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update: auto commit

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Yingjie Wang
2026-04-10 01:21:27 -04:00
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@@ -712,7 +712,7 @@ $}
\] \]
and replace all the spatical derivatives of the original variables with the new auxiliary variables, we got this and replace all the spatical derivatives of the original variables with the new auxiliary variables, we got this
\[ \[
\scalebox{0.6}{$\displaystyle \scalebox{0.5}{$\displaystyle
\begin{aligned} \begin{aligned}
\pt \chi ={}&\frac{2}{3} \chi \left[ \alpha \left( \hat{K} + \pt \chi ={}&\frac{2}{3} \chi \left[ \alpha \left( \hat{K} +
2\Theta \right) - \dshift{^i_i} - \Gam*{^j_j_k} \shift{^k} \right] 2\Theta \right) - \dshift{^i_i} - \Gam*{^j_j_k} \shift{^k} \right]