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Display information for equation id:math.3449.10 on revision:3449
* Page found: Kernzerfälle, Strahlenschutz (eq math.3449.10)
(force rerendering)Occurrences on the following pages:
Hash: 197599933e4fa985bc7e62fb159b9ffd
TeX (original user input):
\begin{align}
t = 0 & N_1(0)\\
t > 0 & N_1 (t) =N_1(0)e^{-\lambda_{12}t}\\
& dN_2/dt = \underbrace{\lambda_{12} N_1(t)}_{\text{Zuwachs}}-\underbrace{\lambda_{23}N_2(t)}_{\text{Zerfall}}
\end{align}
TeX (checked):
{\begin{aligned}t=0&N_{1}(0)\\t>0&N_{1}(t)=N_{1}(0)e^{-\lambda _{12}t}\\&dN_{2}/dt=\underbrace {\lambda _{12}N_{1}(t)} _{\text{Zuwachs}}-\underbrace {\lambda _{23}N_{2}(t)} _{\text{Zerfall}}\end{aligned}}
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MathML (2.263 KB / 444 B) :
<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"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><mi>t</mi><mo>=</mo><mn>0</mn></mtd><mtd><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>t</mi><mo>></mo><mn>0</mn></mtd><mtd><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mn>2</mn></mrow></mrow></msub><mi>t</mi></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mi>d</mi><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>/</mo><mi>d</mi><mi>t</mi><mo>=</mo><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mn>2</mn></mrow></mrow></msub><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>Zuwachs</mtext></mrow></mrow></munder><mo>−</mo><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mn>3</mn></mrow></mrow></msub><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>Zerfall</mtext></mrow></mrow></munder></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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