fix(equation): 删去公式中手动 \! 负间距

\arcsin\!\big(、\Re\!\left\{、\mathbf a_\ell\!\big( 等"函数/算子+定界符"
处的手动负间距由 LaTeX 自动排版处理,无需手动加 \!。全文删 39 处。
主文件 \newcommand{\diff}{\mathop{}\!\mathrm{d}} 中的 \! 是微分号标准间距,保留。
This commit is contained in:
2026-06-16 15:28:12 +08:00
parent 8885e3e7f6
commit 0932cc9f41
9 changed files with 39 additions and 39 deletions
+14 -14
View File
@@ -134,7 +134,7 @@ $\zeta_\ell\in\mathbb C$ 为第 $\ell$ 条链路的未知复干扰系数,$\sig
\begin{equation}
[\mathcal I(\boldsymbol\kappa_{\mathrm{stat}})]_{ij}
=
2\Re\!\left\{
2\Re\left\{
\frac{\partial \boldsymbol\mu^{\Herm}(\boldsymbol\kappa_{\mathrm{stat}})}{\partial \kappa_i}
\mathbf R_n^{-1}
\frac{\partial \boldsymbol\mu(\boldsymbol\kappa_{\mathrm{stat}})}{\partial \kappa_j}
@@ -237,11 +237,11 @@ $\partial\nu_{\ell_{\mathrm{ref}}}/\partial\beta=0$。若改用别的等价参
\begin{equation}
\alpha_\ell^{\mathrm{loc}}
=
\operatorname{atan2}\!\big(u_{\ell,2}^{\mathrm{loc}},u_{\ell,1}^{\mathrm{loc}}\big),
\operatorname{atan2}\big(u_{\ell,2}^{\mathrm{loc}},u_{\ell,1}^{\mathrm{loc}}\big),
\qquad
\beta_\ell^{\mathrm{loc}}
=
\arcsin\!\big(u_{\ell,3}^{\mathrm{loc}}\big).
\arcsin\big(u_{\ell,3}^{\mathrm{loc}}\big).
\end{equation}
对任意 $x\in\{\alpha,\beta\}$,有
@@ -439,7 +439,7 @@ $\mathbf g_\ell=\mathbf q_\ell\otimes \mathbf a_\ell$
=
\sum_{\ell=0}^{L-1}
\frac{2}{\sigma_{n,\ell}^2}
\Re\!\left\{
\Re\left\{
\mathbf J_{\eta,\ell}^{\Herm}\mathbf J_{\eta,\ell}
\right\},
\label{eq:A6_Itt}
@@ -448,9 +448,9 @@ $\mathbf g_\ell=\mathbf q_\ell\otimes \mathbf a_\ell$
\mathcal I_{\eta\psi}
=
\begin{bmatrix}
\dfrac{2}{\sigma_{n,0}^2}\Re\!\left\{\mathbf J_{\eta,0}^{\Herm}\mathbf J_{\psi,0}\right\}
\dfrac{2}{\sigma_{n,0}^2}\Re\left\{\mathbf J_{\eta,0}^{\Herm}\mathbf J_{\psi,0}\right\}
& \cdots &
\dfrac{2}{\sigma_{n,L-1}^2}\Re\!\left\{\mathbf J_{\eta,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
\dfrac{2}{\sigma_{n,L-1}^2}\Re\left\{\mathbf J_{\eta,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
\end{bmatrix},
\label{eq:A6_Itb}
\end{equation}
@@ -459,9 +459,9 @@ $\mathbf g_\ell=\mathbf q_\ell\otimes \mathbf a_\ell$
=
\operatorname{blkdiag}
\left(
\frac{2}{\sigma_{n,0}^2}\Re\!\left\{\mathbf J_{\psi,0}^{\Herm}\mathbf J_{\psi,0}\right\},
\frac{2}{\sigma_{n,0}^2}\Re\left\{\mathbf J_{\psi,0}^{\Herm}\mathbf J_{\psi,0}\right\},
\ldots,
\frac{2}{\sigma_{n,L-1}^2}\Re\!\left\{\mathbf J_{\psi,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
\frac{2}{\sigma_{n,L-1}^2}\Re\left\{\mathbf J_{\psi,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
\right).
\label{eq:A6_Ibb}
\end{equation}
@@ -502,7 +502,7 @@ $\begin{bmatrix}\mathbf g_\ell & j\mathbf g_\ell\end{bmatrix}$。虽然这两个
=
2\sum_{\ell=0}^{L-1}
\frac{1}{\sigma_{n,\ell}^2}
\Re\!\left\{
\Re\left\{
\mathbf J_{\eta,\ell}^{\Herm}
\mathcal P_{\mathbf g_\ell}^{\perp}
\mathbf J_{\eta,\ell}
@@ -517,7 +517,7 @@ $\begin{bmatrix}\mathbf g_\ell & j\mathbf g_\ell\end{bmatrix}$。虽然这两个
=
2\sum_{\ell=0}^{L-1}
\frac{|\zeta_\ell|^2}{\sigma_{n,\ell}^2}
\Re\!\left\{
\Re\left\{
\mathbf D_\ell^{\Herm}
\mathcal P_{\mathbf g_\ell}^{\perp}
\mathbf D_\ell
@@ -596,7 +596,7 @@ $\begin{bmatrix}\mathbf g_\ell & j\mathbf g_\ell\end{bmatrix}$。虽然这两个
\frac{2}{\sigma^2}
\sum_{\ell=0}^{L-1}
|\zeta_\ell|^2
\Re\!\left\{
\Re\left\{
\mathbf D_\ell^{\Herm}\mathcal P_{\mathbf g_\ell}^{\perp}\mathbf D_\ell
\right\}.
\end{equation}
@@ -707,7 +707,7 @@ $\mathbf J_{\psi,\ell}$ 的实参数化二维实子空间与复矩阵 $\mathbf G
=
\sum_{\ell=0}^{L-1}
\frac{2}{\sigma_{n,\ell}^2}
\Re\!\big\{\mathbf J_{\eta,\ell}^\Herm\mathbf J_{\eta,\ell}\big\}.
\Re\big\{\mathbf J_{\eta,\ell}^\Herm\mathbf J_{\eta,\ell}\big\}.
\end{equation}
%
由于 $\mathbf J_{\psi,\ell}$ 的实子空间等价于 $\mathbf G_\ell$ 的复列空间,关于复增益块的 Schur 补化为对 $\mathbf G_\ell$ 列空间正交补的投影。定义
@@ -730,7 +730,7 @@ $\mathbf J_{\psi,\ell}$ 的实参数化二维实子空间与复矩阵 $\mathbf G
=
2\sum_{\ell=0}^{L-1}
\frac{1}{\sigma_{n,\ell}^2}
\Re\!\big\{
\Re\big\{
\mathbf J_{\eta,\ell}^\Herm
\mathcal P_{\mathbf G_\ell}^\perp
\mathbf J_{\eta,\ell}
@@ -745,7 +745,7 @@ $\mathbf J_{\psi,\ell}$ 的实参数化二维实子空间与复矩阵 $\mathbf G
=
2\sum_{\ell=0}^{L-1}
\frac{1}{\sigma_{n,\ell}^2}
\Re\!\Big\{
\Re\Big\{
\zeta_{\ell,k}^*\zeta_{\ell,k'}\,
\mathbf D_{\ell,k}^\Herm
\mathcal P_{\mathbf G_\ell}^\perp