/export/planetary/narration/poisson.html
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class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement" id="Displacement">Displacement</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential">ElectrostaticPotential</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonParameters">PoissonParameters</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" id="Displacement?electric_displacement">electric_displacement</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Displacement_electric_displacement_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Displacement_electric_displacement_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement" data-mmt-position="">D</mo></math></td></tr></tbody></table><math id="-1750826648" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#1478.40.5:1478.40.5" data-mmt-position="1">x</mi><mrow 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class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonEquation" id="PoissonEquation">PoissonEquation</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Displacement">Displacement</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonEquation?poisson_equation" id="PoissonEquation?poisson_equation">poisson_equation</span></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium" id="ThermodynamicEquilibrium">ThermodynamicEquilibrium</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?Charge">Charge</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" id="ThermodynamicEquilibrium?equilibrium_potential_top">equilibrium_potential_top</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_ThermodynamicEquilibrium_equilibrium_potential_top_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_ThermodynamicEquilibrium_equilibrium_potential_top_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math 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style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom" data-mmt-position="">ψ_0_1</mo></math></td></tr></tbody></table></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions" id="PoissonBoundaryConditions">PoissonBoundaryConditions</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium">ThermodynamicEquilibrium</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top" id="PoissonBoundaryConditions?potential_top">potential_top</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_PoissonBoundaryConditions_potential_top_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_PoissonBoundaryConditions_potential_top_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top" data-mmt-position="">ψ_1</mo></math></td></tr></tbody></table><math id="147309941" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" 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table-striped table-condensed" id="not_PoissonBoundaryConditions_potential_bottom_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom" data-mmt-position="">ψ_2</mo></math></td></tr></tbody></table><math id="1477157405" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?addition" data-mmt-position="1">addition</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36" data-mmt-position="0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top" 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data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient" data-mmt-position="">r</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" id="Recombination?recombination_rate">recombination_rate</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_Recombination_recombination_rate_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_Recombination_recombination_rate_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate" data-mmt-position="">R</mo></math></td></tr></tbody></table><math id="-187090076" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow data-mmt-position=""><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">[</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#608.17.6:609.17.7" data-mmt-position="1">xn</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#608.17.6:609.17.7" data-mmt-position="1_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#612.17.10:613.17.11" data-mmt-position="2">xp</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#612.17.10:613.17.11" data-mmt-position="2_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#616.17.14:619.17.17" data-mmt-position="3">xφ_n</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#616.17.14:619.17.17" data-mmt-position="3_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">,</mo><mi data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#622.17.20:625.17.23" data-mmt-position="4">xφ_p</mi><mrow class="reconstructed reconstructed-hidden"><mo>:</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#622.17.20:625.17.23" data-mmt-position="4_1">ℝ</mo></mrow><mo data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?lambda" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="0">]</mo><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#606.17.4:690.17.88" data-mmt-position="5"><mo class="operator opt-brackets opt-brackets-hidden">(</mo><mo 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data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#651.17.49:690.17.88" data-mmt-position="5_3_0"></mspace><mn data-mmt-symref="http://mathhub.info/MitM/Foundation?Literals?pos_lit" data-mmt-position="5_3_2">1</mn><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#651.17.49:690.17.88" data-mmt-position="5_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#651.17.49:690.17.88" data-mmt-position="5_3_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/Models?Base?exp" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:658.17.56" data-mmt-position="5_3_3_1">exp</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:689.17.87" data-mmt-position="5_3_3_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#656.17.54:689.17.87" data-mmt-position="5_3_3_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?real_div" data-mmt-position="5_3_3_2_1">real_div</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_2"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-position="5_3_3_2_2_1">multiplication</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_2">q</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#661.17.59:678.17.76" data-mmt-position="5_3_3_2_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?bin_minus" data-mmt-position="5_3_3_2_2_3_1">bin_minus</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#665.17.63:677.17.75" data-mmt-position="5_3_3_2_2_3_0"></mspace><mi data-mmt-varref="3" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#666.17.64:669.17.67" data-mmt-position="5_3_3_2_2_3_2">xφ_n</mi><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#665.17.63:677.17.75" data-mmt-position="5_3_3_2_2_3_0"></mspace><mi data-mmt-varref="4" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#673.17.71:676.17.74" data-mmt-position="5_3_3_2_2_3_3">xφ_p</mi><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_0"></mspace><mrow data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_3"><mo class="operator brackets">(</mo><mo data-mmt-symref="http://mathhub.info/MitM/numberfields?realarith?multiplication" data-mmt-position="5_3_3_2_3_1">multiplication</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_2">k_B</mo><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#682.17.80:688.17.86" data-mmt-position="5_3_3_2_3_3">T</mo><mo class="operator brackets">)</mo></mrow><mspace width=".2em" data-mmt-symref="http://cds.omdoc.org/urtheories?LambdaPi?apply" data-mmt-source="http://mathhub.info/MitM/Models/recombination.mmt#660.17.58:689.17.87" data-mmt-position="5_3_3_2_0"></mspace><mo data-mmt-symref="http://mathhub.info/MitM/Models/device?DeviceOperationState?prf" data-mmt-position="5_3_3_2_4">prf</mo><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator brackets">)</mo></mrow><mo class="operator opt-brackets opt-brackets-hidden">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content"><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?lambda</csymbol><bvar><ci>xn</ci><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol></bvar><bvar><ci>xp</ci><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol></bvar><bvar><ci>xφ_n</ci><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol></bvar><bvar><ci>xφ_p</ci><csymbol>http://mathhub.info/MitM/numberfields?realnumbers?Realnumbers</csymbol></bvar><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realarith?multiplication</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realarith?multiplication</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realarith?multiplication</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient</csymbol><ci>xn</ci><ci>xp</ci></apply><ci>xn</ci></apply><ci>xp</ci></apply><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realarith?bin_minus</csymbol><cn definitionURL="http://mathhub.info/MitM/Foundation?Literals?pos_lit" encoding="mmt-literal">1</cn><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/Models?Base?exp</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realarith?real_div</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realarith?multiplication</csymbol><csymbol>http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge</csymbol><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realarith?bin_minus</csymbol><ci>xφ_n</ci><ci>xφ_p</ci></apply></apply><apply><csymbol>http://cds.omdoc.org/urtheories?LambdaPi?apply</csymbol><csymbol>http://mathhub.info/MitM/numberfields?realarith?multiplication</csymbol><csymbol>http://mathhub.info/MitM/Models?PhysicalConstants?Boltzmann_constant</csymbol><csymbol>http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur</csymbol></apply><csymbol>http://mathhub.info/MitM/Models/device?DeviceOperationState?prf</csymbol></apply></apply></apply></apply></apply></annotation-xml></semantics></math></div></div></li><li class="mref"><div class="theory"><div class="theory-header"><span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination" id="SpontaneousRecombination">SpontaneousRecombination</span></div><div class="include"><span class="keyword">includes</span> <span data-mmt-symref="http://mathhub.info/MitM/Models/recombination?Recombination">Recombination</span></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" id="SpontaneousRecombination?spontaneous_recombination_coefficient">spontaneous_recombination_coefficient</span> <small><a style="cursor:pointer;" onclick="if (jQuery(this).html() == 'Show Notations') {jQuery(this).html('Hide Notations')} else {jQuery(this).html('Show Notations')};jQuery(document.getElementById('not_SpontaneousRecombination_spontaneous_recombination_coefficient_')).toggle( 'fold' );">Show Notations</a></small><table class="table table-striped table-condensed" id="not_SpontaneousRecombination_spontaneous_recombination_coefficient_" style="display:none;"><thead><tr><th>Languages</th><th>Arguments</th><th>Rendering</th></tr></thead><tbody><tr><td></td><td>0</td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient" data-mmt-position="">B</mo></math></td></tr></tbody></table></div><div class="constant"><span class="keyword">constant</span> <span class="name" data-mmt-symref="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?axiom_spontaneous" id="SpontaneousRecombination?axiom_spontaneous">axiom_spontaneous</span></div></div></li></ul></div></div></body></html>
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diff --git a/narration/VanRoosbroeck.omdoc b/narration/VanRoosbroeck.omdoc
deleted file mode 100644
index cc3e3df..0000000
--- a/narration/VanRoosbroeck.omdoc
+++ /dev/null
@@ -1,11 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<omdoc base="http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#0.0.0:1044.22.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#104.3.0:665.13.6"/></metadata>This is a theory containing the stationary van Roosbroeck system 
-     describung the charge transport of electrons and holes
-     in a one-dimensional (layered) semiconductor device. 
-     The model includes electron and hole 
-     densities according the Boltzmann approximation and 
-     spontaneous radiative recombination processes only. 
-     Furthermore the material properties such as band edges, 
-     density of states, mobilties are assumed to be
-     homogenous (spatially constant). Also a homogenous device
-     temperature is assumed.</opaque><mref name="[http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck]" target="http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#666.14.0:687.14.21"/></metadata></mref></omdoc>
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diff --git a/narration/constants.omdoc b/narration/constants.omdoc
deleted file mode 100644
index 3983c5d..0000000
--- a/narration/constants.omdoc
+++ /dev/null
@@ -1,2 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<omdoc base="http://mathhub.info/MitM/Models/constants.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#0.0.0:1767.44.0"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#140.4.0:201.4.61"/></metadata>This is a theory containing general physical constants</opaque><mref name="[http://mathhub.info/MitM/Models?PhysicalConstants]" target="http://mathhub.info/MitM/Models?PhysicalConstants"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#202.5.0:227.5.25"/></metadata></mref><mref name="[http://mathhub.info/MitM/Models?Base]" target="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#542.14.0:554.14.12"/></metadata></mref></omdoc>
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diff --git a/narration/continuity.omdoc b/narration/continuity.omdoc
deleted file mode 100644
index 4a4ac07..0000000
--- a/narration/continuity.omdoc
+++ /dev/null
@@ -1,5 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<omdoc base="http://mathhub.info/MitM/Models/continuity.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#0.0.0:3601.97.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#101.3.0:188.4.25"/></metadata>This is a theory containing the mobilitiy parameters of 
-     the semiconductor.</opaque><mref name="[http://mathhub.info/MitM/Models/continuity?Mobilities]" target="http://mathhub.info/MitM/Models/continuity?Mobilities"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#190.6.0:208.6.18"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#414.13.0:489.13.75"/></metadata>This is a theory containing the expression for the electron current.</opaque><mref name="[http://mathhub.info/MitM/Models/continuity?CurrentElectrons]" target="http://mathhub.info/MitM/Models/continuity?CurrentElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#492.15.0:516.15.24"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1093.30.0:1164.30.71"/></metadata>This is a theory containing the expression for the hole current.</opaque><mref name="[http://mathhub.info/MitM/Models/continuity?CurrentHoles]" target="http://mathhub.info/MitM/Models/continuity?CurrentHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1166.32.0:1186.32.20"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1749.47.0:1826.47.77"/></metadata>This is a theory containing the continuity equation for the electrons.</opaque><mref name="[http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons]" target="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1829.49.0:1864.49.35"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2280.62.0:2353.62.73"/></metadata>This is a theory containing the continuity equation for the holes.</opaque><mref name="[http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles]" target="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2357.64.0:2388.64.31"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2796.77.0:2921.78.60"/></metadata>This is a theory containing the boundary conditions for the
-     electron continuity equation modeling Ohmic contacts.</opaque><mref name="[http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons]" target="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2925.80.0:2970.80.45"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3204.88.0:3326.89.57"/></metadata>This is a theory containing the boundary conditions for the
-     holes continuity equation modeling Ohmic contacts.</opaque><mref name="[http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles]" target="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3330.91.0:3371.91.41"/></metadata></mref></omdoc>
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diff --git a/narration/densities.omdoc b/narration/densities.omdoc
deleted file mode 100644
index 86c8774..0000000
--- a/narration/densities.omdoc
+++ /dev/null
@@ -1,11 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<omdoc base="http://mathhub.info/MitM/Models/densities.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#0.0.0:2797.78.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#100.3.0:191.4.25"/></metadata>This is a theory containing the bandstructure parameters of 
-     the semiconductor.</opaque><mref name="[http://mathhub.info/MitM/Models/densities?BandstructureParameters]" target="http://mathhub.info/MitM/Models/densities?BandstructureParameters"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#198.6.0:229.6.31"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#810.20.0:961.22.45"/></metadata>This is a theory containing spatial variation of the 
-     quasi-Fermi potential for the electrons. 
-     This is a basic variable of the system</opaque><mref name="[http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons]" target="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#965.24.0:996.24.31"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1190.31.0:1348.33.56"/></metadata>This is a theory containing spatial variation of the 
-     quasi-Fermi potential for the holes. 
-     This is a basic variable (unknown) of the system.</opaque><mref name="[http://mathhub.info/MitM/Models/densities?FermiPotentialHoles]" target="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1355.35.0:1382.35.27"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1571.42.0:1717.44.56"/></metadata>This is a theory containing spatial variation of the 
-     electrostatic potential. 
-     This is a basic variable (unknown) of the system.</opaque><mref name="[http://mathhub.info/MitM/Models/densities?ElectrostaticPotential]" target="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1721.46.0:1751.46.30"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1927.54.0:2045.55.61"/></metadata>This is a theory containing state equation for the 
-	   electron density for the Boltzmann approximation (exp).</opaque><mref name="[http://mathhub.info/MitM/Models/densities?DensityElectrons]" target="http://mathhub.info/MitM/Models/densities?DensityElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2053.57.0:2077.57.24"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2375.68.0:2489.69.57"/></metadata>This is a theory containing state equation for the 
-	   hole density for the Boltzmann approximation (exp).</opaque><mref name="[http://mathhub.info/MitM/Models/densities?DensityHoles]" target="http://mathhub.info/MitM/Models/densities?DensityHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#2496.71.0:2516.71.20"/></metadata></mref></omdoc>
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diff --git a/narration/device.omdoc b/narration/device.omdoc
deleted file mode 100644
index 0a23345..0000000
--- a/narration/device.omdoc
+++ /dev/null
@@ -1,3 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<omdoc base="http://mathhub.info/MitM/Models/device.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#0.0.0:1797.60.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#97.3.0:168.3.71"/></metadata>This theory intentionally left empty. It has a narrative in sTeX</opaque><mref name="[http://mathhub.info/MitM/Models/device?Device]" target="http://mathhub.info/MitM/Models/device?Device"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#169.4.0:183.4.14"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#188.6.0:254.6.66"/></metadata>This is a theory containing description of device geometry.</opaque><mref name="[http://mathhub.info/MitM/Models/device?DeviceGeometry]" target="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#255.7.0:277.7.22"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1016.36.0:1085.36.69"/></metadata>This is a theory containing description of the doping profile.</opaque><mref name="[http://mathhub.info/MitM/Models/device?DopingProfile]" target="http://mathhub.info/MitM/Models/device?DopingProfile"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1092.38.0:1113.38.21"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1235.45.0:1365.46.58"/></metadata>This is a theory containing a description the the operating state,
-     that means applied voltages and device temperature.</opaque><mref name="[http://mathhub.info/MitM/Models/device?DeviceOperationState]" target="http://mathhub.info/MitM/Models/device?DeviceOperationState"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1367.48.0:1395.48.28"/></metadata></mref></omdoc>
\ No newline at end of file
diff --git a/narration/poisson.omdoc b/narration/poisson.omdoc
deleted file mode 100644
index 2f0b01a..0000000
--- a/narration/poisson.omdoc
+++ /dev/null
@@ -1,5 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<omdoc base="http://mathhub.info/MitM/Models/poisson.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#0.0.0:2833.83.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#98.3.0:202.4.28"/></metadata>This is a theory containing the static dielectric permitivity constant
-     of the semiconductor.</opaque><mref name="[http://mathhub.info/MitM/Models/poisson?PoissonParameters]" target="http://mathhub.info/MitM/Models/poisson?PoissonParameters"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#209.6.0:234.6.25"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#492.12.0:596.13.44"/></metadata>This is a theory containing the total charge entering 
-     the right side of Poisson's equation.</opaque><mref name="[http://mathhub.info/MitM/Models/poisson?Charge]" target="http://mathhub.info/MitM/Models/poisson?Charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#599.15.0:613.15.14"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1187.32.0:1248.32.61"/></metadata>This is a theory containing the electric displacement.</opaque><mref name="[http://mathhub.info/MitM/Models/poisson?Displacement]" target="http://mathhub.info/MitM/Models/poisson?Displacement"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1252.34.0:1272.34.20"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1507.43.0:1560.43.53"/></metadata>This is a theory containing Poissons equation.</opaque><mref name="[http://mathhub.info/MitM/Models/poisson?PoissonEquation]" target="http://mathhub.info/MitM/Models/poisson?PoissonEquation"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1562.45.0:1585.45.23"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1767.55.0:1857.56.34"/></metadata>This is a theory containing build-in potential in 
-     thermodynamic equilibrium.</opaque><mref name="[http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium]" target="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1859.58.0:1891.58.32"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2305.72.0:2387.72.82"/></metadata>This is a theory containing the boundary values for the Poisson eqauation.</opaque><mref name="[http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions]" target="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2391.74.0:2424.74.33"/></metadata></mref></omdoc>
\ No newline at end of file
diff --git a/narration/recombination.omdoc b/narration/recombination.omdoc
deleted file mode 100644
index 9947045..0000000
--- a/narration/recombination.omdoc
+++ /dev/null
@@ -1,3 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<omdoc base="http://mathhub.info/MitM/Models/recombination.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#0.0.0:1091.29.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#104.3.0:192.4.28"/></metadata>This is a theory containing the general structure for 
-     a recombination rate.</opaque><mref name="[http://mathhub.info/MitM/Models/recombination?Recombination]" target="http://mathhub.info/MitM/Models/recombination?Recombination"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#199.6.0:220.6.21"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#705.21.0:768.21.63"/></metadata>Kernel for spontaneous recombination with coefficient B.</opaque><mref name="[http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination]" target="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#769.22.0:801.22.32"/></metadata></mref></omdoc>
\ No newline at end of file
diff --git a/relational/VanRoosbroeck.rel b/relational/VanRoosbroeck.rel
deleted file mode 100644
index 5154edb..0000000
--- a/relational/VanRoosbroeck.rel
+++ /dev/null
@@ -1,3 +0,0 @@
-document http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc
-Declares http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc/opaque_873643650
-Declares http://mathhub.info/MitM/Models/VanRoosbroeck.omdoc http://mathhub.info/MitM/Models/VanRoosbroeck?VanRoosbroeck
diff --git a/relational/constants.rel b/relational/constants.rel
deleted file mode 100644
index 1aa40ff..0000000
--- a/relational/constants.rel
+++ /dev/null
@@ -1,4 +0,0 @@
-document http://mathhub.info/MitM/Models/constants.omdoc
-Declares http://mathhub.info/MitM/Models/constants.omdoc http://mathhub.info/MitM/Models/constants.omdoc/opaque_619676994
-Declares http://mathhub.info/MitM/Models/constants.omdoc http://mathhub.info/MitM/Models?PhysicalConstants
-Declares http://mathhub.info/MitM/Models/constants.omdoc http://mathhub.info/MitM/Models?Base
diff --git a/relational/continuity.rel b/relational/continuity.rel
deleted file mode 100644
index 11f9509..0000000
--- a/relational/continuity.rel
+++ /dev/null
@@ -1,15 +0,0 @@
-document http://mathhub.info/MitM/Models/continuity.omdoc
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity.omdoc/opaque_-2106408558
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity?Mobilities
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity.omdoc/opaque_690021467
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity?CurrentElectrons
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity.omdoc/opaque_-341330314
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity?CurrentHoles
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity.omdoc/opaque_17671932
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity.omdoc/opaque_685112538
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity.omdoc/opaque_-565927950
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity.omdoc/opaque_-2023937919
-Declares http://mathhub.info/MitM/Models/continuity.omdoc http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles
diff --git a/relational/densities.rel b/relational/densities.rel
deleted file mode 100644
index abae953..0000000
--- a/relational/densities.rel
+++ /dev/null
@@ -1,13 +0,0 @@
-document http://mathhub.info/MitM/Models/densities.omdoc
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities.omdoc/opaque_-1143466684
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities.omdoc/opaque_1733455611
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities.omdoc/opaque_-2046841392
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities?FermiPotentialHoles
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities.omdoc/opaque_-102717610
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities.omdoc/opaque_439442021
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities?DensityElectrons
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities.omdoc/opaque_-869451777
-Declares http://mathhub.info/MitM/Models/densities.omdoc http://mathhub.info/MitM/Models/densities?DensityHoles
diff --git a/relational/device.rel b/relational/device.rel
deleted file mode 100644
index 76eba98..0000000
--- a/relational/device.rel
+++ /dev/null
@@ -1,9 +0,0 @@
-document http://mathhub.info/MitM/Models/device.omdoc
-Declares http://mathhub.info/MitM/Models/device.omdoc http://mathhub.info/MitM/Models/device.omdoc/opaque_-374580863
-Declares http://mathhub.info/MitM/Models/device.omdoc http://mathhub.info/MitM/Models/device?Device
-Declares http://mathhub.info/MitM/Models/device.omdoc http://mathhub.info/MitM/Models/device.omdoc/opaque_-121207145
-Declares http://mathhub.info/MitM/Models/device.omdoc http://mathhub.info/MitM/Models/device?DeviceGeometry
-Declares http://mathhub.info/MitM/Models/device.omdoc http://mathhub.info/MitM/Models/device.omdoc/opaque_-1469145314
-Declares http://mathhub.info/MitM/Models/device.omdoc http://mathhub.info/MitM/Models/device?DopingProfile
-Declares http://mathhub.info/MitM/Models/device.omdoc http://mathhub.info/MitM/Models/device.omdoc/opaque_-1972481937
-Declares http://mathhub.info/MitM/Models/device.omdoc http://mathhub.info/MitM/Models/device?DeviceOperationState
diff --git a/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.rel b/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.rel
deleted file mode 100644
index 5b7e869..0000000
--- a/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.rel
+++ /dev/null
@@ -1,4 +0,0 @@
-theory http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons
-HasMeta http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models?Base
-Declares http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation
-constant http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation
diff --git a/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.rel b/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.rel
deleted file mode 100644
index df666b1..0000000
--- a/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.rel
+++ /dev/null
@@ -1,29 +0,0 @@
-theory http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles
-HasMeta http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/continuity?CurrentHoles
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?FermiPotentialHoles
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?DensityHoles
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/device?DeviceOperationState
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?Permittivity
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?realarith
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?realnumbers
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?integernumbers
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?ratarith
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?intarith
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?natarith
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?Density
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/continuity?Mobilities
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?CurrentDensity
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?DensityElectrons
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/recombination?Recombination
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?RecombinationRate
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-Declares http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes
-constant http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes
diff --git a/relational/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.rel b/relational/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.rel
deleted file mode 100644
index 5b0910d..0000000
--- a/relational/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.rel
+++ /dev/null
@@ -1,21 +0,0 @@
-theory http://mathhub.info/MitM/Models/continuity?CurrentElectrons
-HasMeta http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/densities?DensityElectrons
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/device?DeviceOperationState
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models?Permittivity
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?realarith
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?realnumbers
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?integernumbers
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?ratarith
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?intarith
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?natarith
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/continuity?Mobilities
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models?CurrentDensity
-Declares http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons_law
-constant http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons_law
diff --git a/relational/http..mathhub.info/MitM/Models/continuity/$Current$Holes.rel b/relational/http..mathhub.info/MitM/Models/continuity/$Current$Holes.rel
deleted file mode 100644
index 42a3d8e..0000000
--- a/relational/http..mathhub.info/MitM/Models/continuity/$Current$Holes.rel
+++ /dev/null
@@ -1,24 +0,0 @@
-theory http://mathhub.info/MitM/Models/continuity?CurrentHoles
-HasMeta http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/densities?FermiPotentialHoles
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/densities?DensityHoles
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/device?DeviceOperationState
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models?Permittivity
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?realarith
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?realnumbers
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?integernumbers
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?ratarith
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?intarith
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?natarith
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models?Density
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/continuity?Mobilities
-Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models?CurrentDensity
-Declares http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes_law
-constant http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes_law
diff --git a/relational/http..mathhub.info/MitM/Models/continuity/$Mobilities.rel b/relational/http..mathhub.info/MitM/Models/continuity/$Mobilities.rel
deleted file mode 100644
index fa685cf..0000000
--- a/relational/http..mathhub.info/MitM/Models/continuity/$Mobilities.rel
+++ /dev/null
@@ -1,6 +0,0 @@
-theory http://mathhub.info/MitM/Models/continuity?Mobilities
-HasMeta http://mathhub.info/MitM/Models/continuity?Mobilities http://mathhub.info/MitM/Models?Base
-Declares http://mathhub.info/MitM/Models/continuity?Mobilities http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons
-constant http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_electrons
-Declares http://mathhub.info/MitM/Models/continuity?Mobilities http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes
-constant http://mathhub.info/MitM/Models/continuity?Mobilities?mobility_holes
diff --git a/relational/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.rel b/relational/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.rel
deleted file mode 100644
index fb1bb49..0000000
--- a/relational/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.rel
+++ /dev/null
@@ -1,11 +0,0 @@
-theory http://mathhub.info/MitM/Models/densities?BandstructureParameters
-HasMeta http://mathhub.info/MitM/Models/densities?BandstructureParameters http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/densities?BandstructureParameters http://mathhub.info/MitM/Models?Density
-Declares http://mathhub.info/MitM/Models/densities?BandstructureParameters http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands
-constant http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands
-Declares http://mathhub.info/MitM/Models/densities?BandstructureParameters http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands
-constant http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands
-Declares http://mathhub.info/MitM/Models/densities?BandstructureParameters http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge
-constant http://mathhub.info/MitM/Models/densities?BandstructureParameters?conduction_band_edge
-Declares http://mathhub.info/MitM/Models/densities?BandstructureParameters http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge
-constant http://mathhub.info/MitM/Models/densities?BandstructureParameters?valence_band_edge
diff --git a/relational/http..mathhub.info/MitM/Models/densities/$Density$Electrons.rel b/relational/http..mathhub.info/MitM/Models/densities/$Density$Electrons.rel
deleted file mode 100644
index b0bd66f..0000000
--- a/relational/http..mathhub.info/MitM/Models/densities/$Density$Electrons.rel
+++ /dev/null
@@ -1,9 +0,0 @@
-theory http://mathhub.info/MitM/Models/densities?DensityElectrons
-HasMeta http://mathhub.info/MitM/Models/densities?DensityElectrons http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/densities?DensityElectrons http://mathhub.info/MitM/Models/device?DeviceOperationState
-Includes http://mathhub.info/MitM/Models/densities?DensityElectrons http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/densities?DensityElectrons http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/densities?DensityElectrons http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/densities?DensityElectrons http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Declares http://mathhub.info/MitM/Models/densities?DensityElectrons http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons
-constant http://mathhub.info/MitM/Models/densities?DensityElectrons?density_electrons
diff --git a/relational/http..mathhub.info/MitM/Models/densities/$Density$Holes.rel b/relational/http..mathhub.info/MitM/Models/densities/$Density$Holes.rel
deleted file mode 100644
index 3e22f7d..0000000
--- a/relational/http..mathhub.info/MitM/Models/densities/$Density$Holes.rel
+++ /dev/null
@@ -1,9 +0,0 @@
-theory http://mathhub.info/MitM/Models/densities?DensityHoles
-HasMeta http://mathhub.info/MitM/Models/densities?DensityHoles http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/densities?DensityHoles http://mathhub.info/MitM/Models/device?DeviceOperationState
-Includes http://mathhub.info/MitM/Models/densities?DensityHoles http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/densities?DensityHoles http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/densities?DensityHoles http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/densities?DensityHoles http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Declares http://mathhub.info/MitM/Models/densities?DensityHoles http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes
-constant http://mathhub.info/MitM/Models/densities?DensityHoles?density_holes
diff --git a/relational/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.rel b/relational/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.rel
deleted file mode 100644
index 2730280..0000000
--- a/relational/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.rel
+++ /dev/null
@@ -1,6 +0,0 @@
-theory http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-HasMeta http://mathhub.info/MitM/Models/densities?ElectrostaticPotential http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/densities?ElectrostaticPotential http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/densities?ElectrostaticPotential http://mathhub.info/MitM/Models/device?Device
-Declares http://mathhub.info/MitM/Models/densities?ElectrostaticPotential http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential
-constant http://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potential
diff --git a/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.rel b/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.rel
deleted file mode 100644
index f11fa2e..0000000
--- a/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.rel
+++ /dev/null
@@ -1,5 +0,0 @@
-theory http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
-HasMeta http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons http://mathhub.info/MitM/Models/device?DeviceGeometry
-Declares http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential
-constant http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential
diff --git a/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.rel b/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.rel
deleted file mode 100644
index 684a98a..0000000
--- a/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.rel
+++ /dev/null
@@ -1,5 +0,0 @@
-theory http://mathhub.info/MitM/Models/densities?FermiPotentialHoles
-HasMeta http://mathhub.info/MitM/Models/densities?FermiPotentialHoles http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/densities?FermiPotentialHoles http://mathhub.info/MitM/Models/device?DeviceGeometry
-Declares http://mathhub.info/MitM/Models/densities?FermiPotentialHoles http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential
-constant http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential
diff --git a/relational/http..mathhub.info/MitM/Models/poisson/$Charge.rel b/relational/http..mathhub.info/MitM/Models/poisson/$Charge.rel
deleted file mode 100644
index f8b3fad..0000000
--- a/relational/http..mathhub.info/MitM/Models/poisson/$Charge.rel
+++ /dev/null
@@ -1,16 +0,0 @@
-theory http://mathhub.info/MitM/Models/poisson?Charge
-HasMeta http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/device?DopingProfile
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/poisson?PoissonParameters
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/densities?DensityElectrons
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/device?DeviceOperationState
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/densities?DensityHoles
-Includes http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/densities?FermiPotentialHoles
-Declares http://mathhub.info/MitM/Models/poisson?Charge http://mathhub.info/MitM/Models/poisson?Charge?total_charge
-constant http://mathhub.info/MitM/Models/poisson?Charge?total_charge
diff --git a/relational/http..mathhub.info/MitM/Models/poisson/$Displacement.rel b/relational/http..mathhub.info/MitM/Models/poisson/$Displacement.rel
deleted file mode 100644
index 19fd02d..0000000
--- a/relational/http..mathhub.info/MitM/Models/poisson/$Displacement.rel
+++ /dev/null
@@ -1,8 +0,0 @@
-theory http://mathhub.info/MitM/Models/poisson?Displacement
-HasMeta http://mathhub.info/MitM/Models/poisson?Displacement http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/poisson?Displacement http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-Includes http://mathhub.info/MitM/Models/poisson?Displacement http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/poisson?Displacement http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/poisson?Displacement http://mathhub.info/MitM/Models/poisson?PoissonParameters
-Declares http://mathhub.info/MitM/Models/poisson?Displacement http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement
-constant http://mathhub.info/MitM/Models/poisson?Displacement?electric_displacement
diff --git a/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.rel b/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.rel
index 41a2a9f..faed7d2 100644
--- a/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.rel
+++ b/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.rel
@@ -1,29 +1,6 @@
 theory http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions
 HasMeta http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models?Base
 Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/poisson?Charge
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/device?DopingProfile
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models?Density
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/poisson?PoissonParameters
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/densities?DensityElectrons
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/device?DeviceOperationState
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models?Permittivity
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?realarith
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?realnumbers
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?integernumbers
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?ratarith
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?intarith
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?natarith
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/densities?DensityHoles
-Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/densities?FermiPotentialHoles
 Declares http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top
 constant http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_top
 Declares http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions?potential_bottom
diff --git a/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.rel b/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.rel
index f14102e..d1de0b1 100644
--- a/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.rel
+++ b/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.rel
@@ -1,28 +1,6 @@
 theory http://mathhub.info/MitM/Models/poisson?PoissonEquation
 HasMeta http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models?Base
 Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/poisson?Charge
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/device?DopingProfile
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models?Density
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/poisson?PoissonParameters
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/densities?DensityElectrons
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/device?DeviceOperationState
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models?Permittivity
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?realarith
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?realnumbers
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?integernumbers
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?ratarith
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?intarith
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?natarith
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/densities?DensityHoles
-Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/densities?FermiPotentialHoles
 Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/poisson?Displacement
 Declares http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/poisson?PoissonEquation?poisson_equation
 constant http://mathhub.info/MitM/Models/poisson?PoissonEquation?poisson_equation
diff --git a/relational/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.rel b/relational/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.rel
index 55b2fc3..2dc995e 100644
--- a/relational/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.rel
+++ b/relational/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.rel
@@ -1,28 +1,6 @@
 theory http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium
 HasMeta http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models?Base
 Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/poisson?Charge
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/device?DopingProfile
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models?Density
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/poisson?PoissonParameters
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/densities?DensityElectrons
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/device?DeviceOperationState
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models?Permittivity
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?realarith
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?realnumbers
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?integernumbers
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?ratarith
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?intarith
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?natarith
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/densities?DensityHoles
-Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/densities?FermiPotentialHoles
 Declares http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top
 constant http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_top
 Declares http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottom
diff --git a/relational/poisson.rel b/relational/poisson.rel
deleted file mode 100644
index c2b498d..0000000
--- a/relational/poisson.rel
+++ /dev/null
@@ -1,13 +0,0 @@
-document http://mathhub.info/MitM/Models/poisson.omdoc
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson.omdoc/opaque_1687517700
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson?PoissonParameters
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson.omdoc/opaque_860198275
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson?Charge
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson.omdoc/opaque_1814960740
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson?Displacement
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson.omdoc/opaque_-1320472146
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson?PoissonEquation
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson.omdoc/opaque_4800748
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson.omdoc/opaque_176234208
-Declares http://mathhub.info/MitM/Models/poisson.omdoc http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions
diff --git a/relational/recombination.rel b/relational/recombination.rel
deleted file mode 100644
index 597c3fa..0000000
--- a/relational/recombination.rel
+++ /dev/null
@@ -1,5 +0,0 @@
-document http://mathhub.info/MitM/Models/recombination.omdoc
-Declares http://mathhub.info/MitM/Models/recombination.omdoc http://mathhub.info/MitM/Models/recombination.omdoc/opaque_-97999180
-Declares http://mathhub.info/MitM/Models/recombination.omdoc http://mathhub.info/MitM/Models/recombination?Recombination
-Declares http://mathhub.info/MitM/Models/recombination.omdoc http://mathhub.info/MitM/Models/recombination.omdoc/opaque_-1649778205
-Declares http://mathhub.info/MitM/Models/recombination.omdoc http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination
-- 
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