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Display information for equation id:math.2038.57 on revision:2038
* Page found: Stabilität und Langzeitverhalten (eq math.2038.57)
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Hash: 9028ffae5d0f8859dad18bf5f8149ca3
TeX (original user input):
\begin{align}
& A=\left( \begin{matrix}
-\sigma & \sigma & 0 \\
-z & -1 & r-x \\
y & x & -b \\
\end{matrix} \right) \\
& \Rightarrow \Lambda =trA=-\left( \sigma +1+b \right) \\
& \Rightarrow V(t)={{e}^{-\left( \sigma +1+b \right)t}}{{V}_{0}}-t->\infty \to 0 \\
\end{align}
TeX (checked):
{\begin{aligned}&A=\left({\begin{matrix}-\sigma &\sigma &0\\-z&-1&r-x\\y&x&-b\\\end{matrix}}\right)\\&\Rightarrow \Lambda =trA=-\left(\sigma +1+b\right)\\&\Rightarrow V(t)={{e}^{-\left(\sigma +1+b\right)t}}{{V}_{0}}-t->\infty \to 0\\\end{aligned}}
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MathML (2.258 KB / 508 B) :
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>A</mi><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><mo stretchy="false">−</mo><mi>σ</mi></mtd><mtd><mi>σ</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo stretchy="false">−</mo><mi>z</mi></mtd><mtd><mo stretchy="false">−</mo><mn>1</mn></mtd><mtd><mi>r</mi><mo stretchy="false">−</mo><mi>x</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd><mtd><mi>x</mi></mtd><mtd><mo stretchy="false">−</mo><mi>b</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>Λ</mi><mo stretchy="false">=</mo><mi>t</mi><mi>r</mi><mi>A</mi><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>σ</mi><mo stretchy="false">+</mo><mn>1</mn><mo stretchy="false">+</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>V</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>σ</mi><mo stretchy="false">+</mo><mn>1</mn><mo stretchy="false">+</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>t</mi></mrow></mrow></msup><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">−</mo><mi>t</mi><mo stretchy="false">−</mo><mo>></mo><mi mathvariant="normal">∞</mi><mo stretchy="false" accent="false">→</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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