Difference between revisions of "Team:Tongji-Software/Template:Example Math"

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<span>\[f{\rm{(r)  =  }}\frac{{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}{{{\rm{ 1  +  }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}} + {\rm{ }}\sum {{r^'} \in {R_N}\backslash {{\left\{ r \right\}}^{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}} }}\]</span>
 
<span>\[f{\rm{(r)  =  }}\frac{{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}{{{\rm{ 1  +  }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}} + {\rm{ }}\sum {{r^'} \in {R_N}\backslash {{\left\{ r \right\}}^{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}} }}\]</span>
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<span>\begin{small}\[f{\rm{(r) = }}\frac{{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}{{{\rm{ 1 + }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}} + {\rm{ }}\sum {{r^'} \in {R_N}\backslash {{\left\{ r \right\}}^{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}} }}\\end{small}</span>
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<span>\begin{small}\[f{\rm{(r)=}}\frac{{{\rm{ }}{{\rm{e}}^{-{\Delta_r}{G^{'\circ/RT}}}}}}{{{\rm{1+}}{{\rm{e}}^{-{\Delta _r}{G^{'\circ /RT}}}}+{\rm{}}\sum{{r^'}\in{R_N}\backslash{{\left\{r\right\}}^{{\rm{}}{{\rm{e}}^{-{\Delta _r}{G^{'\circ/RT}}}}}}}}}\\end{small}</span>
 
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Revision as of 12:59, 13 October 2018

Get the power of blast

Where:

$$X=[x_1,\ x_2,\ x_3,\ ...,\ x_n]^T$$ $$W=[w_1,\ w_2,\ w_3,\ ...,\ w_n]^T$$ $$\varepsilon=[\varepsilon_1,\ \varepsilon_2,\ \varepsilon_3,\ ...,\ \varepsilon_n]^T$$

  The aim is to search for the best W that minimize the mean of e.

\[{e^{{\rm{ - }}\Delta {\rm{r}}{G^{' \circ }}/RT}}\] $$\hat p=\sigma(\theta^T \cdot x_b)=\frac{1}{1+\mathbf{e}^{-{\theta^{T \cdot x_b}}}}$$ \[f{\rm{(r) = }}\frac{{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}{{{\rm{ 1 + }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}} + {\rm{ }}\sum {{r^'} \in {R_N}\backslash {{\left\{ r \right\}}^{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}} }}\] \begin{small}\[f{\rm{(r)=}}\frac{{{\rm{ }}{{\rm{e}}^{-{\Delta_r}{G^{'\circ/RT}}}}}}{{{\rm{1+}}{{\rm{e}}^{-{\Delta _r}{G^{'\circ /RT}}}}+{\rm{}}\sum{{r^'}\in{R_N}\backslash{{\left\{r\right\}}^{{\rm{}}{{\rm{e}}^{-{\Delta _r}{G^{'\circ/RT}}}}}}}}}\\end{small}