Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.2033.13 on revision:2033

* Page found: Vektorfelder als dynamische Systeme (eq math.2033.13)

(force rerendering)

Occurrences on the following pages:

Hash: 8c0bad61f513564c13fb930409402c79

TeX (original user input):

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

TeX (checked):

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

LaTeXML (experimentell; verwendet MathML) rendering

MathML (7.448 KB / 1.214 KB) :

Φ ( x ¯ 0 , t ) = Φ t ( x ¯ 0 ) = x ¯ ( t , x ¯ 0 ) Φ subscript ¯ 𝑥 0 𝑡 subscript Φ 𝑡 subscript ¯ 𝑥 0 ¯ 𝑥 𝑡 subscript ¯ 𝑥 0 {\displaystyle{\displaystyle\Phi({{\bar{x}}_{0}},t)={{\Phi}_{t}}({{\bar{x}}_{0% }})=\bar{x}(t,{{\bar{x}}_{0}})}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\Phi({{\bar{x}}_{0}},t)={{\Phi}_{t}}({{\bar{x}}_{0%&#10;}})=\bar{x}(t,{{\bar{x}}_{0}})}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">
      <mrow id="p1.1.m1.1.23.2" xref="p1.1.m1.1.23.2.cmml">
        <mi mathvariant="normal" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">Φ</mi>
        <mo id="p1.1.m1.1.23.2.1" xref="p1.1.m1.1.23.2.1.cmml"></mo>
        <mrow id="p1.1.m1.1.23.2.2" xref="p1.1.m1.1.23.2.2.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.23.2.2.1.cmml">(</mo>
          <msub id="p1.1.m1.1.23.2.2.2" xref="p1.1.m1.1.23.2.2.2.cmml">
            <mover accent="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
              <mi id="p1.1.m1.1.3.2" xref="p1.1.m1.1.3.2.cmml">x</mi>
              <mo stretchy="false" id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">¯</mo>
            </mover>
            <mn id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">0</mn>
          </msub>
          <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.23.2.2.1.cmml">,</mo>
          <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">t</mi>
          <mo stretchy="false" id="p1.1.m1.1.7" xref="p1.1.m1.1.23.2.2.1.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">=</mo>
      <mrow id="p1.1.m1.1.23.3" xref="p1.1.m1.1.23.3.cmml">
        <msub id="p1.1.m1.1.23.3.2" xref="p1.1.m1.1.23.3.2.cmml">
          <mi mathvariant="normal" id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">Φ</mi>
          <mi id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">t</mi>
        </msub>
        <mo id="p1.1.m1.1.23.3.1" xref="p1.1.m1.1.23.3.1.cmml"></mo>
        <mrow id="p1.1.m1.1.23.3.3" xref="p1.1.m1.1.23.3.3.2.cmml">
          <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.23.3.3.2.cmml">(</mo>
          <msub id="p1.1.m1.1.23.3.3.2" xref="p1.1.m1.1.23.3.3.2.cmml">
            <mover accent="true" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
              <mi id="p1.1.m1.1.12.2" xref="p1.1.m1.1.12.2.cmml">x</mi>
              <mo stretchy="false" id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">¯</mo>
            </mover>
            <mn id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">0</mn>
          </msub>
          <mo stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.23.3.3.2.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">=</mo>
      <mrow id="p1.1.m1.1.23.4" xref="p1.1.m1.1.23.4.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>
        <mo id="p1.1.m1.1.23.4.1" xref="p1.1.m1.1.23.4.1.cmml"></mo>
        <mrow id="p1.1.m1.1.23.4.2" xref="p1.1.m1.1.23.4.2.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.17" xref="p1.1.m1.1.23.4.2.1.cmml">(</mo>
          <mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">t</mi>
          <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.23.4.2.1.cmml">,</mo>
          <msub id="p1.1.m1.1.23.4.2.2" xref="p1.1.m1.1.23.4.2.2.cmml">
            <mover accent="true" id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">
              <mi id="p1.1.m1.1.20.2" xref="p1.1.m1.1.20.2.cmml">x</mi>
              <mo stretchy="false" id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">¯</mo>
            </mover>
            <mn id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">0</mn>
          </msub>
          <mo stretchy="false" id="p1.1.m1.1.22" xref="p1.1.m1.1.23.4.2.1.cmml">)</mo>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">
        <and id="p1.1.m1.1.23a.cmml" xref="p1.1.m1.1.23"/>
        <apply id="p1.1.m1.1.23b.cmml" xref="p1.1.m1.1.23">
          <eq id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
          <apply id="p1.1.m1.1.23.2.cmml" xref="p1.1.m1.1.23.2">
            <times id="p1.1.m1.1.23.2.1.cmml" xref="p1.1.m1.1.23.2.1"/>
            <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">Φ</ci>
            <interval closure="open" id="p1.1.m1.1.23.2.2.1.cmml" xref="p1.1.m1.1.23.2.2">
              <apply id="p1.1.m1.1.23.2.2.2.cmml" xref="p1.1.m1.1.23.2.2.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.23.2.2.2.1.cmml" xref="p1.1.m1.1.23.2.2.2">subscript</csymbol>
                <apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
                  <ci id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">¯</ci>
                  <ci id="p1.1.m1.1.3.2.cmml" xref="p1.1.m1.1.3.2">𝑥</ci>
                </apply>
                <cn type="integer" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">0</cn>
              </apply>
              <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝑡</ci>
            </interval>
          </apply>
          <apply id="p1.1.m1.1.23.3.cmml" xref="p1.1.m1.1.23.3">
            <times id="p1.1.m1.1.23.3.1.cmml" xref="p1.1.m1.1.23.3.1"/>
            <apply id="p1.1.m1.1.23.3.2.cmml" xref="p1.1.m1.1.23.3.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.23.3.2.1.cmml" xref="p1.1.m1.1.23.3.2">subscript</csymbol>
              <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">Φ</ci>
              <ci id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">𝑡</ci>
            </apply>
            <apply id="p1.1.m1.1.23.3.3.2.cmml" xref="p1.1.m1.1.23.3.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.23.3.3.2.1.cmml" xref="p1.1.m1.1.23.3.3">subscript</csymbol>
              <apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
                <ci id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">¯</ci>
                <ci id="p1.1.m1.1.12.2.cmml" xref="p1.1.m1.1.12.2">𝑥</ci>
              </apply>
              <cn type="integer" id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">0</cn>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.23c.cmml" xref="p1.1.m1.1.23">
          <eq id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15"/>
          <share href="#p1.1.m1.1.23.3.cmml" id="p1.1.m1.1.23d.cmml" xref="p1.1.m1.1.23"/>
          <apply id="p1.1.m1.1.23.4.cmml" xref="p1.1.m1.1.23.4">
            <times id="p1.1.m1.1.23.4.1.cmml" xref="p1.1.m1.1.23.4.1"/>
            <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>
            <interval closure="open" id="p1.1.m1.1.23.4.2.1.cmml" xref="p1.1.m1.1.23.4.2">
              <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">𝑡</ci>
              <apply id="p1.1.m1.1.23.4.2.2.cmml" xref="p1.1.m1.1.23.4.2.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.23.4.2.2.1.cmml" xref="p1.1.m1.1.23.4.2.2">subscript</csymbol>
                <apply id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">
                  <ci id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">¯</ci>
                  <ci id="p1.1.m1.1.20.2.cmml" xref="p1.1.m1.1.20.2">𝑥</ci>
                </apply>
                <cn type="integer" id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">0</cn>
              </apply>
            </interval>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\Phi({{\bar{x}}_{0}},t)={{\Phi}_{t}}({{\bar{x}}_{0%
}})=\bar{x}(t,{{\bar{x}}_{0}})}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimentell; keine Bilder) rendering

MathML (1.122 KB / 280 B) :

Φ(x¯0,t)=Φt(x¯0)=x¯(t,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"><mi mathvariant="normal">&#x03A6;</mi><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>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi mathvariant="normal">&#x03A6;</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></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><mo>=</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mi>t</mi><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 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 Vektorfelder als dynamische Systeme page

Identifiers

  • Φ
  • x¯0
  • t
  • Φt
  • x¯0
  • x¯
  • t
  • x¯0

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results