Difference between revisions of "Team:SEU/Model"
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<h3>Computation method</h3> | <h3>Computation method</h3> | ||
<p >Addition: \(A_1 \xrightarrow{k_1} O,\quad A_2 \xrightarrow{k_2} O\)</p> | <p >Addition: \(A_1 \xrightarrow{k_1} O,\quad A_2 \xrightarrow{k_2} O\)</p> | ||
| − | <p style="font-size=36px">Proof: \(\dfrac{d A_i}{d t}=-k_i[A_i](t) \Rightarrow [A_i](t)=[A_i](0)e^{-k_it} \Rightarrow \dfrac{d O}{d t}=\sum_{i=1}^2 k_i[A_i](t) \Rightarrow [O](\infty)= [A_1](0)/k_1+[A_2](0)/k_2.\) If \(k_1\approx k_2\), then addition is successfully implemented.</p> | + | <p style="font-size=36px">Proof: \(\dfrac{d A_i}{d t}=-k_i[A_i](t)\) \(\Rightarrow [A_i](t)=[A_i](0)e^{-k_it}\) \(\Rightarrow \dfrac{d O}{d t}=\sum_{i=1}^2 k_i[A_i](t)\) \(\Rightarrow [O](\infty)= [A_1](0)/k_1+[A_2](0)/k_2.\) If \(k_1\approx k_2\), then addition is successfully implemented.</p> |
<p style="font-size=36px">Subtraction: \(A+B \xrightarrow{k_1} \phi\)</p> | <p style="font-size=36px">Subtraction: \(A+B \xrightarrow{k_1} \phi\)</p> | ||
<p style="font-size=36px">Multiplication: \(\alpha \xrightarrow{k} \phi, A+B+\alpha \xrightarrow{k} A+B+\alpha+C\)</p> | <p style="font-size=36px">Multiplication: \(\alpha \xrightarrow{k} \phi, A+B+\alpha \xrightarrow{k} A+B+\alpha+C\)</p> | ||
Revision as of 07:42, 2 October 2019
Model
Computation method
Addition: \(A_1 \xrightarrow{k_1} O,\quad A_2 \xrightarrow{k_2} O\)
Proof: \(\dfrac{d A_i}{d t}=-k_i[A_i](t)\) \(\Rightarrow [A_i](t)=[A_i](0)e^{-k_it}\) \(\Rightarrow \dfrac{d O}{d t}=\sum_{i=1}^2 k_i[A_i](t)\) \(\Rightarrow [O](\infty)= [A_1](0)/k_1+[A_2](0)/k_2.\) If \(k_1\approx k_2\), then addition is successfully implemented.
Subtraction: \(A+B \xrightarrow{k_1} \phi\)
Multiplication: \(\alpha \xrightarrow{k} \phi, A+B+\alpha \xrightarrow{k} A+B+\alpha+C\)