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<math>
\begin{gathered}
\begin{gathered}
\mathcal{\Delta J}\equiv \frac{EI(F)}{m}-\frac{EI(f)}{n}\approx -\frac{\sum_{i=1}^n\ln\sigma_i}{n}+\frac{\sum_{i=1}^m\ln\sigma'_i}{m}+\frac{1}{n}\cdot\mathbb{E}_{x\sim \mathcal{U}([-\frac{L}{2},\frac{L}{2}]^n)}(\ln|\det(\partial_{x}f(x)))|)-\frac{1}{m}\cdot\mathbb{E}_{X\sim \mathcal{U}([-\frac{L}{2},\frac{L}{2}]^m)}(\ln|\det(\partial_{X}F(X)))|)
\mathcal{\Delta J}\equiv \frac{EI(F)}{m}-\frac{EI(f)}{n}\approx -\frac{\sum_{i=1}^n\ln\sigma_i}{n}+\frac{\sum_{i=1}^m\ln\sigma'_i}{m}+\frac{1}{n}\cdot\mathbb{E}_{x\sim \mathcal{U}([-\frac{L}{2},\frac{L}{2}]^n)}(\ln|\det(\partial_{x}F(x)))|)-\frac{1}{m}\cdot\mathbb{E}_{X\sim \mathcal{U}([-\frac{L}{2},\frac{L}{2}]^m)}(\ln|\det(\partial_{X}f(X)))|)
\end{gathered}
\end{gathered}
</math>
</math>