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Yingjie Wang
2026-04-10 02:01:20 -04:00
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@@ -831,11 +831,15 @@ $}
We have to add some constraint terms that equals to zero, while contributes to the principal symbol, until the principal symbol matrix is diagonalizable with real eigenvalues. We have to add some constraint terms that equals to zero, while contributes to the principal symbol, until the principal symbol matrix is diagonalizable with real eigenvalues.
Available terms to add: Available terms to add:
\begin{gather*} \[
\scalebox{0.8}{$\displaystyle
\begin{aligned}
\constraintA{_i} \qc \constraintB{^i_j} \qc \constraintC*{_i} \qc \constraintD*{_i_j_k},\\ \constraintA{_i} \qc \constraintB{^i_j} \qc \constraintC*{_i} \qc \constraintD*{_i_j_k},\\
\Partial{_{[i}} \constraintA{_{j]}} = \Partial{_{[i}} \dlapse{_{j]}} \qc \Partial{_{[i}} \constraintB{^j_{k]}} = \Partial{_{[i}} \dshift{^j_{k]}} \qc \Partial{_{[i}} \constraintC*{_{j]}} = \Partial{_{[i}} \dchi*{_{j]}} \qc \Partial{_{[i}} \constraintD*{_{j]kl}} = \Partial{_{[i}} \dsmetric*{_{j]kl}},\\ \Partial{_{[i}} \constraintA{_{j]}} = \Partial{_{[i}} \dlapse{_{j]}} \qc \Partial{_{[i}} \constraintB{^j_{k]}} = \Partial{_{[i}} \dshift{^j_{k]}} \qc \Partial{_{[i}} \constraintC*{_{j]}} = \Partial{_{[i}} \dchi*{_{j]}} \qc \Partial{_{[i}} \constraintD*{_{j]kl}} = \Partial{_{[i}} \dsmetric*{_{j]kl}},\\
\Partial{_i} \left( \smetric*{^j^k} \Ktf*{_j_k} \right) \qc \Partial{_i} \left( \smetric*{^k^l} \dsmetric*{_j_k_l} \right) \Partial{_i} \left( \smetric*{^j^k} \Ktf*{_j_k} \right) \qc \Partial{_i} \left( \smetric*{^k^l} \dsmetric*{_j_k_l} \right)
\end{gather*} \end{aligned}
$}
\]
\end{frame} \end{frame}
\begin{frame}{References} \begin{frame}{References}