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fix: 行内分式用 \dfrac、行间用 \frac

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B/E/D 行间 equation/align 内 37 处 \dfrac 改 \frac；sec5 行内 1 处 \frac 改 \dfrac。行内已是 \dfrac 的保留；导数斜杠记号 ∂f/∂x 非分式、未动。
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josh
2026-06-22 12:42:41 +08:00
parent 722a97f629
commit ae79e1d60b
4 changed files with 24 additions and 24 deletions
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parts/E-multiSatStaticCrb.tex
+12 -12
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@@ -193,7 +193,7 @@ $\zeta_\ell\in\mathbb C$ 为第 $\ell$ 条链路的未知复干扰系数，$\sig
\frac{\partial \nu_\ell}{\partial \boldsymbol\eta^\Tran}
=
\begin{bmatrix}
\dfrac{\partial \Delta\nu_\ell(\boldsymbol\xi)}{\partial \boldsymbol\xi^\Tran}
\frac{\partial \Delta\nu_\ell(\boldsymbol\xi)}{\partial \boldsymbol\xi^\Tran}
& 1
\end{bmatrix}
\in\mathbb R^{1\times3},
@@ -242,15 +242,15 @@ $\zeta_\ell\in\mathbb C$ 为第 $\ell$ 条链路的未知复干扰系数，$\sig
\frac{\partial \boldsymbol\xi_\ell^{\mathrm{loc}}}{\partial \boldsymbol\xi^\Tran}
=
\begin{bmatrix}
\dfrac{
u_{\ell,1}^{\mathrm{loc}}\,\dfrac{\partial u_{\ell,2}^{\mathrm{loc}}}{\partial \boldsymbol\xi^\Tran}
\frac{
u_{\ell,1}^{\mathrm{loc}}\,\frac{\partial u_{\ell,2}^{\mathrm{loc}}}{\partial \boldsymbol\xi^\Tran}
-
u_{\ell,2}^{\mathrm{loc}}\,\dfrac{\partial u_{\ell,1}^{\mathrm{loc}}}{\partial \boldsymbol\xi^\Tran}
u_{\ell,2}^{\mathrm{loc}}\,\frac{\partial u_{\ell,1}^{\mathrm{loc}}}{\partial \boldsymbol\xi^\Tran}
}{
\big(u_{\ell,1}^{\mathrm{loc}}\big)^2 + \big(u_{\ell,2}^{\mathrm{loc}}\big)^2
}
\\[1.2em]
\dfrac{\partial u_{\ell,3}^{\mathrm{loc}}/\partial \boldsymbol\xi^\Tran}{\sqrt{1-\big(u_{\ell,3}^{\mathrm{loc}}\big)^2}}
\frac{\partial u_{\ell,3}^{\mathrm{loc}}/\partial \boldsymbol\xi^\Tran}{\sqrt{1-\big(u_{\ell,3}^{\mathrm{loc}}\big)^2}}
\end{bmatrix}
\in\mathbb R^{2\times2},
\label{eq:A6_local_angle_chain}
@@ -264,9 +264,9 @@ $\zeta_\ell\in\mathbb C$ 为第 $\ell$ 条链路的未知复干扰系数，$\sig
\frac{\partial \mathbf a_\ell}{\partial (\boldsymbol\xi_\ell^{\mathrm{loc}})^\Tran}
=
\begin{bmatrix}
\dfrac{\partial \mathbf a_\ell}{\partial \alpha_\ell^{\mathrm{loc}}}
\frac{\partial \mathbf a_\ell}{\partial \alpha_\ell^{\mathrm{loc}}}
&
\dfrac{\partial \mathbf a_\ell}{\partial \beta_\ell^{\mathrm{loc}}}
\frac{\partial \mathbf a_\ell}{\partial \beta_\ell^{\mathrm{loc}}}
\end{bmatrix}
\in\mathbb C^{M_\ell\times2}.
\label{eq:A6_a_local_jac}
@@ -325,11 +325,11 @@ $\zeta_\ell\in\mathbb C$ 为第 $\ell$ 条链路的未知复干扰系数，$\sig
\frac{\partial \mathbf g_\ell}{\partial \boldsymbol\eta^\Tran}
=
\begin{bmatrix}
\mathbf q_\ell\otimes\dfrac{\partial \mathbf a_\ell}{\partial \boldsymbol\xi^\Tran}
\mathbf q_\ell\otimes\frac{\partial \mathbf a_\ell}{\partial \boldsymbol\xi^\Tran}
+
\dfrac{\partial \mathbf q_\ell}{\partial \boldsymbol\xi^\Tran}\otimes\mathbf a_\ell
\frac{\partial \mathbf q_\ell}{\partial \boldsymbol\xi^\Tran}\otimes\mathbf a_\ell
&
\dfrac{\partial \mathbf q_\ell}{\partial \nu_\ell}\otimes\mathbf a_\ell
\frac{\partial \mathbf q_\ell}{\partial \nu_\ell}\otimes\mathbf a_\ell
\end{bmatrix}
\in \mathbb C^{M_\ell T \times 3},
\label{eq:A6_Dl}
@@ -403,9 +403,9 @@ $\zeta_\ell\in\mathbb C$ 为第 $\ell$ 条链路的未知复干扰系数，$\sig
\mathcal I_{\eta\psi}
=
\begin{bmatrix}
\dfrac{2}{\sigma_0}\Re\left\{\mathbf J_{\eta,0}^{\Herm}\mathbf J_{\psi,0}\right\}
\frac{2}{\sigma_0}\Re\left\{\mathbf J_{\eta,0}^{\Herm}\mathbf J_{\psi,0}\right\}
& \cdots &
\dfrac{2}{\sigma_{L-1}}\Re\left\{\mathbf J_{\eta,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
\frac{2}{\sigma_{L-1}}\Re\left\{\mathbf J_{\eta,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
\end{bmatrix},
\label{eq:A6_Itb}
\end{equation}