Home » railML newsgroups » railml.rollingstock » TrainResistance definition in MathML
TrainResistance definition in MathML [message #1213] Tue, 27 August 2013 12:17 Go to next message
Thomas Albrecht is currently offline  Thomas Albrecht
Messages: 2
Registered: August 2013
Junior Member
Dear colleagues,
we want to exchange rolling stock data for train running simulation in
the context of a traffic management system.
Therefore we need a description of the train resistance, the wiki and
rolling stock schema say:
http://wiki.railml.org/index.php?title=RS:trainResistance

There are two possibilities to describe the resistance: 1) valueTable or
2)mathml.
ValueTable should be straightforward, but in practice, it seems that
rather formulas of the kind
fW = A + C * (V + X) (A, C parameters, V speed of train, X wind speed)
or similar are given, which is probably better formulated using MathML.
There is no documentation so far on the usage of MathML, therefore some
questions here for the forum on experiences:

A) Has anyone worked with MathML?
B) Should we use standard symbols and units in order to make it
understandable?

Best regards
Thomas Albrecht
TU Dresden
Chair for Traffic Control Systems and Process Automation
tu-dresden.de/vlp
Re: TrainResistance definition in MathML [message #1214 is a reply to message #1213] Thu, 29 August 2013 14:05 Go to previous messageGo to next message
Susanne Wunsch is currently offline  Susanne Wunsch
Messages: 180
Registered: March 2008
Senior Member
Hello Thomas,

Thomas Albrecht <ThomasKAlbrecht(at)tu-dresdende> writes:
> or 2)mathml.
> ValueTable should be straightforward, but in practice, it seems that
> rather formulas of the kind
> fW = A + C * (V + X) (A, C parameters, V speed of train, X wind speed)
> or similar are given, which is probably better formulated using MathML.
>
> A) Has anyone worked with MathML?

No experiences from my side.

> B) Should we use standard symbols and units in order to make it
> understandable?

Of course! ;-)

I checked the current MathML standard (version 3.0) and tried to make a
proposal for usage in the railML context.

MathML is now widely understood in different tools, but there seems to be
great differences between the MathML versions and the degree of
implementation completeness.

* Apache OpenOffice4 displays the "Presentation-Mode" if it's separated
into a file.
* Firefox23 displays the "Presentation-Mode" if it's separated into a
file without the "Content-Mode".
* LibreOffice4.1 doesn't understand this MathML-version.

I would be interested in further reports about usability of the
following MathML code: Mathematica?, MATLAB?, M$ Office?, IE?, Chrome?,
Opera? ...

Copy the following lines into a file. Maybe you should snip the MathML
part out for testing in MathML-aware tools.

?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE math [
<!ENTITY middot "&#x000B7;"> <!--MIDDLE DOT -->
<!ENTITY InvisibleTimes "&#x02062;" ><!--INVISIBLE TIMES -->
]>
<!-- First proposal for definition of formulas inside railML elements
Following references were used:
* Mathematical Markup Language (MathML) Version 3.0, Chapter 5 Mixing Markup Languages for Mathematical Expressions,
W3C Recommendation 21 October 2010: http://www.w3.org/TR/MathML3/chapter5.html#mixing.parallel
* Units in MathML,
W3C Working Group Note 10 November 2003: http://www.w3.org/TR/mathml-units/
* Definition identifier URNs in OGC namespace, Version 1.3, OGC document number 07-092r3
Open Geospatial Consortium Inc.: http://portal.opengeospatial.org/files/?artifact_id=30575
* The Unified Code for Units of Measure (UCUM), XML releases of the formal part of the specification,
UCUM: http://unitsofmeasure.org/ucum-essence.xml
* XML Entity Definitions for Characters, The expanded set of HTML and MathML entity definitions,
W3C Recommendation 01 April 2010: http://www.w3.org/2003/entities/2007/htmlmathml-f.ent
-->
<railml xmlns="http://www.railml.org/schemas/2013"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:mml="http://www.w3.org/1998/Math/MathML">
<rollingstock id="r1">
<metadata>
<dc:title>railML rollingstock sample</dc:title>
<dc:description>Proposal for train resistance definition with a formula</dc:description>
<dc:creator>Susanne Wunsch</dc:creator>
</metadata>
<vehicles>
<vehicle id="v1"/>
<vehicle id="v2"/>
</vehicles>
<formations>
<formation id="f1">
<trainOrder>
<vehicleRef orderNumber="1" vehicleRef="v1"/>
<vehicleRef orderNumber="2" vehicleRef="v2" vehicleCount="9"/>
</trainOrder>
<trainResistance>
<mml:math>
<mml:semantics>
<!-- Content mathematical expression: 17,456 N + 5,677 Ns/m * v + 1,234 Ns^2/m^2 * v^2 -->
<!-- TODO: Currently missing: definition of uom for variable 'v'-->
<mml:apply>
<mml:plus/>
<mml:apply>
<mml:times/>
<mml:cn type="constant">17,456</mml:cn>
<mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::N">N</mml:csymbol>
</mml:apply>
<mml:apply>
<mml:times/>
<mml:cn href="">5,677</mml:cn>
<mml:apply>
<mml:times/>
<mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::N">N</mml:csymbol>
<mml:apply>
<mml:divide/>
<mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::s">s</mml:csymbol>
<mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::m">m</mml:csymbol>
</mml:apply>
</mml:apply>
<mml:ci>v</mml:ci>
</mml:apply>
<mml:apply>
<mml:times/>
<mml:cn type="constant">1,234</mml:cn>
<mml:apply>
<mml:times/>
<mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::N">N</mml:csymbol>
<mml:apply>
<mml:power/>
<mml:apply>
<mml:divide/>
<mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::s">s</mml:csymbol>
<mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::m">m</mml:csymbol>
</mml:apply>
<mml:cn>2</mml:cn>
</mml:apply>
</mml:apply>
<mml:apply>
<mml:power/>
<mml:ci>v</mml:ci>
<mml:cn>2</mml:cn>
</mml:apply>
</mml:apply>
</mml:apply>
<mml:annotation-xml style="MathML-Presentation">
<!-- Presentation mathematical expression: 17,456 N + 5,677 Ns/m * v + 1,234 Ns^2/m^2 * v^2 -->
<mml:mrow>
<mml:mn>17,456</mml:mn>
<mml:mo rspace='thickmathspace'>&InvisibleTimes;</mml:mo>
<mml:mi mathvariant='normal' class='MathML-Unit'>N</mml:mi>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:mn>5,677</mml:mn>
<mml:mo rspace='thickmathspace'>&InvisibleTimes;</mml:mo>
<mml:mrow>
<mml:mi mathvariant='normal' class='MathML-Unit'>N</mml:mi>
<mml:mo>&middot;</mml:mo>
<mml:mfrac>
<mml:mi mathvariant='normal' class='MathML-Unit'>s</mml:mi>
<mml:mi mathvariant='normal' class='MathML-Unit'>m</mml:mi>
</mml:mfrac>
</mml:mrow>
<mml:mo>&InvisibleTimes;</mml:mo>
<mml:mi>v</mml:mi>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:mn>1,234</mml:mn>
<mml:mo rspace='thickmathspace'>&InvisibleTimes;</mml:mo>
<mml:mrow>
<mml:mi mathvariant='normal' class='MathML-Unit'>N</mml:mi>
<mml:mo>&middot;</mml:mo>
<mml:mfrac>
<mml:msup>
<mml:mi mathvariant='normal' class='MathML-Unit'>s</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:msup>
<mml:mi mathvariant='normal' class='MathML-Unit'>m</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mfrac>
</mml:mrow>
<mml:mo>&InvisibleTimes;</mml:mo>
<mml:msup>
<mml:mi>v</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mrow>
</mml:annotation-xml>
</mml:semantics>
</mml:math>
</trainResistance>
</formation>
</formations>
</rollingstock>
</railml>

Kind regards...
Susanne

--
Susanne Wunsch
Schema Coordinator: railML.common
Re: TrainResistance definition in MathML [message #1215 is a reply to message #1214] Wed, 11 September 2013 19:10 Go to previous messageGo to next message
Joerg von Lingen is currently offline  Joerg von Lingen
Messages: 59
Registered: May 2011
Member
Hi Thomas,

in 2003 I had already presented some ideas about using MathML bearing in mind that there are quite few forms of polynoms
needed for the purpose.

Best Jörg.

Susanne Wunsch wrote the following on 29.08.2013 14:05:
> Hello Thomas,
>
> Thomas Albrecht <ThomasKAlbrecht(at)tu-dresdende> writes:
>> or 2)mathml.
>> ValueTable should be straightforward, but in practice, it seems that
>> rather formulas of the kind
>> fW = A + C * (V + X) (A, C parameters, V speed of train, X wind speed)
>> or similar are given, which is probably better formulated using MathML.
>>
>> A) Has anyone worked with MathML?
>
> No experiences from my side.
>
>> B) Should we use standard symbols and units in order to make it
>> understandable?
>
> Of course! ;-)
>
> I checked the current MathML standard (version 3.0) and tried to make a
> proposal for usage in the railML context.
>
> MathML is now widely understood in different tools, but there seems to be
> great differences between the MathML versions and the degree of
> implementation completeness.
>
> * Apache OpenOffice4 displays the "Presentation-Mode" if it's separated
> into a file.
> * Firefox23 displays the "Presentation-Mode" if it's separated into a
> file without the "Content-Mode".
> * LibreOffice4.1 doesn't understand this MathML-version.
>
> I would be interested in further reports about usability of the
> following MathML code: Mathematica?, MATLAB?, M$ Office?, IE?, Chrome?,
> Opera? ...
>
> Copy the following lines into a file. Maybe you should snip the MathML
> part out for testing in MathML-aware tools.
>
> ?xml version="1.0" encoding="UTF-8"?>
> <!DOCTYPE math [
> <!ENTITY middot "&#x000B7;"> <!--MIDDLE DOT -->
> <!ENTITY InvisibleTimes "&#x02062;" ><!--INVISIBLE TIMES -->
> ]>
> <!-- First proposal for definition of formulas inside railML elements
> Following references were used:
> * Mathematical Markup Language (MathML) Version 3.0, Chapter 5 Mixing Markup Languages for Mathematical Expressions,
> W3C Recommendation 21 October 2010: http://www.w3.org/TR/MathML3/chapter5.html#mixing.parallel
> * Units in MathML,
> W3C Working Group Note 10 November 2003: http://www.w3.org/TR/mathml-units/
> * Definition identifier URNs in OGC namespace, Version 1.3, OGC document number 07-092r3
> Open Geospatial Consortium Inc.: http://portal.opengeospatial.org/files/?artifact_id=30575
> * The Unified Code for Units of Measure (UCUM), XML releases of the formal part of the specification,
> UCUM: http://unitsofmeasure.org/ucum-essence.xml
> * XML Entity Definitions for Characters, The expanded set of HTML and MathML entity definitions,
> W3C Recommendation 01 April 2010: http://www.w3.org/2003/entities/2007/htmlmathml-f.ent
> -->
> <railml xmlns="http://www.railml.org/schemas/2013"
> xmlns:dc="http://purl.org/dc/elements/1.1/"
> xmlns:mml="http://www.w3.org/1998/Math/MathML">
> <rollingstock id="r1">
> <metadata>
> <dc:title>railML rollingstock sample</dc:title>
> <dc:description>Proposal for train resistance definition with a formula</dc:description>
> <dc:creator>Susanne Wunsch</dc:creator>
> </metadata>
> <vehicles>
> <vehicle id="v1"/>
> <vehicle id="v2"/>
> </vehicles>
> <formations>
> <formation id="f1">
> <trainOrder>
> <vehicleRef orderNumber="1" vehicleRef="v1"/>
> <vehicleRef orderNumber="2" vehicleRef="v2" vehicleCount="9"/>
> </trainOrder>
> <trainResistance>
> <mml:math>
> <mml:semantics>
> <!-- Content mathematical expression: 17,456 N + 5,677 Ns/m * v + 1,234 Ns^2/m^2 * v^2 -->
> <!-- TODO: Currently missing: definition of uom for variable 'v'-->
> <mml:apply>
> <mml:plus/>
> <mml:apply>
> <mml:times/>
> <mml:cn type="constant">17,456</mml:cn>
> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::N">N</mml:csymbol>
> </mml:apply>
> <mml:apply>
> <mml:times/>
> <mml:cn href="">5,677</mml:cn>
> <mml:apply>
> <mml:times/>
> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::N">N</mml:csymbol>
> <mml:apply>
> <mml:divide/>
> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::s">s</mml:csymbol>
> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::m">m</mml:csymbol>
> </mml:apply>
> </mml:apply>
> <mml:ci>v</mml:ci>
> </mml:apply>
> <mml:apply>
> <mml:times/>
> <mml:cn type="constant">1,234</mml:cn>
> <mml:apply>
> <mml:times/>
> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::N">N</mml:csymbol>
> <mml:apply>
> <mml:power/>
> <mml:apply>
> <mml:divide/>
> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::s">s</mml:csymbol>
> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::m">m</mml:csymbol>
> </mml:apply>
> <mml:cn>2</mml:cn>
> </mml:apply>
> </mml:apply>
> <mml:apply>
> <mml:power/>
> <mml:ci>v</mml:ci>
> <mml:cn>2</mml:cn>
> </mml:apply>
> </mml:apply>
> </mml:apply>
> <mml:annotation-xml style="MathML-Presentation">
> <!-- Presentation mathematical expression: 17,456 N + 5,677 Ns/m * v + 1,234 Ns^2/m^2 * v^2 -->
> <mml:mrow>
> <mml:mn>17,456</mml:mn>
> <mml:mo rspace='thickmathspace'>&InvisibleTimes;</mml:mo>
> <mml:mi mathvariant='normal' class='MathML-Unit'>N</mml:mi>
> <mml:mo>+</mml:mo>
> <mml:mrow>
> <mml:mn>5,677</mml:mn>
> <mml:mo rspace='thickmathspace'>&InvisibleTimes;</mml:mo>
> <mml:mrow>
> <mml:mi mathvariant='normal' class='MathML-Unit'>N</mml:mi>
> <mml:mo>&middot;</mml:mo>
> <mml:mfrac>
> <mml:mi mathvariant='normal' class='MathML-Unit'>s</mml:mi>
> <mml:mi mathvariant='normal' class='MathML-Unit'>m</mml:mi>
> </mml:mfrac>
> </mml:mrow>
> <mml:mo>&InvisibleTimes;</mml:mo>
> <mml:mi>v</mml:mi>
> </mml:mrow>
> <mml:mo>+</mml:mo>
> <mml:mrow>
> <mml:mn>1,234</mml:mn>
> <mml:mo rspace='thickmathspace'>&InvisibleTimes;</mml:mo>
> <mml:mrow>
> <mml:mi mathvariant='normal' class='MathML-Unit'>N</mml:mi>
> <mml:mo>&middot;</mml:mo>
> <mml:mfrac>
> <mml:msup>
> <mml:mi mathvariant='normal' class='MathML-Unit'>s</mml:mi>
> <mml:mn>2</mml:mn>
> </mml:msup>
> <mml:msup>
> <mml:mi mathvariant='normal' class='MathML-Unit'>m</mml:mi>
> <mml:mn>2</mml:mn>
> </mml:msup>
> </mml:mfrac>
> </mml:mrow>
> <mml:mo>&InvisibleTimes;</mml:mo>
> <mml:msup>
> <mml:mi>v</mml:mi>
> <mml:mn>2</mml:mn>
> </mml:msup>
> </mml:mrow>
> </mml:mrow>
> </mml:annotation-xml>
> </mml:semantics>
> </mml:math>
> </trainResistance>
> </formation>
> </formations>
> </rollingstock>
> </railml>
>
> Kind regards...
> Susanne
>
Re: TrainResistance definition in MathML [message #1216 is a reply to message #1215] Thu, 12 September 2013 10:37 Go to previous message
Thomas Albrecht is currently offline  Thomas Albrecht
Messages: 2
Registered: August 2013
Junior Member
Hi Joerg and Susanne,
Thanks for your replies.
We still need to describe:
- which symbol is used for which physical quantity
- which units of measurements are used for which variable (these might
vary significantly e.g. for speed from m/s, km/h to mph)

Can that be done in MathML or within railML?

The "MathML semantic layer" looks like a good way to represent the
formulas. However, if we exchange data in that way between different
tools, every tool must do some MathML parsing and interpretation of the
nested structure of the formulas. That might be time-critical for some
real-time applications.

Still hope that someone has actually used this in practice for data
exchange and can contribute to that forum ...

Thomas


Am 11.09.2013 19:10, schrieb Joerg von Lingen:
> Hi Thomas,
>
> in 2003 I had already presented some ideas about using MathML bearing in mind that there are quite few forms of polynoms
> needed for the purpose.
>
> Best Jörg.
>
> Susanne Wunsch wrote the following on 29.08.2013 14:05:
>> Hello Thomas,
>>
>> Thomas Albrecht <ThomasKAlbrecht(at)tu-dresdende> writes:
>>> or 2)mathml.
>>> ValueTable should be straightforward, but in practice, it seems that
>>> rather formulas of the kind
>>> fW = A + C * (V + X) (A, C parameters, V speed of train, X wind speed)
>>> or similar are given, which is probably better formulated using MathML.
>>>
>>> A) Has anyone worked with MathML?
>>
>> No experiences from my side.
>>
>>> B) Should we use standard symbols and units in order to make it
>>> understandable?
>>
>> Of course! ;-)
>>
>> I checked the current MathML standard (version 3.0) and tried to make a
>> proposal for usage in the railML context.
>>
>> MathML is now widely understood in different tools, but there seems to be
>> great differences between the MathML versions and the degree of
>> implementation completeness.
>>
>> * Apache OpenOffice4 displays the "Presentation-Mode" if it's separated
>> into a file.
>> * Firefox23 displays the "Presentation-Mode" if it's separated into a
>> file without the "Content-Mode".
>> * LibreOffice4.1 doesn't understand this MathML-version.
>>
>> I would be interested in further reports about usability of the
>> following MathML code: Mathematica?, MATLAB?, M$ Office?, IE?, Chrome?,
>> Opera? ...
>>
>> Copy the following lines into a file. Maybe you should snip the MathML
>> part out for testing in MathML-aware tools.
>>
>> ?xml version="1.0" encoding="UTF-8"?>
>> <!DOCTYPE math [
>> <!ENTITY middot "&#x000B7;"> <!--MIDDLE DOT -->
>> <!ENTITY InvisibleTimes "&#x02062;" ><!--INVISIBLE TIMES -->
>> ]>
>> <!-- First proposal for definition of formulas inside railML elements
>> Following references were used:
>> * Mathematical Markup Language (MathML) Version 3.0, Chapter 5 Mixing Markup Languages for Mathematical Expressions,
>> W3C Recommendation 21 October 2010: http://www.w3.org/TR/MathML3/chapter5.html#mixing.parallel
>> * Units in MathML,
>> W3C Working Group Note 10 November 2003: http://www.w3.org/TR/mathml-units/
>> * Definition identifier URNs in OGC namespace, Version 1.3, OGC document number 07-092r3
>> Open Geospatial Consortium Inc.: http://portal.opengeospatial.org/files/?artifact_id=30575
>> * The Unified Code for Units of Measure (UCUM), XML releases of the formal part of the specification,
>> UCUM: http://unitsofmeasure.org/ucum-essence.xml
>> * XML Entity Definitions for Characters, The expanded set of HTML and MathML entity definitions,
>> W3C Recommendation 01 April 2010: http://www.w3.org/2003/entities/2007/htmlmathml-f.ent
>> -->
>> <railml xmlns="http://www.railml.org/schemas/2013"
>> xmlns:dc="http://purl.org/dc/elements/1.1/"
>> xmlns:mml="http://www.w3.org/1998/Math/MathML">
>> <rollingstock id="r1">
>> <metadata>
>> <dc:title>railML rollingstock sample</dc:title>
>> <dc:description>Proposal for train resistance definition with a formula</dc:description>
>> <dc:creator>Susanne Wunsch</dc:creator>
>> </metadata>
>> <vehicles>
>> <vehicle id="v1"/>
>> <vehicle id="v2"/>
>> </vehicles>
>> <formations>
>> <formation id="f1">
>> <trainOrder>
>> <vehicleRef orderNumber="1" vehicleRef="v1"/>
>> <vehicleRef orderNumber="2" vehicleRef="v2" vehicleCount="9"/>
>> </trainOrder>
>> <trainResistance>
>> <mml:math>
>> <mml:semantics>
>> <!-- Content mathematical expression: 17,456 N + 5,677 Ns/m * v + 1,234 Ns^2/m^2 * v^2 -->
>> <!-- TODO: Currently missing: definition of uom for variable 'v'-->
>> <mml:apply>
>> <mml:plus/>
>> <mml:apply>
>> <mml:times/>
>> <mml:cn type="constant">17,456</mml:cn>
>> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::N">N</mml:csymbol>
>> </mml:apply>
>> <mml:apply>
>> <mml:times/>
>> <mml:cn href="">5,677</mml:cn>
>> <mml:apply>
>> <mml:times/>
>> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::N">N</mml:csymbol>
>> <mml:apply>
>> <mml:divide/>
>> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::s">s</mml:csymbol>
>> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::m">m</mml:csymbol>
>> </mml:apply>
>> </mml:apply>
>> <mml:ci>v</mml:ci>
>> </mml:apply>
>> <mml:apply>
>> <mml:times/>
>> <mml:cn type="constant">1,234</mml:cn>
>> <mml:apply>
>> <mml:times/>
>> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::N">N</mml:csymbol>
>> <mml:apply>
>> <mml:power/>
>> <mml:apply>
>> <mml:divide/>
>> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::s">s</mml:csymbol>
>> <mml:csymbol definitionURL="urn:ogc:def:uom:UCUM::m">m</mml:csymbol>
>> </mml:apply>
>> <mml:cn>2</mml:cn>
>> </mml:apply>
>> </mml:apply>
>> <mml:apply>
>> <mml:power/>
>> <mml:ci>v</mml:ci>
>> <mml:cn>2</mml:cn>
>> </mml:apply>
>> </mml:apply>
>> </mml:apply>
>> <mml:annotation-xml style="MathML-Presentation">
>> <!-- Presentation mathematical expression: 17,456 N + 5,677 Ns/m * v + 1,234 Ns^2/m^2 * v^2 -->
>> <mml:mrow>
>> <mml:mn>17,456</mml:mn>
>> <mml:mo rspace='thickmathspace'>&InvisibleTimes;</mml:mo>
>> <mml:mi mathvariant='normal' class='MathML-Unit'>N</mml:mi>
>> <mml:mo>+</mml:mo>
>> <mml:mrow>
>> <mml:mn>5,677</mml:mn>
>> <mml:mo rspace='thickmathspace'>&InvisibleTimes;</mml:mo>
>> <mml:mrow>
>> <mml:mi mathvariant='normal' class='MathML-Unit'>N</mml:mi>
>> <mml:mo>&middot;</mml:mo>
>> <mml:mfrac>
>> <mml:mi mathvariant='normal' class='MathML-Unit'>s</mml:mi>
>> <mml:mi mathvariant='normal' class='MathML-Unit'>m</mml:mi>
>> </mml:mfrac>
>> </mml:mrow>
>> <mml:mo>&InvisibleTimes;</mml:mo>
>> <mml:mi>v</mml:mi>
>> </mml:mrow>
>> <mml:mo>+</mml:mo>
>> <mml:mrow>
>> <mml:mn>1,234</mml:mn>
>> <mml:mo rspace='thickmathspace'>&InvisibleTimes;</mml:mo>
>> <mml:mrow>
>> <mml:mi mathvariant='normal' class='MathML-Unit'>N</mml:mi>
>> <mml:mo>&middot;</mml:mo>
>> <mml:mfrac>
>> <mml:msup>
>> <mml:mi mathvariant='normal' class='MathML-Unit'>s</mml:mi>
>> <mml:mn>2</mml:mn>
>> </mml:msup>
>> <mml:msup>
>> <mml:mi mathvariant='normal' class='MathML-Unit'>m</mml:mi>
>> <mml:mn>2</mml:mn>
>> </mml:msup>
>> </mml:mfrac>
>> </mml:mrow>
>> <mml:mo>&InvisibleTimes;</mml:mo>
>> <mml:msup>
>> <mml:mi>v</mml:mi>
>> <mml:mn>2</mml:mn>
>> </mml:msup>
>> </mml:mrow>
>> </mml:mrow>
>> </mml:annotation-xml>
>> </mml:semantics>
>> </mml:math>
>> </trainResistance>
>> </formation>
>> </formations>
>> </rollingstock>
>> </railml>
>>
>> Kind regards...
>> Susanne
>>
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