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\begin{aligned} R^2= \left( \frac{\sum_{j=1}^{n} (\log_{10} H_{exp,j}- \overline{\log_{10} H_{exp}})(\log_{10} H_{pred,j}- \overline{\log_{10} H_{pred}})} {\sqrt{\sum_{j=1}^{n}(\log_{10} H_{exp,j}- \overline{\log_{10} H_{exp}})^2} \sqrt{\sum_{j=1}^{n}(\log_{10} H_{pred,j}- \overline{\log_{10} H_{pred}})^2}}\right)^2 \nonumber\end{aligned}

\begin{aligned} RMSE = \sqrt{\frac{1}{n} \sum_{j=1}^{n} \left(\log_{10} H_{exp,j}- {\log_{10} H_{pred,j}}\right)^2} \nonumber\end{aligned}

\begin{aligned} MUE = \frac{1}{n} \sum_{j=1}^{n} \left|\log_{10} H_{exp,j}- {\log_{10} H_{pred,j}}\right| \nonumber\end{aligned}

\begin{aligned} \lambda_{b:a}=\lambda_{o:w}\lambda_{w:a} ( a + 0.3\, b)+ \lambda_{w:a}(c+ 0.7\, b) \nonumber\end{aligned}

\begin{aligned} \lambda_{f:a}=\lambda_{o:w}\lambda_{w:a} ( A + 0.3\, B)+ \lambda_{w:a}(C+ 0.7\, B) \nonumber\end{aligned}

\begin{aligned} H_{TS}'=\frac{H_r \exp(-\frac{\Delta H_{\nu,TS}}{R_c})(\frac{1}{T_S}-\frac{1}{T_R})}{RT_S} \nonumber\end{aligned}

\begin{aligned} H_{TS}'(\mathrm{CS_2})=\frac{10^{-2.45} \exp(-\frac{26.74\, [\frac{kJ}{mol}]\times 239.005736\, [\frac{cal}{kJ}]}{1.9872})(\frac{1}{310.15}-\frac{1}{298.15})}{0.00008205 \times 310.15} \, [\frac{c_{air}}{c_{water}}] = 0.2128\nonumber\end{aligned}

### References

1. CMS/CERN. A New Boson with a Mass of 125 GeV Observed with the CMS Experiment at the Large Hadron Collider. Science 338, 1569-1575 (2012). Link

2. Barry R Holstein. The mysterious disappearance of Ettore Majorana. J. Phys.: Conf. Ser. 173, 012019 IOP Publishing, 2009. Link