Team:Tongji-Software/Template:Example Math

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.

\[{e^{{\rm{ - }}\Delta {\rm{r}}{G^{' \circ }}/RT}}\] $$\hat p=\sigma(\theta^T \cdot x_b)=\frac{1}{1+\mathbf{e}^{-{\theta^{T \cdot x_b}}}}$$ \begin{small}\[f{\rm{(r) = }}\frac{{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}{{{\rm{ 1 + }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}} + {\rm{ }}\sum {{r^'} \in {R_N}\backslash {{\left\{ r \right\}}^{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}} }}\] % MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqr % pepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs % 0-yqaqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaai % aabeqaamaabaabauaakeaacaWGMbGaaeikaiaabkhacaqGPaGaaeii % aiaab2dacaqGGaWaaSaaaeaacaqGGaGaaeyzamaaCaaaleqabaGaey % OeI0IaeyiLdq0aaSbaaWqaaiaadkhaaeqaaSGaam4ramaaCaaameqa % baGaai4jaiablIHiVjaac+cacaWGsbGaamivaaaaaaaakeaacaqGGa % GaaeymaiaabccacaqGRaGaaeiiaiaabwgadaahaaWcbeqaaiabgkHi % Tiabgs5aenaaBaaameaacaWGYbaabeaaliaadEeadaahaaadbeqaai % aacEcacqWIyiYBcaGGVaGaamOuaiaadsfaaaaaaOGaey4kaSIaaeii % amaaqaeabaGaamOCamaaCaaaleqabaGaai4jaaaakiabgIGiolaadk % fadaWgaaWcbaGaamOtaaqabaGccaGGCbWaaiWaaeaacaWGYbaacaGL % 7bGaayzFaaWaaWbaaSqabeaacaqGGaGaaeyzamaaCaaameqabaGaey % OeI0IaeyiLdq0aaSbaaeaacaWGYbaabeaacaWGhbWaaWbaaeqabaGa % ai4jaiablIHiVjaac+cacaWGsbGaamivaaaaaaaaaaWcbeqab0Gaey % yeIuoaaaaaaa!738A! \[f{\rm{(r) = }}\frac{{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}{{{\rm{ 1 + }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}} + {\rm{ }}\sum {{r^'} \in {R_N}\backslash {{\left\{ r \right\}}^{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}} }}\]