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update: auto commit

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Yingjie Wang
2026-04-10 01:22:33 -04:00
parent 08f981b21b
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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{0.45}{$\displaystyle \scalebox{0.47}{$\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]