Jump to navigation Jump to search

General

Display information for equation id:math.1970.1 on revision:1970

* Page found: Der Satz von Liouville (eq math.1970.1)

(force rerendering)

Occurrences on the following pages:

Hash: a90e713939d5245138e1f999c1eb15d8

TeX (original user input):

\bar{x}\left( t,{{t}_{0}},{{{\bar{x}}}_{0}} \right)=:{{\bar{\Phi }}_{t,{{t}_{0}}}}({{\bar{x}}_{0}})

TeX (checked):

{\bar {x}}\left(t,{{t}_{0}},{{\bar {x}}_{0}}\right)=:{{\bar {\Phi }}_{t,{{t}_{0}}}}({{\bar {x}}_{0}})

LaTeXML (experimental; uses MathML) rendering

MathML (6.691 KB / 1.182 KB) :

x ¯ ( t , t 0 , x ¯ 0 ) = : Φ ¯ t , t 0 ( x ¯ 0 ) fragments ¯ 𝑥 fragments ( t , subscript 𝑡 0 , subscript ¯ 𝑥 0 ) : subscript ¯ Φ 𝑡 subscript 𝑡 0 fragments ( subscript ¯ 𝑥 0 ) {\displaystyle{\displaystyle\bar{x}\left(t,{{t}_{0}},{{{\bar{x}}}_{0}}\right)=% :{{\bar{\Phi}}_{t,{{t}_{0}}}}({{\bar{x}}_{0}})}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\bar{x}\left(t,{{t}_{0}},{{{\bar{x}}}_{0}}\right)=%&#10;:{{\bar{\Phi}}_{t,{{t}_{0}}}}({{\bar{x}}_{0}})}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1b">
      <mover accent="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
        <mi id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">x</mi>
        <mo stretchy="false" id="p1.1.m1.1.1.1" xref="p1.1.m1.1.1.1.cmml">¯</mo>
      </mover>
      <mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
        <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">(</mo>
        <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">t</mi>
        <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">,</mo>
        <msub id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">
          <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">t</mi>
          <mn id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">0</mn>
        </msub>
        <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">,</mo>
        <msub id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">
          <mover accent="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
            <mi id="p1.1.m1.1.8.2" xref="p1.1.m1.1.8.2.cmml">x</mi>
            <mo stretchy="false" id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">¯</mo>
          </mover>
          <mn id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">0</mn>
        </msub>
        <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">)</mo>
      </mrow>
      <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">=</mo>
      <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">:</mo>
      <msub id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">
        <mover accent="true" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
          <mi mathvariant="normal" id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">Φ</mi>
          <mo stretchy="false" id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">¯</mo>
        </mover>
        <mrow id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.5.cmml">
          <mi id="p1.1.m1.1.14.1.1" xref="p1.1.m1.1.14.1.1.cmml">t</mi>
          <mo id="p1.1.m1.1.14.1.2" xref="p1.1.m1.1.14.1.5.cmml">,</mo>
          <msub id="p1.1.m1.1.14.1.6" xref="p1.1.m1.1.14.1.6.cmml">
            <mi id="p1.1.m1.1.14.1.3" xref="p1.1.m1.1.14.1.3.cmml">t</mi>
            <mn id="p1.1.m1.1.14.1.4.1" xref="p1.1.m1.1.14.1.4.1.cmml">0</mn>
          </msub>
        </mrow>
      </msub>
      <mrow id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
        <mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">(</mo>
        <msub id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">
          <mover accent="true" id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">
            <mi id="p1.1.m1.1.16.2" xref="p1.1.m1.1.16.2.cmml">x</mi>
            <mo stretchy="false" id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">¯</mo>
          </mover>
          <mn id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">0</mn>
        </msub>
        <mo stretchy="false" id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">)</mo>
      </mrow>
    </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>
        <apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
          <ci id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.1">¯</ci>
          <ci id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">𝑥</ci>
        </apply>
        <cerror id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
          <csymbol cd="ambiguous" id="p1.1.m1.1.6a.cmml" xref="p1.1.m1.1.6">fragments</csymbol>
          <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">(</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">t</csymbol>
          <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">,</ci>
          <apply id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">
            <csymbol cd="ambiguous" id="p1.1.m1.1.19.1.cmml" xref="p1.1.m1.1.19">subscript</csymbol>
            <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑡</ci>
            <cn type="integer" id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">0</cn>
          </apply>
          <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">,</ci>
          <apply id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">
            <csymbol cd="ambiguous" id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20">subscript</csymbol>
            <apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
              <ci id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">¯</ci>
              <ci id="p1.1.m1.1.8.2.cmml" xref="p1.1.m1.1.8.2">𝑥</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">0</cn>
          </apply>
          <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">)</ci>
        </cerror>
        <eq id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
        <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">:</ci>
        <apply id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">
          <csymbol cd="ambiguous" id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21">subscript</csymbol>
          <apply id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">
            <ci id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">¯</ci>
            <ci id="p1.1.m1.1.13.2.cmml" xref="p1.1.m1.1.13.2">Φ</ci>
          </apply>
          <list id="p1.1.m1.1.14.1.5.cmml" xref="p1.1.m1.1.14.1">
            <ci id="p1.1.m1.1.14.1.1.cmml" xref="p1.1.m1.1.14.1.1">𝑡</ci>
            <apply id="p1.1.m1.1.14.1.6.cmml" xref="p1.1.m1.1.14.1.6">
              <csymbol cd="ambiguous" id="p1.1.m1.1.14.1.6.1.cmml" xref="p1.1.m1.1.14.1.6">subscript</csymbol>
              <ci id="p1.1.m1.1.14.1.3.cmml" xref="p1.1.m1.1.14.1.3">𝑡</ci>
              <cn type="integer" id="p1.1.m1.1.14.1.4.1.cmml" xref="p1.1.m1.1.14.1.4.1">0</cn>
            </apply>
          </list>
        </apply>
        <cerror id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
          <csymbol cd="ambiguous" id="p1.1.m1.1.9a.cmml" xref="p1.1.m1.1.9">fragments</csymbol>
          <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">(</ci>
          <apply id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">
            <csymbol cd="ambiguous" id="p1.1.m1.1.22.1.cmml" xref="p1.1.m1.1.22">subscript</csymbol>
            <apply id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">
              <ci id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">¯</ci>
              <ci id="p1.1.m1.1.16.2.cmml" xref="p1.1.m1.1.16.2">𝑥</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">0</cn>
          </apply>
          <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">)</ci>
        </cerror>
      </cerror>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle\bar{x}\left(t,{{t}_{0}},{{{\bar{x}}}_{0}}\right)=%
:{{\bar{\Phi}}_{t,{{t}_{0}}}}({{\bar{x}}_{0}})}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimental; no images) rendering

MathML (1.191 KB / 312 B) :

x¯(t,t0,x¯0)=:Φ¯t,t0(x¯0)
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo>,</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>:</mi><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">&#x03A6;</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>t</mi><mo>,</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></msub><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></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 Der Satz von Liouville page

Identifiers

  • x¯
  • t
  • t0
  • x¯0
  • Φ¯t,t0
  • x¯0

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results