Jump to navigation Jump to search

General

Display information for equation id:math.1355.185 on revision:1355

* Page found: Dynamische Systeme und deterministisches Chaos (eq math.1355.185)

(force rerendering)

Occurrences on the following pages:

Hash: e1053c923d3cb3b417322f533107cea2

TeX (original user input): 

\left| \Phi (t,{{{\bar{x}}}_{0}})-\Phi (t,{{{\bar{y}}}_{0}}) \right|\tilde{\ }{{e}^{\lambda t}}

LaTeXML (experimental; uses MathML) rendering

MathML (7.198 KB / 1.24 KB) :

| Φ ⁢ ( t , x ¯ 0 ) - Φ ⁢ ( t , y ¯ 0 ) | ⁢ ~ ⁢ e λ ⁢ t Φ 𝑡 subscript ¯ 𝑥 0 Φ 𝑡 subscript ¯ 𝑦 0 ~ absent superscript 𝑒 𝜆 𝑡 {\displaystyle{\displaystyle\left|\Phi(t,{{{\bar{x}}}_{0}})-\Phi(t,{{{\bar{y}}% }_{0}})\right|\tilde{\ }{{e}^{\lambda t}}}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\left|\Phi(t,{{{\bar{x}}}_{0}})-\Phi(t,{{{\bar{y}}%&#10;}_{0}})\right|\tilde{\ }{{e}^{\lambda t}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">
      <mrow id="p1.1.m1.1.21.2" xref="p1.1.m1.1.21.2.1.cmml">
        <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.21.2.1.1.cmml">|</mo>
        <mrow id="p1.1.m1.1.21.2.2" xref="p1.1.m1.1.21.2.2.cmml">
          <mrow id="p1.1.m1.1.21.2.2.1" xref="p1.1.m1.1.21.2.2.1.cmml">
            <mi mathvariant="normal" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">Φ</mi>
            <mo id="p1.1.m1.1.21.2.2.1.1" xref="p1.1.m1.1.21.2.2.1.1.cmml">⁢</mo>
            <mrow id="p1.1.m1.1.21.2.2.1.2" xref="p1.1.m1.1.21.2.2.1.2.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.3" xref="p1.1.m1.1.21.2.2.1.2.1.cmml">(</mo>
              <mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">t</mi>
              <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.21.2.2.1.2.1.cmml">,</mo>
              <msub id="p1.1.m1.1.21.2.2.1.2.2" xref="p1.1.m1.1.21.2.2.1.2.2.cmml">
                <mover accent="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
                  <mi id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">x</mi>
                  <mo stretchy="false" id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">¯</mo>
                </mover>
                <mn id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">0</mn>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.21.2.2.1.2.1.cmml">)</mo>
            </mrow>
          </mrow>
          <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">-</mo>
          <mrow id="p1.1.m1.1.21.2.2.2" xref="p1.1.m1.1.21.2.2.2.cmml">
            <mi mathvariant="normal" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">Φ</mi>
            <mo id="p1.1.m1.1.21.2.2.2.1" xref="p1.1.m1.1.21.2.2.2.1.cmml">⁢</mo>
            <mrow id="p1.1.m1.1.21.2.2.2.2" xref="p1.1.m1.1.21.2.2.2.2.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.21.2.2.2.2.1.cmml">(</mo>
              <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">t</mi>
              <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.21.2.2.2.2.1.cmml">,</mo>
              <msub id="p1.1.m1.1.21.2.2.2.2.2" xref="p1.1.m1.1.21.2.2.2.2.2.cmml">
                <mover accent="true" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">
                  <mi id="p1.1.m1.1.14.2" xref="p1.1.m1.1.14.2.cmml">y</mi>
                  <mo stretchy="false" id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">¯</mo>
                </mover>
                <mn id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">0</mn>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.16" xref="p1.1.m1.1.21.2.2.2.2.1.cmml">)</mo>
            </mrow>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.21.2.1.1.cmml">|</mo>
      </mrow>
      <mo id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">⁢</mo>
      <mover accent="true" id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
        <mi id="p1.1.m1.1.18.2" xref="p1.1.m1.1.18.2.cmml"/>
        <mo stretchy="false" id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">~</mo>
      </mover>
      <mo id="p1.1.m1.1.21.1a" xref="p1.1.m1.1.21.1.cmml">⁢</mo>
      <msup id="p1.1.m1.1.21.3" xref="p1.1.m1.1.21.3.cmml">
        <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">e</mi>
        <mrow id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">
          <mi id="p1.1.m1.1.20.1.1" xref="p1.1.m1.1.20.1.1.cmml">λ</mi>
          <mo id="p1.1.m1.1.20.1.3" xref="p1.1.m1.1.20.1.3.cmml">⁢</mo>
          <mi id="p1.1.m1.1.20.1.2" xref="p1.1.m1.1.20.1.2.cmml">t</mi>
        </mrow>
      </msup>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">
        <times id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1"/>
        <apply id="p1.1.m1.1.21.2.1.cmml" xref="p1.1.m1.1.21.2">
          <abs id="p1.1.m1.1.21.2.1.1.cmml" xref="p1.1.m1.1.1"/>
          <apply id="p1.1.m1.1.21.2.2.cmml" xref="p1.1.m1.1.21.2.2">
            <minus id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
            <apply id="p1.1.m1.1.21.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.1">
              <times id="p1.1.m1.1.21.2.2.1.1.cmml" xref="p1.1.m1.1.21.2.2.1.1"/>
              <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">Φ</ci>
              <interval closure="open" id="p1.1.m1.1.21.2.2.1.2.1.cmml" xref="p1.1.m1.1.21.2.2.1.2">
                <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝑡</ci>
                <apply id="p1.1.m1.1.21.2.2.1.2.2.cmml" xref="p1.1.m1.1.21.2.2.1.2.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.1.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.1.2.2">subscript</csymbol>
                  <apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
                    <ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">¯</ci>
                    <ci id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">𝑥</ci>
                  </apply>
                  <cn type="integer" id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">0</cn>
                </apply>
              </interval>
            </apply>
            <apply id="p1.1.m1.1.21.2.2.2.cmml" xref="p1.1.m1.1.21.2.2.2">
              <times id="p1.1.m1.1.21.2.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.2.1"/>
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">Φ</ci>
              <interval closure="open" id="p1.1.m1.1.21.2.2.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.2.2">
                <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝑡</ci>
                <apply id="p1.1.m1.1.21.2.2.2.2.2.cmml" xref="p1.1.m1.1.21.2.2.2.2.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.2.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.2.2.2">subscript</csymbol>
                  <apply id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">
                    <ci id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">¯</ci>
                    <ci id="p1.1.m1.1.14.2.cmml" xref="p1.1.m1.1.14.2">𝑦</ci>
                  </apply>
                  <cn type="integer" id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">0</cn>
                </apply>
              </interval>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
          <ci id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">~</ci>
          <csymbol cd="latexml" id="p1.1.m1.1.18.2.cmml" xref="p1.1.m1.1.18.2">absent</csymbol>
        </apply>
        <apply id="p1.1.m1.1.21.3.cmml" xref="p1.1.m1.1.21.3">
          <csymbol cd="ambiguous" id="p1.1.m1.1.21.3.1.cmml" xref="p1.1.m1.1.21.3">superscript</csymbol>
          <ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">𝑒</ci>
          <apply id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">
            <times id="p1.1.m1.1.20.1.3.cmml" xref="p1.1.m1.1.20.1.3"/>
            <ci id="p1.1.m1.1.20.1.1.cmml" xref="p1.1.m1.1.20.1.1">𝜆</ci>
            <ci id="p1.1.m1.1.20.1.2.cmml" xref="p1.1.m1.1.20.1.2">𝑡</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\left|\Phi(t,{{{\bar{x}}}_{0}})-\Phi(t,{{{\bar{y}}%
}_{0}})\right|\tilde{\ }{{e}^{\lambda t}}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimental; no images) rendering

MathML (1.082 KB / 339 B) :

|Φ(t,x¯0)−Φ(t,y¯0)|~eλt
<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="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">&#x03A6;</mi><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><mo>&#x2212;</mo><mi mathvariant="normal">&#x03A6;</mi><mo stretchy="false">(</mo><mi>t</mi><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>y</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo>~</mo></mover></mrow></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x03BB;</mi><mi>t</mi></mrow></mrow></msup></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 Dynamische Systeme und deterministisches Chaos page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "http://physikerwelt.de:8080/w/index.php?title=Special:FormulaInfo"