Zur Navigation springen
Zur Suche springen
General
Display information for equation id:math.2536.5 on revision:2536
* Page found: Das elektrochemische Potenzial (eq math.2536.5)
(force rerendering)Occurrences on the following pages:
Hash: d4667193d14e5c0ce351245615fd3514
TeX (original user input):
\delta G=-S\delta T+V\delta p+\int_{{}}^{{}}{{{d}^{3}}r}\sum\limits_{i}^{{}}{{}}\left( {{\mu }_{i}}+{{e}_{i}}\phi \left( {\bar{r}} \right) \right)\delta {{n}_{i}}\left( {\bar{r}} \right)=!=0
LaTeXML (experimentell; verwendet MathML) rendering
MathML (8.841 KB / 1.604 KB) :
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\delta G=-S\delta T+V\delta p+\int{{{d}^{3}}r}\sum% \limits_{i}{{}}\left({{\mu}_{i}}+{{e}_{i}}\phi\left({\bar{r}}\right)\right)% \delta{{n}_{i}}\left({\bar{r}}\right)=!=0}}" display="inline">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1b">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">δ</mi>
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">G</mi>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">-</mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">S</mi>
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">δ</mi>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">T</mi>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">+</mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">V</mi>
<mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">δ</mi>
<mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">p</mi>
<mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">+</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
<mo largeop="true" symmetric="true" id="p1.1.m1.1.13a" xref="p1.1.m1.1.13.cmml">∫</mo>
</mstyle>
<msup id="p1.1.m1.1.40" xref="p1.1.m1.1.40.cmml">
<mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">d</mi>
<mn id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">3</mn>
</msup>
<mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">r</mi>
<mstyle displaystyle="true" id="p1.1.m1.1.41" xref="p1.1.m1.1.41.cmml">
<munder id="p1.1.m1.1.41a" xref="p1.1.m1.1.41.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">∑</mo>
<mi id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">i</mi>
</munder>
</mstyle>
<mrow id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
<mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">(</mo>
<msub id="p1.1.m1.1.42" xref="p1.1.m1.1.42.cmml">
<mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">μ</mi>
<mi id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">i</mi>
</msub>
<mo id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">+</mo>
<msub id="p1.1.m1.1.43" xref="p1.1.m1.1.43.cmml">
<mi id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">e</mi>
<mi id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">i</mi>
</msub>
<mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">ϕ</mi>
<mrow id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
<mo id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">(</mo>
<mover accent="true" id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">
<mi id="p1.1.m1.1.27.2" xref="p1.1.m1.1.27.2.cmml">r</mi>
<mo stretchy="false" id="p1.1.m1.1.27.1" xref="p1.1.m1.1.27.1.cmml">¯</mo>
</mover>
<mo id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">)</mo>
</mrow>
<mo id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">)</mo>
</mrow>
<mi id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">δ</mi>
<msub id="p1.1.m1.1.44" xref="p1.1.m1.1.44.cmml">
<mi id="p1.1.m1.1.31" xref="p1.1.m1.1.31.cmml">n</mi>
<mi id="p1.1.m1.1.32.1" xref="p1.1.m1.1.32.1.cmml">i</mi>
</msub>
<mrow id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">
<mo id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml">(</mo>
<mover accent="true" id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">
<mi id="p1.1.m1.1.34.2" xref="p1.1.m1.1.34.2.cmml">r</mi>
<mo stretchy="false" id="p1.1.m1.1.34.1" xref="p1.1.m1.1.34.1.cmml">¯</mo>
</mover>
<mo id="p1.1.m1.1.35" xref="p1.1.m1.1.35.cmml">)</mo>
</mrow>
<mo id="p1.1.m1.1.36" xref="p1.1.m1.1.36.cmml">=</mo>
<mo lspace="0pt" rspace="3.5pt" id="p1.1.m1.1.37" xref="p1.1.m1.1.37.cmml">!</mo>
<mo id="p1.1.m1.1.38" xref="p1.1.m1.1.38.cmml">=</mo>
<mn id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">0</mn>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
<cerror id="p1.1.m1.1d">
<csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
<csymbol cd="unknown" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">δ</csymbol>
<csymbol cd="unknown" id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">G</csymbol>
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<minus id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
<csymbol cd="unknown" id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">S</csymbol>
<csymbol cd="unknown" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">δ</csymbol>
<csymbol cd="unknown" id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">T</csymbol>
<plus id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<csymbol cd="unknown" id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">V</csymbol>
<csymbol cd="unknown" id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">δ</csymbol>
<csymbol cd="unknown" id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">p</csymbol>
<plus id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12"/>
<int id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
<apply id="p1.1.m1.1.40.cmml" xref="p1.1.m1.1.40">
<csymbol cd="ambiguous" id="p1.1.m1.1.40.1.cmml" xref="p1.1.m1.1.40">superscript</csymbol>
<ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">𝑑</ci>
<cn type="integer" id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">3</cn>
</apply>
<csymbol cd="unknown" id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">r</csymbol>
<apply id="p1.1.m1.1.41.cmml" xref="p1.1.m1.1.41">
<csymbol cd="ambiguous" id="p1.1.m1.1.41.1.cmml" xref="p1.1.m1.1.41">subscript</csymbol>
<sum id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17"/>
<ci id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">𝑖</ci>
</apply>
<cerror id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
<csymbol cd="ambiguous" id="p1.1.m1.1.18a.cmml" xref="p1.1.m1.1.18">fragments</csymbol>
<ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">(</ci>
<apply id="p1.1.m1.1.42.cmml" xref="p1.1.m1.1.42">
<csymbol cd="ambiguous" id="p1.1.m1.1.42.1.cmml" xref="p1.1.m1.1.42">subscript</csymbol>
<ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">𝜇</ci>
<ci id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">𝑖</ci>
</apply>
<plus id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22"/>
<apply id="p1.1.m1.1.43.cmml" xref="p1.1.m1.1.43">
<csymbol cd="ambiguous" id="p1.1.m1.1.43.1.cmml" xref="p1.1.m1.1.43">subscript</csymbol>
<ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">𝑒</ci>
<ci id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">𝑖</ci>
</apply>
<csymbol cd="unknown" id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">ϕ</csymbol>
<cerror id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">
<csymbol cd="ambiguous" id="p1.1.m1.1.15a.cmml" xref="p1.1.m1.1.15">fragments</csymbol>
<ci id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">(</ci>
<apply id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">
<ci id="p1.1.m1.1.27.1.cmml" xref="p1.1.m1.1.27.1">¯</ci>
<ci id="p1.1.m1.1.27.2.cmml" xref="p1.1.m1.1.27.2">𝑟</ci>
</apply>
<ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">)</ci>
</cerror>
<ci id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">)</ci>
</cerror>
<csymbol cd="unknown" id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">δ</csymbol>
<apply id="p1.1.m1.1.44.cmml" xref="p1.1.m1.1.44">
<csymbol cd="ambiguous" id="p1.1.m1.1.44.1.cmml" xref="p1.1.m1.1.44">subscript</csymbol>
<ci id="p1.1.m1.1.31.cmml" xref="p1.1.m1.1.31">𝑛</ci>
<ci id="p1.1.m1.1.32.1.cmml" xref="p1.1.m1.1.32.1">𝑖</ci>
</apply>
<cerror id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">
<csymbol cd="ambiguous" id="p1.1.m1.1.21a.cmml" xref="p1.1.m1.1.21">fragments</csymbol>
<ci id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33">(</ci>
<apply id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34">
<ci id="p1.1.m1.1.34.1.cmml" xref="p1.1.m1.1.34.1">¯</ci>
<ci id="p1.1.m1.1.34.2.cmml" xref="p1.1.m1.1.34.2">𝑟</ci>
</apply>
<ci id="p1.1.m1.1.35.cmml" xref="p1.1.m1.1.35">)</ci>
</cerror>
<eq id="p1.1.m1.1.36.cmml" xref="p1.1.m1.1.36"/>
<factorial id="p1.1.m1.1.37.cmml" xref="p1.1.m1.1.37"/>
<eq id="p1.1.m1.1.38.cmml" xref="p1.1.m1.1.38"/>
<cn type="integer" id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">0</cn>
</cerror>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle\delta G=-S\delta T+V\delta p+\int{{{d}^{3}}r}\sum%
\limits_{i}{{}}\left({{\mu}_{i}}+{{e}_{i}}\phi\left({\bar{r}}\right)\right)%
\delta{{n}_{i}}\left({\bar{r}}\right)=!=0}}</annotation>
</semantics>
</math>
SVG image empty. Force Re-Rendering
SVG (0 B / 8 B) :
MathML (experimentell; keine Bilder) rendering
MathML (1.586 KB / 398 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>δ</mi><mi>G</mi><mo>=</mo><mo>−</mo><mi>S</mi><mi>δ</mi><mi>T</mi><mo>+</mo><mi>V</mi><mi>δ</mi><mi>p</mi><mo>+</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi></mrow><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo>+</mo><msub><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mi>ϕ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>δ</mi><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>!</mi><mo>=</mo><mn>0</mn></mstyle></mrow></math>
Translations to Computer Algebra Systems
Translation to Maple
In Maple:
Translation to Mathematica
In Mathematica:
Similar pages
Calculated based on the variables occurring on the entire Das elektrochemische Potenzial page
Identifiers
MathML observations
0results
0results
no statistics present please run the maintenance script ExtractFeatures.php
0 results
0 results