Kitajiang/test2_ICPR2024 · Datasets at Hugging Face

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	\[\begin{aligned}\operatorname{Gr}\left(\boldsymbol{S}_{1},\boldsymbol{S}_{2},\ldots,\boldsymbol{S}_{N}\right)=\mid\begin{array}{c c c c}\left(\boldsymbol{S}_{1},\boldsymbol{S}_{1}\right)&\left(\boldsymbol{S}_{1},\boldsymbol{S}_{2}\right)&\cdots&\left(\boldsymbol{S}_{1},\boldsymbol{S}_{N}\right)\\ \left(\boldsymbol{S}_{2},\boldsymbol{S}_{1}\right)&\left(\boldsymbol{S}_{2},\boldsymbol{S}_{2}\right)&\cdots&\left(\boldsymbol{S}_{2},\boldsymbol{S}_{N}\right)\\ \ldots&\cdots&\cdots&\ldots\\ \left(\boldsymbol{S}_{N},\boldsymbol{S}_{1}\right)&\left(\boldsymbol{S}_{N},\boldsymbol{S}_{2}\right)&\cdots&\left(\boldsymbol{S}_{N},\boldsymbol{S}_{N}\right)\end{array}\end{aligned}\]
	\[\begin{aligned}&B_{p p}=B_{\mathrm{B.E.~}}\\ &B_{p o}=\frac{1}{2}\left(B_{\mathrm{B.E.~}}+B_{\mathrm{F.D.~}}\right)\\ &B_{o o}=\frac{1}{9}\left(5B_{\mathrm{B.E.~}}+4B_{\mathrm{F.D.~}}\right)\end{aligned}\]
	\[\begin{array}{l}\Delta G_{0}=R T\log\frac{x}{y}-\left(f_{11}-1\right)\Delta E_{0}+\left(h_{11}-1\right)p\Delta V_{0}+d_{12}\left\{E_{0}^{l}(1-x)^{2}-E_{0}^{v}(1-y)^{2}\right\}\\ \mathrm{~nd~}\quad\Delta G_{0}=R T\log\frac{1-x}{1-y}-\left(f_{22}-1\right)\Delta E_{0}+\left(h_{22}-1\right)p\Delta V_{0}+d_{12}\left\{E_{0}^{l}x^{2}-E_{0}^{v}y^{2}\right\}\end{array}\]
	\[\begin{aligned}\zeta(v,w)=\left\{\begin{array}{l l}0v\leq(1-\delta)w\\ 1v>(1-\delta)w\end{array}\right.\end{aligned}\]
	\[\begin{array}{c}H_{2}A_{e}-k A_{1}=L\\ =H_{2}\xi_{n}^{-1}C_{n}-k D_{n}\\ =\mathscr{H}_{q}[D(\xi)\cdot r]\end{array}\]
	\[\begin{aligned}Y_{\mu\nu}=\left[\begin{array}{c c c}\left(\partial_{\mu}m_{\nu}-\partial_{\nu}m_{\mu}\right.&\left(\partial_{\mu}Q_{\nu}-\partial_{\nu}Q_{\mu}\right),&\frac{1}{2\sqrt{2}}\left(Q^{\mu}L^{\nu}-Q^{\nu}L^{\mu}\right)\\ \left.-\frac{1}{2}Q_{\mu}Q+\frac{1}{2}Q_{\nu}Q_{\mu}\right),&&\\ \left(-\frac{1}{2}\partial_{\mu}Q_{\nu}+\frac{1}{2}\partial_{\nu}Q_{\mu}\right),&\left(\partial_{\mu}n_{\nu}-\partial_{\nu}n_{\mu}-\frac{1}{2}Q_{\mu}Q_{\nu}+\frac{1}{2}Q_{\nu}Q_{\mu}\right),&\frac{1}{2\sqrt{2}}\left(\partial_{\mu}L_{\nu}-\partial_{\nu}L_{\mu}\right)\\ \frac{1}{4\sqrt{2}}\left(L^{\dagger\nu}Q^{\mu}-L^{+\mu}Q^{\nu}\right),&\frac{1}{2\sqrt{2}}\left(\partial_{\mu}L_{\nu}^{\dagger}-\partial_{\nu}L_{\mu}^{\dagger}\right)&+\frac{1}{4\sqrt{2}}\left(L_{\mu}C_{\nu}-L_{\nu}C_{\mu}\right)\\ &+\frac{1}{4\sqrt{2}\sqrt{2}}\left(C_{\mu}L_{\nu}^{+}-C_{\nu}L_{\mu}^{+}\right),&\frac{1}{2}\left(\partial_{\mu}C_{\nu}-\partial_{\nu}C_{\mu}\right)\end{array}\right]\end{aligned}\]
	\[\begin{aligned}\tau_{w}&=\frac{(1-C)}{\eta\left(R/R_{i}\right)^{3}+\alpha^{2}\beta\left(R/R_{n}\right)}\\ &=\frac{(1-C)}{\eta\left(1-\delta/R_{o}\right)^{3}+\alpha^{2}\beta\left(1-\delta/R_{x}\right)}\end{aligned}\]
	\[\begin{array}{l}\omega_{1}=\mathrm{d}x\wedge\mathrm{d}y+\mathrm{d}p\wedge\mathrm{d}y+\mathrm{d}x\wedge\mathrm{d}q+\left(1-c^{2}\right)\mathrm{d}p\wedge\mathrm{d}q\\ =c(\mathrm{~d}x\wedge\mathrm{d}q+\mathrm{d}p\wedge\mathrm{d}y+2\mathrm{~d}p\wedge\mathrm{d}q)\\ =-c(\mathrm{~d}x\wedge\mathrm{d}p+\mathrm{d}y\wedge\mathrm{d}q)\end{array}\]
	\[\begin{array}{r}p+Z_{\mathrm{cyl}}v_{r}=0\\ p_{\mathrm{inc}}+\mathrm{Z}_{\mathrm{inc}}v_{r,\mathrm{~inc~}}=0\\ p_{\mathrm{scat}}-Z_{\mathrm{scat}}v_{r,\mathrm{scat}}=0\end{array}\]
	\[\begin{aligned}\left\{\begin{array}{c}s\left(\xi^{(1)}\right)\\ \vdots\\ s\left(\xi^{(Q)}\right)\end{array}\right\}=\left[\begin{array}{c c c}\Psi_{0}\left(\xi^{(1)}\right)&\ldots&\Psi_{P-1}\left(\xi^{(1)}\right)\\ \vdots&&\vdots\\ \Psi_{0}\left(\xi^{(Q)}\right)&\ldots&\Psi_{P-1}\left(\xi^{(Q)}\right)\end{array}\right]\left\{\begin{array}{c}\gamma_{0}\\ \vdots\\ \gamma_{P-1}\end{array}\right\}\end{aligned}\]
	\[\begin{array}{c}Q_{\mathrm{aeration~}}=G\rho_{g}C_{p g}\left(T_{b}-T_{g}\right)\\ Q_{\mathrm{met~}}=V_{l}\Delta H_{\mathrm{met~}}\\ Q_{\mathrm{evap~}}=G\lambda_{w}\left(H_{g o}-H_{g i}\right)\end{array}\]
	\[\begin{array}{l}\left(D^{2}-b_{5}\right)\psi_{1}^{}-b_{6}\psi_{2}^{}+b_{7}\phi^{}-b_{8}T^{}=o\\ =b_{4}\psi_{1}^{}+\left(D^{2}-b_{9}\right)\psi_{2}^{}\\ =-a_{6}\left(D^{2}-a^{2}\right)\psi_{1}^{}+\left(D^{2}-b_{16}\right)\phi^{}+a_{9}T^{}\\ =-b_{12}\left(D^{2}-a^{2}\right)\psi_{1}^{}-b_{14}\phi^{}+\left(D^{2}-b_{13}\right)T^{}\end{array}\]
	\[\begin{aligned}g\left(\begin{array}{c c}n_{1}&n_{2}\\ m_{1}&m_{2}\end{array}\right)=g_{V}\delta_{n_{1},n_{2}}\delta_{m_{1},m_{2}}\end{aligned}\]
	\[\begin{aligned}\Sigma\frac{n f^{n-1}}{p_{n^{\prime}}}&=2\alpha g e^{-1Y+\alpha^{2}/4\beta^{2}}\int_{-\infty}^{+\infty}e^{-y^{2}}\left(\frac{3y^{2}}{2}+\frac{\alpha^{2}}{8\beta^{2}}\right)d y\\ &=e^{-1C+\alpha^{2}/4\beta^{2}}\frac{\alpha g\sqrt{\pi}}{\beta^{5}}\left\{\frac{3}{2}+\frac{\alpha^{2}}{4\beta^{2}}\right\}\end{aligned}\]
	\[\begin{array}{c}\frac{\mathrm{d}\arg D\left(E_{\bar{\phi}}^{\ddagger}\right)}{\mathrm{d}\alpha_{r}}=-\mathscr{I}\operatorname{tr}\left[G\left(E_{\bar{\phi}}^{\pm}\right)\|r\rangle\langle r\|\right]\\ \quad=\sum_{n}\langle n\mid r\rangle(\mp2\beta\sin\phi)\langle r\mid n\rangle\end{array}\]
	\[\begin{aligned}&K_{A A^{\prime}B B^{\prime}}=u_{A}u_{B}\epsilon_{A^{\prime}B^{\prime}},\mathrm{~charge~}+3\\ &L_{A A^{\prime}B B^{\prime}}=\bar{u}_{A}\bar{u}_{B}\epsilon_{A^{\prime}B^{\prime}},\mathrm{~charge~}-3\\ &J_{A A^{\prime}B B^{\prime}}=\mathrm{i}\left(u_{A}\bar{u}_{B}+\bar{u}_{A}u_{B}\right)\epsilon_{A^{\prime}B^{\prime}},\mathrm{~charge~}0\end{aligned}\]
	\[\begin{aligned}&\boldsymbol{\mu}(\xi)=-e\sum_{\alpha}\left(\boldsymbol{q}_{\alpha(\xi)}-\boldsymbol{R}_{\xi}\right)\\ &\boldsymbol{m}(\xi)=-\frac{e}{2m c}\sum_{\alpha}\boldsymbol{l}_{\alpha(\xi)}\end{aligned}\]
	\[\begin{aligned}B_{4}/B_{6}&=\left(-3B_{4}^{\prime}/2\right)/\left(9B_{6}^{\prime}/16\right)\\ &=-\frac{7\left\langle r^{4}\right\rangle R_{2}^{2}\langle J\\|\beta\\|J\rangle}{2\left\langle r^{6}\right\rangle\langle J\\|\gamma\\|J\rangle}\end{aligned}\]
	\[\begin{array}{l}T_{s}/T_{E}=2\left\{\gamma M^{2}(\gamma-1)+2\gamma\right\}/(\gamma+1)^{2}\\ =2\gamma M^{2}/(\gamma+1)\end{array}\]
	\[\begin{array}{l}n^{\prime}=F^{\prime}S M_{2}\tau\\ =F_{u}S^{2}M_{1}M_{2}\tau/4\pi D^{2}\end{array}\]
	\[\begin{aligned}\left.\begin{array}{l}\dot{x}=f(x,u)\\ y=\lambda_{n}x_{n}\end{array}\right\}\end{aligned}\]
	\[\begin{array}{l}\mathrm{~Maximum~principal~stress~}=\frac{f_{2}}{2}+\sqrt{\frac{f_{2}^{2}}{4}+f_{1}^{2}}\\ \mathrm{~Maximum~shear~stress~}=\sqrt{\frac{f_{2}^{2}}{4}+f_{1}^{2}}\end{array}\]
	\[\begin{aligned}\left\|\begin{array}{l l l}x-x_{1}&y-y_{1}&z-z_{1}\\ x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\ x_{3}-x_{1}&y_{3}-y_{1}&z_{3}-z_{1}\end{array}\right\|=\left\|\begin{array}{l l l}x-x_{1}&y-y_{1}&z-z_{1}\\ x-x_{2}&y-y_{2}&z-z_{2}\\ x-x_{3}&y-y_{3}&z-z_{3}\end{array}\right\|=0\end{aligned}\]
	\[\begin{aligned}\left.\begin{array}{l}N(c)=X-Y\frac{K_{0}^{2}}{K^{2}}-Z\ln\left(\frac{K^{2}}{K_{0}^{2}}\right)\\ Z=\frac{R^{2}}{\pi A(\Delta R)^{4}},\quad Y=\frac{\omega K_{1,\mathrm{c}}^{2}}{K_{0}^{2}}Z\\ X=\left\{\frac{K_{1,\mathrm{c}}^{2}}{K_{0}^{2}}+1-\frac{1}{\omega}\right\}Z\end{array}\right\}\end{aligned}\]
	\[\begin{aligned}\rho^{(1)}(1\cdot u\cdot j)\rho^{(2)}(i\cdot v\cdot1)&=\left[\rho^{(1)}\left(1\cdot u^{\prime}\cdot j^{\prime}\right)e\right]\rho^{(2)}(i\cdot v\cdot1)\\ &=\rho^{(1)}\left(1\cdot u^{\prime}\cdot j^{\prime}\right)\left[e\rho^{(2)}(i\cdot v\cdot1)\right]\\ &=\rho^{(1)}\left(1\cdot u^{\prime}\cdot j^{\prime}\right)\rho^{(2)}\left(i^{\prime}\cdot v^{\prime}\cdot1\right)\end{aligned}\]
	\[\begin{array}{l}\mathbf{r}_{l}^{+}=b\left(\cos\omega x\mathbf{e}_{1}+\sin\omega x\mathbf{e}_{2}\right)+x\mathbf{e}_{3}\\ =b\left(\cos(\omega x+\alpha)\mathbf{e}_{1}+\sin(\omega x+\alpha)\mathbf{e}_{2}\right)+x\mathbf{e}_{3}\end{array}\]
	\[\begin{aligned}\left.\begin{array}{l}P_{11}^{\prime}=\frac{2\eta_{0}D^{2}\left(\lambda_{1}-\lambda_{2}\right)}{1+\mu_{0}\lambda_{1}D^{2}}\\ P_{12}^{\prime}=\frac{\eta_{0}D\left(1+\mu_{0}\lambda_{2}D^{2}\right)}{1+\mu_{0}\lambda_{1}D^{2}}\\ P_{12}^{\prime}=0=P_{33}^{\prime}\end{array}\right\}\end{aligned}\]
	\[\begin{array}{c}W_{1}=\frac{\pi^{2}E}{2\left(1-\sigma^{2}\right)}\int_{F}^{c}r\left(1-r^{2}/c^{2}\right)^{\frac{1}{2}}d r\int_{3}^{\epsilon}\epsilon d\epsilon\\ =\frac{\pi^{2}E c\epsilon^{2}}{12\left(1-\sigma^{2}\right)}\end{array}\]
	\[\begin{array}{l}I_{2}^{M}:=\frac{\{\boldsymbol{\theta}\cdot\boldsymbol{\theta}\}_{2}}{M}\cdot I_{3}^{M}:\cdot\frac{\left\{\boldsymbol{\theta}^{3}\cdot\mathbf{t}\right\}_{6}}{M^{2}}\cdot I_{4}^{M}:\cdot\frac{\left\{\boldsymbol{\theta}^{4}\cdot\{\mathbf{t}\cdot\mathbf{t}\}_{2}\right\}_{8}}{M^{3}}\\ =\left\{\{\boldsymbol{\theta}\cdot\mathbf{f}\}_{1}\cdot\{\mathbf{t}\cdot\mathbf{t}\}_{2}\right\}_{8}\frac{\left\{\boldsymbol{\theta}^{6}\cdot\mathbf{j}\right\}_{12}}{M^{6}}\\ =\left(\frac{36\left\{\boldsymbol{\theta}^{2}\mathbf{f}\cdot\mathbf{j}\right\}_{12}}{M^{2}}-\frac{28\left\{\left\{\boldsymbol{\theta}^{2}\cdot\mathbf{f}\right\}_{3}\cdot\mathbf{t}\right\}_{6}}{5M}\right)\frac{\left\{\boldsymbol{\theta}^{6}\cdot\mathbf{j}\right\}_{12}}{M^{5}}\\ =\frac{2\left\{\mathbf{f}\boldsymbol{\theta}^{3}\cdot\mathbf{t}\{\mathbf{t}\cdot\mathbf{t}\}_{2}\right\}_{14}}{M^{3}}+\frac{2M\left\{\left\{\mathbf{f}\cdot\boldsymbol{\theta}^{3}\right\}_{1}\cdot\mathbf{j}\right\}_{12}}{7M^{3}}-\frac{7q\left\{\left\{\mathbf{f}\cdot\boldsymbol{\theta}^{3}\right\}_{4}\cdot\mathbf{t}\right\}_{6}}{99M^{2}}\end{array}\]
	\[\begin{aligned}\left[\begin{array}{l l}K_{11}&K_{12}\\ K_{21}&K_{22}\end{array}\right]\left[\begin{array}{l}x_{1}\\ x_{2}\end{array}\right]=\left[\begin{array}{l}F_{1}\\ F_{2}\end{array}\right]\end{aligned}\]
	\[\begin{array}{l}\mathbf{E}_{1}=\mathbf{F}_{1}b\frac{\pi\mathbf{D}}{\mathbf{N}t}1i-8\\ =\mathbf{F}_{2}b\frac{\pi\mathbf{D}}{\mathbf{N}t}1Q-8\\ =\mathbf{F}_{3}b\frac{\pi\mathbf{D}}{\mathbf{N}t}1r-8\end{array}\]
	\[\begin{aligned}&p(x)=\sum_{x^{\prime}\in\mathcal{X}}p\left(x\mid x^{\prime}\right)p\left(x^{\prime}\right)\\ &p\left(x\mid x^{\prime}\right)=\mathbb{E}_{z\sim p(z)}\left[p_{\mathrm{edit~}}\left(x\mid x^{\prime},z\right)\right]\end{aligned}\]
	\[\begin{aligned}U_{e,-1}=\frac{1}{\sqrt{E_{e}+m_{e}}}\left(\begin{array}{c}0\\ E_{e}+m_{e}\\ 0\\ -p_{e z}\end{array}\right)\end{aligned}\]
	\[\begin{array}{l}\kappa_{g}=\frac{8k^{2}\zeta^{2}\Theta}{3\pi h}\left(\frac{D}{\zeta}\right)^{2}\left(\frac{T}{\Theta}\right)^{2}\Sigma\Lambda_{j}P_{j,4},\\ \Im_{g}=\sqrt{2}k\left(\frac{D}{\zeta}\right)^{\frac{3}{2}}\left(\frac{T}{\Theta}\right)^{3}\sum_{j}P_{j,5}\end{array}\]
	\[\begin{array}{l}T(x\cdot z)=T_{11}\cdot-Y z\kappa+e\partial_{3}P_{3}\\ =-\partial_{3}\phi\cdot a_{33}P(x\cdot z)+(e-\mu)\kappa\end{array}\]
	\[\begin{aligned}\left.\begin{array}{r}\left\{c_{11}l^{2}+c_{44}\left(m^{2}+n^{2}\right)-\rho V_{i}^{2}\right\}A_{i}+\left(c_{12}+c_{44}\right)\left(\operatorname{lm}B_{i}+n l C_{i}\right)=0\\ \left\{c_{11}m^{2}+c_{44}\left(l^{2}+n^{2}\right)-\rho V_{i}^{2}\right\}B_{i}+\left(c_{12}+c_{44}\right)\left(\operatorname{lm}A_{i}+m n C_{i}\right)=0\\ \left\{c_{11}n^{2}+c_{44}\left(l^{2}+m^{2}\right)-\rho V_{i}^{2}\right\}C_{i}+\left(c_{12}+c_{44}\right)\left(\ln A_{i}+m n B_{i}\right)=0\end{array}\right\}\end{aligned}\]
	\[\begin{aligned}b_{b}T=\left[\begin{array}{c c c c}c_{\phi_{i}}&-s_{\phi_{i}}&0&-r_{b}\left(c_{\phi_{i}}\right)\\ s_{\phi_{i}}&c_{\phi_{i}}&0&-r_{b}\left(s_{\phi_{i}}\right)\\ 0&0&1&0\\ 0&0&0&1\end{array}\right]\end{aligned}\]
	\[\begin{array}{c}\frac{\mathrm{LN}-\mathrm{M}^{2}}{\mathrm{EG}-\mathrm{F}^{2}}=\frac{1}{\rho_{1}\rho_{2}}\cdot\mathrm{K}\\ =4\mathrm{~V}^{2}\mathrm{H}\left(w^{\prime}\right)\end{array}\]
	\[\begin{aligned}\mu&=\mu_{\max}\cdot\operatorname{EXP}\left(-\frac{2.3}{15}\cdot\left\|T-T_{o p t}\right\|\right.\\ &\times)\cdot\frac{I}{I+K_{I}}\cdot\frac{C_{n}}{C_{n}+K_{N}}\cdot\frac{C_{p}}{C_{p}+K_{P}}\cdot f\left(u_{w}\right)\end{aligned}\]
	\[\begin{aligned}H_{A}&=F_{h}\\ &=\frac{F_{v}\cdot a}{a+b+c}\\ &=F_{v}-V_{C}\end{aligned}\]
	\[\begin{aligned}\mathbb{J}_{N}=\left(\begin{array}{l l l l}0&0&0&1\\ 0&0&1&0\\ 0&.\cdot&0&0\\ 1&0&0&0\end{array}\right),\end{aligned}\]
	\[\begin{aligned}\operatorname{diag}_{2}=\left(\begin{array}{c c c}\sqrt{\rho}&0&0\\ 0&\mathrm{i}\sqrt{2\eta}&0\\ 0&0&\mathrm{i}\sqrt{2\eta}\end{array}\right)\end{aligned}\]
	\[\begin{array}{l}\mathrm{~low-frequency:~}\frac{\partial\rho_{3}^{\prime}}{\partial t}=-\frac{\alpha\beta c^{4}\tau_{\nu}}{c_{p}\rho_{0}}\left(\frac{\partial\rho_{1}}{\partial x}\right)^{2}+\frac{\alpha c}{2\rho_{0}}\frac{\partial\rho_{1}^{\prime2}}{\partial x}\\ \mathrm{~high-frequency:~}\frac{\partial\rho_{3}^{\prime}}{\partial t}=-\frac{\alpha\beta c^{2}}{\tau_{\nu}c_{p}\rho_{0}}\rho_{1}^{\prime2}\end{array}\]
	\[\begin{array}{l}p^{i}:\mathrm{u}_{f}(t)=e^{-t}\\ =\mathrm{u}_{8}(t)\int_{M}^{t}\frac{t^{2}}{2e^{(t+s)}}H_{L}(s)d s\\ =\mathrm{u}_{l}(t)\int_{7}^{t}\frac{t^{2}}{2e^{(t+s)}}H_{1}(s)d s+\mathrm{u}_{1}(t)\int_{F}^{t}\frac{t^{2}}{2e^{(t+s)}}H_{b}(s)d s\end{array}\]
	\[\begin{aligned}\mathrm{d}\ln A_{n}/\mathrm{d}t&=\nabla_{\perp}\cdot\boldsymbol{c}\\ &=\nabla\boldsymbol{k}:\Omega_{k k}+\operatorname{tr}\left(\Omega_{k x_{\perp\perp}}\right)\\ &=\nabla_{\perp}\boldsymbol{n}:\left(k\Omega_{k k}\right)+\operatorname{tr}\left(v_{n x_{\perp\perp}}\right)\end{aligned}\]
	\[\begin{array}{l}E_{g}=\frac{1240}{\lambda_{\mathrm{peak~}}}\\ E_{g}=E_{g}^{b}+\frac{h}{8D^{2}}\left(\frac{1}{m_{e}}+\frac{1}{m_{h}}\right)\end{array}\]
	\[\begin{aligned}f(\operatorname{Re})=\left\{\begin{array}{l l}\frac{24}{\operatorname{Re}}\left(1+\frac{3}{16}\operatorname{Re}\right)\mathrm{Re}<0.01\\ \frac{24}{\operatorname{Re}}\left(1+0.1315\mathrm{Re}^{0.82-0.05\log_{10}\operatorname{Re}}\right)0.01\leq\operatorname{Re}\leq20\end{array}\right.\end{aligned}\]
	\[\begin{aligned}\mu_{1}\left(z_{1}b_{1}^{\vee}\right)&=\mu_{1}\left(z_{2}b_{2}^{\vee}\right)\cdot j\\ &=P_{j-1}\left(A_{1}\cdot\ldots\cdot A_{j-1}\right)w_{j}P_{n-j}\left(A_{j+1}^{\prime}\cdot\ldots\cdot A_{n}^{\prime}\right)b_{1}^{\vee}\\ &=-v_{1}\left(T_{1}^{\prime}\right)^{-1}b_{1}^{\vee}\\ &=\mu_{1}\left(v_{2}x_{2}^{\vee}\right)\end{aligned}\]
	\[\begin{array}{c}\left(u_{0e}^{\prime}+a_{0e}^{\prime}\right)\left\{\left(u_{0e}+a_{0e}\right)-\tan\theta\right\}=0\\ \left(u_{0e}^{\prime}-a_{0e}^{\prime}\right)\left\{\left(u_{0e}-a_{0e}\right)-\tan\theta\right\}=0\\ u_{0e}^{\prime}=\mathrm{d}u_{0e}/\mathrm{d}\theta,\quad\mathrm{~etc}\end{array}\]
	\[\begin{aligned}\boldsymbol{B}(x\cdot W)&=\boldsymbol{b}(x)\cdot\boldsymbol{B}\left(x\cdot R^{+}\right)\cdot\boldsymbol{B}\left(x\cdot m^{-}\right)\\ &=-\boldsymbol{i}_{x}l\cdot\boldsymbol{B}(x\cdot a)-\boldsymbol{B}(x\cdot-a)\cdot-\boldsymbol{i}_{y}2a\\ &=\nabla\boldsymbol{B}(g\cdot y)\cdot\nabla\boldsymbol{B}(x\cdot-a)\cdot\nabla\boldsymbol{B}(x\cdot a)\end{aligned}\]
	\[\begin{aligned}\bar{\mathbf{C}}=\left[\begin{array}{l l}2\xi_{h0}\omega_{h0}&\\ &2\xi_{\alpha0}\omega_{\alpha0}\end{array}\right],\bar{\mathbf{K}}=\left[\begin{array}{l l}\omega_{h0}^{2}&\\ &\omega_{\alpha0}^{2}\end{array}\right],\quad\mathbf{C}_{s e}=\left[\begin{array}{l l}H_{1}&H_{2}\\ A_{1}&A_{2}\end{array}\right],\quad\mathbf{K}_{s e}=\left[\begin{array}{c c}H_{4}&H_{3}\\ A_{4}&A_{3}\end{array}\right](6)\end{aligned}\]
	\[\begin{aligned}W^{-1}(\tau)=\mathrm{e}^{F(\tau)}\left(\begin{array}{c c}w_{22}(\tau)&-w_{12}(\tau)\\ -w_{21}(\tau)&w_{11}(\tau)\end{array}\right)\end{aligned}\]
	\[\begin{array}{c}\frac{d^{2}A}{d t^{2}}=-2\left[\left(c^{2}+\frac{1}{3}\bar{u^{2}}\right)k^{2}-4\pi G\bar{\rho}\right]A\\ k^{2}<\frac{4\pi G\bar{\rho}}{c^{2}+\frac{1}{3}\bar{u^{2}}}\end{array}\]
	\[\begin{array}{c}\mathcal{S}^{\prime}=\left\{s_{a}:a\in\Delta_{\mathrm{aff}}^{\prime}\right\}\\ =\left\{w\in\mathcal{W}_{\chi_{C}}:w\left(\mathcal{A}^{\prime}\right)\cdot\mathcal{A}^{\prime}\right\}\end{array}\]
	\[\begin{array}{l}\mathrm{~Eswirl~}(\%)=\left[\frac{1}{\left(1+\frac{F S}{m}\right)}\right]100\\ A E(\%)=\left[1-\frac{1+\frac{F S}{m}}{1+F S}\right]100\end{array}\]
	\[\begin{aligned}S=\left[\begin{array}{l}r-i\\ -g h\frac{\partial Z}{\partial x}-g\frac{n^{2}u\sqrt{u^{2}+v^{2}}}{h^{1/3}}\\ -g h\frac{\partial Z}{\partial x}-g\frac{n^{2}u\sqrt{u^{2}+v^{2}}}{h^{1/3}}\end{array}\right]\end{aligned}\]
	\[\begin{array}{l}\quad x+2y+2(x+y-1)t+(x-2)t^{2}-\frac{2t^{3}}{3}=\frac{\theta_{p}}{\beta u_{y}}\\ \mathrm{~where~}t=\left(\frac{x}{2}-1\right)+\left(\frac{x^{2}}{4}+y\right)^{\frac{1}{2}}\end{array}\]
	\[\begin{aligned}&F_{\theta}=F_{\alpha}-F_{\mathrm{frame~}}\\ &m\frac{d v}{d\theta}=m\frac{d v}{d\alpha}-m\frac{d v}{d t}\end{aligned}\]
	\[\begin{array}{c}\Phi_{\Xi}\left(g_{2}\right)=\int_{K_{2}}f_{\Xi}\left(k_{2}g_{2}\right)d k_{2}\cdot\Phi_{\xi}\left(g_{W}\right)\cdot\int_{K_{C}}f_{\xi}\left(k_{i}g_{X}\right)d k_{2}\\ =\int_{L\left(\mathfrak{o}_{F}\right)}\omega_{\psi}\left(h g_{s}\right)\mathbf{1}_{L^{*}\left(\mathfrak{o}_{F}\right)}(x)d x\end{array}\]
	\[\begin{array}{l}\rho_{G L}=\left(1+e^{\alpha_{G L}\left(\Theta_{G L}-V_{L}+V_{R}\right)}\right)^{-1}\\ =\left(1+e^{\alpha_{G R}\left(\Theta_{G R}-V_{R}+V_{L}\right)}\right)^{-1}\end{array}\]
	\[\begin{aligned}\frac{\mathrm{d}}{\mathrm{d}t}E(Y I)&=\alpha E\left(I^{2}\right)-(\xi+\delta)E(Y I)+\frac{\beta V}{H}E\left(Y^{2}\right)\\ &-\frac{\alpha}{H}E\left(Y I^{2}\right)-\frac{\beta}{H}E\left(Y^{2}I\right)\end{aligned}\]
	\[\begin{aligned}\left(\begin{array}{c}Z\\ Z^{\prime}\end{array}\right)=\left(\begin{array}{c c}c_{\phi}&s_{\phi}\\ -s_{\phi}&c_{\phi}\end{array}\right)\left(\begin{array}{l}Z_{0}\\ Z_{1}\end{array}\right)\end{aligned}\]
	\[\begin{aligned}&\left\langle q\left\|T_{1}\right\|q^{\prime}\right\rangle=\sum_{s,s^{\prime}\geqslant1}^{\infty}\frac{\mathrm{i}}{\omega_{s,s^{\prime}}}\varphi_{s}(q)\varphi_{s^{\prime}}^{}\left(q^{\prime}\right)\\ &\left\langle q\left\|T_{M}\right\|q^{\prime}\right\rangle=\sum_{s,s^{\prime}\geqslant1}^{\infty}\sum_{r,r^{\prime}\geqslant1}^{M}\frac{\mathrm{i}}{\omega_{s,s^{\prime}}}\varphi_{s,r}(q)\varphi_{s^{\prime},r^{\prime}}^{}\left(q^{\prime}\right)\end{aligned}\]
	\[\begin{aligned}&\mathrm{Mo}-\mathrm{Mo}=2\cdot79\mathrm{~A}\\ &\mathrm{~and~}=3\cdot71\mathrm{~A}\end{aligned}\]
	\[\begin{array}{l}\mathcal{D}^{+}=\left\{\boldsymbol{x}\in\mathcal{D}\mid h_{\mathcal{P}}(\boldsymbol{x})>Z\right\}\\ =\left\{\boldsymbol{x}\in\mathcal{D}\mid h_{\mathcal{P}}(\boldsymbol{x})\cdot D\right\}\\ =\left\{\boldsymbol{x}\in\mathcal{D}\mid h_{\mathcal{P}}(\boldsymbol{x})<E\right\}\end{array}\]
	\[\begin{aligned}A_{\mathrm{m}}&=s^{2}a^{2}E(k)+\left(a^{2}-a^{2}s^{2}\right)K(k)+\left(a^{2}s^{2}+s^{2}b^{2}-2a^{2}\right)\Pi\left(s^{2}k^{2}\cdot k\right)\\ &=\left(a^{4}-s^{4}a^{2}b^{2}\right)E(k)+\left(s^{4}a^{2}b^{2}-2s^{2}a^{2}b^{2}+a^{2}b^{2}\right)K(k)\\ &+\left(-a^{4}-s^{4}a^{2}b^{2}+4s^{2}a^{2}b^{2}-a^{2}b^{2}-s^{4}b^{4}\right)\Pi\left(s^{2}k^{2}\cdot k\right)\end{aligned}\]
	\[\begin{aligned}\frac{\partial\rho(u\cdot v\cdot t)}{\partial t}&=\frac{\partial}{\partial u}\left(\gamma_{u}u\rho\right)+\frac{\partial}{\partial v}\left(\gamma_{v}v\rho\right)+\sigma(t)\left\{\rho\left(u-h_{u}\cdot v\right)-\rho(u\cdot v)\right\}\\ &+\sigma(t)\delta(u)\int_{1-h_{u}}^{1}d u^{\prime}\rho\left(u\cdot v-h_{v}\cdot t\right)d u^{\prime}+\sigma(t)\delta(u)\delta(v)\\ &\times\int_{1-h_{u}}^{1}d u^{\prime}\int_{1-h_{v}}^{1}d v^{\prime}\rho\left(u^{\prime}\cdot v^{\prime}\cdot t\right)\end{aligned}\]
	\[\begin{aligned}&\frac{1}{v_{\mathrm{p}}}\frac{\partial I_{\mathrm{p}}}{\partial t}+\mu\frac{\partial I_{\mathrm{p}}}{\partial x}\\ &=\frac{(1/2)\int_{-1}^{1}I_{\mathrm{p}}d\mu-I_{\mathrm{p}}}{\Lambda_{\mathrm{p}}}-\frac{G}{2}\left(\frac{1}{C_{\mathrm{p}}v_{\mathrm{p}}}\int_{-1}^{1}I_{\mathrm{p}}d\mu-\frac{1}{C_{\mathrm{e}}v_{\mathrm{e}}}\int_{-1}^{1}I_{\mathrm{e}}d\mu\right)\end{aligned}\]
	\[\begin{aligned}P_{X}(z)&:=1\cdot Q_{M}(z):\cdot1\\ &=P_{k}(z)+z^{2^{k}}Q_{k}(z)\\ &=P_{k}(z)-z^{2^{k}}Q_{k}(z)\end{aligned}\]
	\[\begin{aligned}\left(\begin{array}{l l}A&B\\ C&D\end{array}\right)=\left(\begin{array}{l l}A&0\\ C&1\end{array}\right)\left(\begin{array}{c c}1&A^{-1}B\\ 0&D-C A^{-1}B\end{array}\right)\end{aligned}\]
	\[\begin{aligned}y_{v_{r}v_{s}}\left(\omega_{\mathrm{e}}\right)&=\int_{t}^{l}\int_{u}^{l}\left\{\int_{-\infty}^{\infty}y_{v}(x:\xi\cdot\tau)\mathrm{e}^{-\mathrm{i}\omega_{\mathrm{e}}\tau}d\tau\right\}v_{r}(\xi)v_{s}(x)\mathrm{d}x\mathrm{~d}\xi\\ &=\int_{Z}^{l}\int_{J}^{l}y_{v}\left(x:\xi\cdot\omega_{\mathrm{e}}\right)v_{r}(\xi)v_{s}(x)\mathrm{d}x\mathrm{~d}\xi\\ &=y_{v_{r}v_{s}}^{R}\left(\omega_{\mathrm{e}}\right)+\mathrm{i}y_{v_{r}v_{s}}^{I}\left(\omega_{\mathrm{e}}\right)\end{aligned}\]
	\[\begin{aligned}\left(\begin{array}{c c}m_{1}&\\ &m_{2}\end{array}\right)=\sqrt{m_{1}m_{2}}e^{-\xi\sigma_{3}},\quad\xi=\frac{1}{2}\ln\left(m_{2}/m_{1}\right)\end{aligned}\]
	\[\begin{array}{r}Z\left(x_{P}+V t\cdot t\right)=\frac{1}{4\pi^{2}\left(x_{R}+V t\right)}\int_{\mathrm{i}\sigma-\infty}^{\mathrm{i}\sigma+\infty}\int_{-\infty}^{\infty}\boldsymbol{B}^{\mathrm{R}}\left(x_{O}+V t\cdot\omega+V k\right)\\ \times\left[\mathrm{i}k\boldsymbol{I}-\boldsymbol{A}^{\mathrm{R}}(\omega+V k)\right]^{-2}\left[\boldsymbol{B}^{\mathrm{R}}(8\cdot\omega+V k)\right]^{-1}\\ \times\boldsymbol{D}^{\mathrm{R}}(\omega+V k)H(\omega+V k)\mathrm{e}^{\mathrm{i}\left(k x_{M}-\omega t\right)}\mathrm{d}k\mathrm{~d}\omega.\end{array}\]
	\[\begin{aligned}\left.\begin{array}{l}\mathrm{A}\frac{d\omega_{1}}{d t}-(\mathrm{B}-\mathrm{C})\omega_{2}\omega_{3}=\mathrm{X}_{1}\\ \mathrm{~B}\frac{d\omega_{2}}{d t}-(\mathrm{C}-\mathrm{A})\omega_{3}\omega_{1}=\mathrm{Y}_{1}\\ \mathrm{C}\frac{d\omega_{3}}{d t}-(\mathrm{A}-\mathrm{B})\omega_{1}\omega_{2}=\mathrm{Z}_{1}\end{array}\right\}\end{aligned}\]
	\[\begin{aligned}\left.\begin{array}{r l}\sigma_{x}=\frac{E}{1-\mu^{2}}\left(e_{x}+\mu e_{\theta}\right)\\ \sigma_{x,}=E e_{x}\\ e_{x}=E_{x}-z X_{x}=e_{x_{\imath}}\\ e_{\theta}=E_{\theta}-z X_{\theta}\end{array}\right\}\end{aligned}\]
	\[\begin{aligned}\mathbf{I}_{\mathbf{s}}=\left[\begin{array}{c c c}941.129&0.477&0.061\\ 0.477&864.456&43.457\\ 0.061&43.457&918.303\end{array}\right]\mathrm{kg}\cdot\mathrm{m}^{2}\end{aligned}\]
	\[\begin{aligned}N_{1}&=\left(\Gamma\left(\frac{c}{a}\right)\right)^{3}\Gamma\left(\frac{4+c}{a}\right)-4\Gamma\left(\frac{1+c}{a}\right)\left(\Gamma\left(\frac{c}{a}\right)\right)^{2}\Gamma\left(\frac{3+c}{a}\right)\\ &=6\left(\Gamma\left(\frac{1+c}{a}\right)\right)^{2}\Gamma\left(\frac{c}{a}\right)\Gamma\left(\frac{c+2}{a}\right)-3\left(\Gamma\left(\frac{1+c}{a}\right)\right)^{4}\\ &=\left(\Gamma\left(\frac{c+2}{a}\right)\Gamma\left(\frac{c}{a}\right)-\left(\Gamma\left(\frac{1+c}{a}\right)\right)^{2}\right)^{2}.\end{aligned}\]
	\[\begin{aligned}\left.\begin{array}{l}F_{\mathrm{A}}^{\mathrm{IV}}=-6\pi\mu r_{\mathrm{A}}\left\{v_{\mathrm{A}}^{\mathrm{IV}}f_{1}^{\mathrm{IV}}(k,\epsilon)+v_{\mathrm{B}}^{\mathrm{IV}}f_{2}^{\mathrm{IV}}\left(k^{-1},\epsilon k^{-1}\right)\right\},\\ F_{\mathrm{B}}^{\mathrm{IV}}=-6\pi\mu r_{\mathrm{B}}\left\{v_{\mathrm{A}}^{\mathrm{I}}f_{2}^{\mathrm{IV}}(k,\epsilon)+v_{\mathrm{B}}^{\mathrm{I}}f_{1}^{\mathrm{IV}}\left(k^{-1},\epsilon k^{-1}\right)\right\}\end{array}\right\}\end{aligned}\]
	\[\begin{array}{l}\mathrm{~1.~}\mathcal{Y}_{0}=\left\{x_{0}\right\}\\ \mathrm{~2.~For~}i\geq0,\quad\mathcal{Y}_{i+1}=\mathcal{Y}_{i}\cup w_{0}\left(\mathcal{Y}_{i}\right)\cup w_{1}\left(\mathcal{Y}_{i}\right)\quad\left(\mathrm{~Note:~}\mathcal{Y}_{i+1}\supseteq\mathcal{Y}_{i}\right)\\ \mathrm{~3.~}\mathcal{A}_{0}=\lim_{i\rightarrow\infty}\mathcal{Y}_{i}\end{array}\]
	\[\begin{array}{l}\frac{\partial u}{\partial t}=D\frac{\partial^{2}u}{\partial x^{2}}+\lambda(r)u-\omega(r)v\\ =D\frac{\partial^{2}v}{\partial x^{2}}+\omega(r)u+\lambda(r)v\end{array}\]
	\[\begin{aligned}\left.\begin{array}{l}a_{r}^{\dagger}a_{r}\Psi_{N}=0\\ a_{-r}^{\dagger}a_{-r}\Psi_{N}=\Psi_{N}\end{array}\right\}\quad r>N\end{aligned}\]
	\[\begin{aligned}k^{2}E_{x}&=-\frac{\mathrm{d}}{\mathrm{d}z}\left[\mathrm{i}k\sin\theta(1/l+1)E_{z}\right]\\ &=-\mathrm{i}k\sin\theta\alpha\vartheta\left(\frac{1-v}{\sin^{2}\theta}E_{z}\right)\\ &=\frac{1}{\mathrm{i}h\sin\theta}\vartheta\left[(1-v)E_{z}\right]\end{aligned}\]
	\[\begin{aligned}\left.\begin{array}{l}U_{m}=\int_{0}^{\pi}\left\{\cos\left(\frac{\alpha}{\sin\phi}\right)+\sin\left(\frac{\alpha}{\sin\phi}\right)\right\}\frac{\cos m\phi}{(\sin\phi)^{3/2}}d\phi\\ \mathrm{V}_{m}=\int_{0}^{\pi}\left\{\cos\left(\frac{\alpha}{\sin\phi}\right)-\sin\left(\frac{\alpha}{\sin\phi}\right)\right\}\frac{\sin m\phi}{(\sin\phi)^{3/2}}d\phi\end{array}\right\}\end{aligned}\]
	\[\begin{aligned}\left.\begin{array}{c}\epsilon_{\lambda\beta}^{(3)}s^{\lambda\beta}=\epsilon\rho\epsilon_{\lambda\beta}s^{(2)}d d_{\alpha}^{\lambda}\\ \partial s^{(3)}/\partial\rho=-\left.s^{\alpha\beta}\right\|_{\alpha}+\epsilon d_{\alpha}^{\beta}{}^{(2)}s^{\alpha3}\\ \partial s^{*33}/\partial\rho=-d_{\alpha\beta}{}^{(3)}s^{\alpha\beta}-\left.(\delta/\epsilon)s^{\alpha3}\right\|_{\alpha}\end{array}\right\}\end{aligned}\]
	\[\begin{array}{l}p\left(v_{n+1\cdot m}^{(h)}-v_{n\cdot m}^{(h)}\right)+u_{n+1\cdot m}^{(h)}v_{n\cdot m}^{(h)}=U_{n\cdot m}^{(h)}(1\cdot-1)\\ =q\left(v_{n\cdot m+1}^{(h)}-v_{n\cdot m}^{(h)}\right)+u_{n\cdot m+1}^{(h)}v_{n\cdot m}^{(h)}\\ =u_{n+1\cdot m}^{(h)}v_{n\cdot m}^{(h)}\end{array}\]
	\[\begin{aligned}&p_{x x}-p_{0}=-\frac{4}{675}\frac{1}{2h}\mathrm{C}_{0}c_{x x}\sum_{0}^{\infty}\left(\nu_{1}\gamma_{r}+\nu_{2}\gamma_{-r}\right)\\ &p_{x y}=-\frac{4}{675}\frac{1}{2h}\mathrm{C}_{0}c_{x y}\sum_{0}^{\infty}\left(\nu_{1}\gamma_{r}+\nu_{2}\gamma_{-r}\right)\end{aligned}\]
	\[\begin{aligned}\left\{\begin{array}{c}M=J\frac{d\omega_{1}}{d t}\\ M=F_{1}r_{2}\cos\theta-F_{2}r_{3}\\ r_{1}=f(\varphi)=f\left(\omega_{1}t\right)\\ v_{1}=\frac{d r_{1}}{d t}\\ v_{1y}=v_{1}\cos\alpha_{1}\\ \omega_{2}=\frac{v_{1y}\cos\alpha_{2}}{l_{1}}=\frac{v_{2}\cos\alpha_{2}}{t_{2}}\\ \omega_{3}=\frac{v_{2}\cos\beta_{1}}{l_{3}}=\frac{v_{3}\cos\beta_{2}}{t_{4}}\\ s=\int_{0}^{t}v_{3}d t\end{array}\right.\end{aligned}\]
	\[\begin{aligned}q_{i j}(h)&=\frac{1}{\gamma+\eta\omega_{i}}\left(\alpha+\frac{\eta}{\gamma}\omega_{i}p_{j}\right)-\frac{1}{\gamma}p_{i j}(h)\\ &=\frac{1}{\gamma}\left[P_{j}+\frac{\gamma\left(\alpha-P_{j}\right)}{\gamma+\eta\omega_{i}}-p_{i j}(h)\right]\\ &=\frac{1}{\gamma}\left[\bar{h}_{j}-p_{i j}(h)\right]\end{aligned}\]
	\[\begin{aligned}\frac{\partial e_{2}}{h\partial x_{2}}&=-\left[\frac{\mathrm{d}h}{h\mathrm{~d}z}\right]e_{3}\\ &=\left[\frac{\mathrm{d}h}{h\mathrm{~d}z}\right]e_{2}\end{aligned}\]
	\[\begin{aligned}\left.\begin{array}{r l}p=\left(\chi_{i}\right)_{1}\left(\chi_{f}\right)_{1}^{}+\left(\chi_{i}\right)_{2}\left(\chi_{f}\right)_{2}^{}+\left(\chi_{i}\right)_{3}\left(\chi_{f}\right)_{3}^{}+\left(\chi_{i}\right)_{4}\left(\chi_{f}\right)_{4}\\ j_{x}=\left(\chi_{i}\right)_{1}\left(\chi_{f}\right)_{4}^{}+\left(\chi_{i}\right)_{2}\left(\chi_{f}\right)_{3}+\left(\chi_{i}\right)_{3}\left(\chi_{f}\right)_{2}^{}+\left(\chi_{i}\right)_{4}\left(\chi_{f}\right)_{1}\\ j_{y}=i\left(\chi_{i}\right)_{1}\left(\chi_{f}\right)_{4}^{}-i\left(\chi_{i}\right)_{2}\left(\chi_{f}\right)_{3}^{}+i\left(\chi_{i}\right)_{3}\left(\chi_{f}\right)_{2}^{}-i\left(\chi_{i}\right)_{4}\left(\chi_{f}\right)_{1}\\ j_{2}=\left(\chi_{i}\right)_{1}\left(\chi_{f}\right)_{3}^{}-\left(\chi_{i}\right)_{2}\left(\chi_{f}\right)_{4}^{}+\left(\chi_{i}\right)_{3}\left(\chi_{f}\right)_{1}^{}-\left(\chi_{i}\right)_{4}\left(\chi_{f}\right)_{2}^{}\end{array}\right\}\end{aligned}\]
	\[\begin{aligned}G^{*}&=\frac{1}{B D^{2}-A^{2}}[C(C D+A)+(A B C D)]+\frac{1}{2\left(B D^{2}-A^{2}\right)^{2}}\\ &{\left[B D(C D+A)+A(C D+A)(B D-A C)+D^{2}(B D-A C)\right]}\end{aligned}\]
	\[\begin{array}{l}\alpha_{u}=k_{\mathrm{u}}\left(\frac{K_{\mathrm{u}}+K_{\mathrm{c}}}{2K_{\mathrm{c}}}\right)\\ =k_{1}\left(\frac{K_{1}+K_{\mathrm{c}}}{2K_{\mathrm{c}}}\right)\end{array}\]
	\[\begin{aligned}\delta_{y}&={\left[\frac{3k^{2}-4k-3}{(k+1)^{2}}\left(\frac{\alpha_{1}}{t}+\alpha_{2}\right)^{2}-\frac{2k\alpha_{1}}{(k+1)t^{2}}\right]}\\ &={\left[\frac{2(k-1)\alpha_{1}}{(k+1)t^{2}}-\frac{(3k+1)(k-1)}{(k+1)^{2}}\left(\frac{\alpha_{1}}{t}+\alpha_{2}\right)^{2}\right]}\\ &\times\left\{3\left[\eta_{1}\left(\frac{\alpha_{1}}{t}+\alpha_{2}\right)-\frac{\eta_{2}\alpha_{1}}{t^{2}}+\frac{2\alpha_{1}\eta_{3}}{3t^{2}\left(\alpha_{1}+\alpha_{2}t\right)}\right]\right\}^{-1}\end{aligned}\]
	\[\begin{array}{l}u=\frac{F(y)}{r^{\frac{1}{2}}}+\frac{F_{1}(y)}{r^{\frac{3}{2}}}+\ldots\\ =\frac{G(y)}{r^{\frac{1}{2}}}+\frac{G_{1}(y)}{r^{\frac{3}{2}}}+\ldots\end{array}\]
	\[\begin{aligned}&(1+2\lambda\cos\theta)\left(x^{\prime\prime}-2y^{\prime}\right)=p x\\ &(1+2\lambda\cos\theta)\left(y^{\prime\prime}+2x^{\prime}\right)=q y\\ &\mathrm{~stitute~}\quad\sum_{-\infty}^{\infty}\mathrm{A}_{n}e^{i(k+n)\theta},\quad y=\sum_{-\infty}^{\infty}\mathrm{B}_{n}e^{i(k+n)\theta}\end{aligned}\]
	\[\begin{aligned}\tau_{z_{1}}\left(z_{1}\cdot z_{2}\right)&:=x_{2}-x_{1}+y_{2}\left(y_{2}-y_{1}\right)\\ &=x_{2}-x_{1}+y_{1}\left(y_{2}-y_{1}\right)\end{aligned}\]
	\[\begin{array}{l}\kappa_{x l_{i}}=l_{i}\Delta\kappa_{x}\cdot\kappa_{z l_{i}}\cdot l_{i}\Delta\kappa_{z}l_{i}\cdot q\cdot1\cdot\mathrm{~K}\cdot N_{i}-1\\ =\kappa_{x u}/N_{1}\cdot\Delta\kappa_{z}\cdot\kappa_{z u}/N_{2}\end{array}\]
	\[\begin{aligned}&\{1-2v+\varpi(1+2v)\sin\phi\}\dot{\sigma}_{r}+2\{1-2v-\varpi\sin\phi\}\dot{\sigma}_{\theta}\\ &=E\left\{(1+\varpi\sin\phi)\frac{\partial v}{\partial r}+2(1-\varpi\sin\phi)\frac{v}{r}\right\}\end{aligned}\]
	\[\begin{aligned}\eta&=\sqrt{}\left(2\log_{\theta}\nu T-2\log_{\theta}\xi\right)\\ &=\sqrt{\left[2\log\nu T\left(1-\frac{\log\xi}{\log\nu T}\right)\right]}\\ &=\sqrt{}(2\log\nu T)-\frac{\log\xi}{\sqrt{}(2\log\nu T)}-\frac{1}{2}\frac{\log^{2}\xi}{\sqrt{}(2\log\nu T)^{3}}+\ldots\end{aligned}\]
	\[\begin{array}{c}g_{2^{\prime}4}=\frac{1}{2}a^{2}\left(t^{\prime2}+t^{2}-\gamma\right)\\ =\frac{1}{2}a^{2}\left(x-x^{\prime}\right)\left[\left(t^{\prime}+t\right)^{2}-\gamma\right]^{\frac{1}{2}}\\ =\frac{1}{2}a^{2}\left(x^{\prime}-x\right)\left[\left(t^{\prime}+t\right)^{2}-\gamma\right]^{\frac{1}{2}}\\ =\frac{1}{2}a^{2}\left(x^{\prime}-x\right)\left(y-y^{\prime}\right)\\ =\frac{1}{2}a^{2}\left(x^{\prime}-x\right)\left(x-x^{\prime}\right)-a^{2}t^{\prime}t\\ =V_{\mu\alpha^{\prime}}\left(x\cdot x^{\prime}\right)\\ =V_{\left(\alpha^{\prime}\beta^{\prime}\right)(\mu\nu)}\cdot V_{\mu\nu\alpha^{\prime}\beta^{\prime}}\left(x\cdot x^{\prime}\right)\end{array}\]

\[\begin{aligned}\operatorname{Gr}\left(\boldsymbol{S}_{1},\boldsymbol{S}_{2},\ldots,\boldsymbol{S}_{N}\right)=\mid\begin{array}{c c c c}\left(\boldsymbol{S}_{1},\boldsymbol{S}_{1}\right)&\left(\boldsymbol{S}_{1},\boldsymbol{S}_{2}\right)&\cdots&\left(\boldsymbol{S}_{1},\boldsymbol{S}_{N}\right)\\ \left(\boldsymbol{S}_{2},\boldsymbol{S}_{1}\right)&\left(\boldsymbol{S}_{2},\boldsymbol{S}_{2}\right)&\cdots&\left(\boldsymbol{S}_{2},\boldsymbol{S}_{N}\right)\\ \ldots&\cdots&\cdots&\ldots\\ \left(\boldsymbol{S}_{N},\boldsymbol{S}_{1}\right)&\left(\boldsymbol{S}_{N},\boldsymbol{S}_{2}\right)&\cdots&\left(\boldsymbol{S}_{N},\boldsymbol{S}_{N}\right)\end{array}\end{aligned}\]

\[\begin{aligned}&B_{p p}=B_{\mathrm{B.E.~}}\\ &B_{p o}=\frac{1}{2}\left(B_{\mathrm{B.E.~}}+B_{\mathrm{F.D.~}}\right)\\ &B_{o o}=\frac{1}{9}\left(5B_{\mathrm{B.E.~}}+4B_{\mathrm{F.D.~}}\right)\end{aligned}\]

\[\begin{array}{l}\Delta G_{0}=R T\log\frac{x}{y}-\left(f_{11}-1\right)\Delta E_{0}+\left(h_{11}-1\right)p\Delta V_{0}+d_{12}\left\{E_{0}^{l}(1-x)^{2}-E_{0}^{v}(1-y)^{2}\right\}\\ \mathrm{~nd~}\quad\Delta G_{0}=R T\log\frac{1-x}{1-y}-\left(f_{22}-1\right)\Delta E_{0}+\left(h_{22}-1\right)p\Delta V_{0}+d_{12}\left\{E_{0}^{l}x^{2}-E_{0}^{v}y^{2}\right\}\end{array}\]

\[\begin{aligned}\zeta(v,w)=\left\{\begin{array}{l l}0v\leq(1-\delta)w\\ 1v>(1-\delta)w\end{array}\right.\end{aligned}\]

\[\begin{array}{c}H_{2}A_{e}-k A_{1}=L\\ =H_{2}\xi_{n}^{-1}C_{n}-k D_{n}\\ =\mathscr{H}_{q}[D(\xi)\cdot r]\end{array}\]

\[\begin{aligned}Y_{\mu\nu}=\left[\begin{array}{c c c}\left(\partial_{\mu}m_{\nu}-\partial_{\nu}m_{\mu}\right.&\left(\partial_{\mu}Q_{\nu}-\partial_{\nu}Q_{\mu}\right),&\frac{1}{2\sqrt{2}}\left(Q^{\mu}L^{\nu}-Q^{\nu}L^{\mu}\right)\\ \left.-\frac{1}{2}Q_{\mu}Q+\frac{1}{2}Q_{\nu}Q_{\mu}\right),&&\\ \left(-\frac{1}{2}\partial_{\mu}Q_{\nu}+\frac{1}{2}\partial_{\nu}Q_{\mu}\right),&\left(\partial_{\mu}n_{\nu}-\partial_{\nu}n_{\mu}-\frac{1}{2}Q_{\mu}Q_{\nu}+\frac{1}{2}Q_{\nu}Q_{\mu}\right),&\frac{1}{2\sqrt{2}}\left(\partial_{\mu}L_{\nu}-\partial_{\nu}L_{\mu}\right)\\ \frac{1}{4\sqrt{2}}\left(L^{\dagger\nu}Q^{\mu}-L^{+\mu}Q^{\nu}\right),&\frac{1}{2\sqrt{2}}\left(\partial_{\mu}L_{\nu}^{\dagger}-\partial_{\nu}L_{\mu}^{\dagger}\right)&+\frac{1}{4\sqrt{2}}\left(L_{\mu}C_{\nu}-L_{\nu}C_{\mu}\right)\\ &+\frac{1}{4\sqrt{2}\sqrt{2}}\left(C_{\mu}L_{\nu}^{+}-C_{\nu}L_{\mu}^{+}\right),&\frac{1}{2}\left(\partial_{\mu}C_{\nu}-\partial_{\nu}C_{\mu}\right)\end{array}\right]\end{aligned}\]

\[\begin{aligned}\tau_{w}&=\frac{(1-C)}{\eta\left(R/R_{i}\right)^{3}+\alpha^{2}\beta\left(R/R_{n}\right)}\\ &=\frac{(1-C)}{\eta\left(1-\delta/R_{o}\right)^{3}+\alpha^{2}\beta\left(1-\delta/R_{x}\right)}\end{aligned}\]

\[\begin{array}{l}\omega_{1}=\mathrm{d}x\wedge\mathrm{d}y+\mathrm{d}p\wedge\mathrm{d}y+\mathrm{d}x\wedge\mathrm{d}q+\left(1-c^{2}\right)\mathrm{d}p\wedge\mathrm{d}q\\ =c(\mathrm{~d}x\wedge\mathrm{d}q+\mathrm{d}p\wedge\mathrm{d}y+2\mathrm{~d}p\wedge\mathrm{d}q)\\ =-c(\mathrm{~d}x\wedge\mathrm{d}p+\mathrm{d}y\wedge\mathrm{d}q)\end{array}\]

\[\begin{array}{r}p+Z_{\mathrm{cyl}}v_{r}=0\\ p_{\mathrm{inc}}+\mathrm{Z}_{\mathrm{inc}}v_{r,\mathrm{~inc~}}=0\\ p_{\mathrm{scat}}-Z_{\mathrm{scat}}v_{r,\mathrm{scat}}=0\end{array}\]

\[\begin{aligned}\left\{\begin{array}{c}s\left(\xi^{(1)}\right)\\ \vdots\\ s\left(\xi^{(Q)}\right)\end{array}\right\}=\left[\begin{array}{c c c}\Psi_{0}\left(\xi^{(1)}\right)&\ldots&\Psi_{P-1}\left(\xi^{(1)}\right)\\ \vdots&&\vdots\\ \Psi_{0}\left(\xi^{(Q)}\right)&\ldots&\Psi_{P-1}\left(\xi^{(Q)}\right)\end{array}\right]\left\{\begin{array}{c}\gamma_{0}\\ \vdots\\ \gamma_{P-1}\end{array}\right\}\end{aligned}\]

\[\begin{array}{c}Q_{\mathrm{aeration~}}=G\rho_{g}C_{p g}\left(T_{b}-T_{g}\right)\\ Q_{\mathrm{met~}}=V_{l}\Delta H_{\mathrm{met~}}\\ Q_{\mathrm{evap~}}=G\lambda_{w}\left(H_{g o}-H_{g i}\right)\end{array}\]

\[\begin{array}{l}\left(D^{2}-b_{5}\right)\psi_{1}^{*}-b_{6}\psi_{2}^{*}+b_{7}\phi^{*}-b_{8}T^{*}=o\\ =b_{4}\psi_{1}^{*}+\left(D^{2}-b_{9}\right)\psi_{2}^{*}\\ =-a_{6}\left(D^{2}-a^{2}\right)\psi_{1}^{*}+\left(D^{2}-b_{16}\right)\phi^{*}+a_{9}T^{*}\\ =-b_{12}\left(D^{2}-a^{2}\right)\psi_{1}^{*}-b_{14}\phi^{*}+\left(D^{2}-b_{13}\right)T^{*}\end{array}\]

\[\begin{aligned}g\left(\begin{array}{c c}n_{1}&n_{2}\\ m_{1}&m_{2}\end{array}\right)=g_{V}\delta_{n_{1},n_{2}}\delta_{m_{1},m_{2}}\end{aligned}\]

\[\begin{aligned}\Sigma\frac{n f^{n-1}}{p_{n^{\prime}}}&=2\alpha g e^{-1Y+\alpha^{2}/4\beta^{2}}\int_{-\infty}^{+\infty}e^{-y^{2}}\left(\frac{3y^{2}}{2}+\frac{\alpha^{2}}{8\beta^{2}}\right)d y\\ &=e^{-1C+\alpha^{2}/4\beta^{2}}\frac{\alpha g\sqrt{\pi}}{\beta^{5}}\left\{\frac{3}{2}+\frac{\alpha^{2}}{4\beta^{2}}\right\}\end{aligned}\]

\[\begin{array}{c}\frac{\mathrm{d}\arg D\left(E_{\bar{\phi}}^{\ddagger}\right)}{\mathrm{d}\alpha_{r}}=-\mathscr{I}\operatorname{tr}\left[G\left(E_{\bar{\phi}}^{\pm}\right)|r\rangle\langle r|\right]\\ \quad=\sum_{n}\langle n\mid r\rangle(\mp2\beta\sin\phi)\langle r\mid n\rangle\end{array}\]

\[\begin{aligned}&K_{A A^{\prime}B B^{\prime}}=u_{A}u_{B}\epsilon_{A^{\prime}B^{\prime}},\mathrm{~charge~}+3\\ &L_{A A^{\prime}B B^{\prime}}=\bar{u}_{A}\bar{u}_{B}\epsilon_{A^{\prime}B^{\prime}},\mathrm{~charge~}-3\\ &J_{A A^{\prime}B B^{\prime}}=\mathrm{i}\left(u_{A}\bar{u}_{B}+\bar{u}_{A}u_{B}\right)\epsilon_{A^{\prime}B^{\prime}},\mathrm{~charge~}0\end{aligned}\]

\[\begin{aligned}&\boldsymbol{\mu}(\xi)=-e\sum_{\alpha}\left(\boldsymbol{q}_{\alpha(\xi)}-\boldsymbol{R}_{\xi}\right)\\ &\boldsymbol{m}(\xi)=-\frac{e}{2m c}\sum_{\alpha}\boldsymbol{l}_{\alpha(\xi)}\end{aligned}\]

\[\begin{aligned}B_{4}/B_{6}&=\left(-3B_{4}^{\prime}/2\right)/\left(9B_{6}^{\prime}/16\right)\\ &=-\frac{7\left\langle r^{4}\right\rangle R_{2}^{2}\langle J\|\beta\|J\rangle}{2\left\langle r^{6}\right\rangle\langle J\|\gamma\|J\rangle}\end{aligned}\]

\[\begin{array}{l}T_{s}/T_{E}=2\left\{\gamma M^{2}(\gamma-1)+2\gamma\right\}/(\gamma+1)^{2}\\ =2\gamma M^{2}/(\gamma+1)\end{array}\]

\[\begin{array}{l}n^{\prime}=F^{\prime}S M_{2}\tau\\ =F_{u}S^{2}M_{1}M_{2}\tau/4\pi D^{2}\end{array}\]

\[\begin{aligned}\left.\begin{array}{l}\dot{x}=f(x,u)\\ y=\lambda_{n}x_{n}\end{array}\right\}\end{aligned}\]

\[\begin{array}{l}\mathrm{~Maximum~principal~stress~}=\frac{f_{2}}{2}+\sqrt{\frac{f_{2}^{2}}{4}+f_{1}^{2}}\\ \mathrm{~Maximum~shear~stress~}=\sqrt{\frac{f_{2}^{2}}{4}+f_{1}^{2}}\end{array}\]

\[\begin{aligned}\left|\begin{array}{l l l}x-x_{1}&y-y_{1}&z-z_{1}\\ x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\ x_{3}-x_{1}&y_{3}-y_{1}&z_{3}-z_{1}\end{array}\right|=\left|\begin{array}{l l l}x-x_{1}&y-y_{1}&z-z_{1}\\ x-x_{2}&y-y_{2}&z-z_{2}\\ x-x_{3}&y-y_{3}&z-z_{3}\end{array}\right|=0\end{aligned}\]

\[\begin{aligned}\left.\begin{array}{l}N(c)=X-Y\frac{K_{0}^{2}}{K^{2}}-Z\ln\left(\frac{K^{2}}{K_{0}^{2}}\right)\\ Z=\frac{R^{2}}{\pi A(\Delta R)^{4}},\quad Y=\frac{\omega K_{1,\mathrm{c}}^{2}}{K_{0}^{2}}Z\\ X=\left\{\frac{K_{1,\mathrm{c}}^{2}}{K_{0}^{2}}+1-\frac{1}{\omega}\right\}Z\end{array}\right\}\end{aligned}\]

\[\begin{aligned}\rho^{(1)}(1\cdot u\cdot j)\rho^{(2)}(i\cdot v\cdot1)&=\left[\rho^{(1)}\left(1\cdot u^{\prime}\cdot j^{\prime}\right)e\right]\rho^{(2)}(i\cdot v\cdot1)\\ &=\rho^{(1)}\left(1\cdot u^{\prime}\cdot j^{\prime}\right)\left[e\rho^{(2)}(i\cdot v\cdot1)\right]\\ &=\rho^{(1)}\left(1\cdot u^{\prime}\cdot j^{\prime}\right)\rho^{(2)}\left(i^{\prime}\cdot v^{\prime}\cdot1\right)\end{aligned}\]

\[\begin{array}{l}\mathbf{r}_{l}^{+}=b\left(\cos\omega x\mathbf{e}_{1}+\sin\omega x\mathbf{e}_{2}\right)+x\mathbf{e}_{3}\\ =b\left(\cos(\omega x+\alpha)\mathbf{e}_{1}+\sin(\omega x+\alpha)\mathbf{e}_{2}\right)+x\mathbf{e}_{3}\end{array}\]

\[\begin{aligned}\left.\begin{array}{l}P_{11}^{\prime}=\frac{2\eta_{0}D^{2}\left(\lambda_{1}-\lambda_{2}\right)}{1+\mu_{0}\lambda_{1}D^{2}}\\ P_{12}^{\prime}=\frac{\eta_{0}D\left(1+\mu_{0}\lambda_{2}D^{2}\right)}{1+\mu_{0}\lambda_{1}D^{2}}\\ P_{12}^{\prime}=0=P_{33}^{\prime}\end{array}\right\}\end{aligned}\]

\[\begin{array}{c}W_{1}=\frac{\pi^{2}E}{2\left(1-\sigma^{2}\right)}\int_{F}^{c}r\left(1-r^{2}/c^{2}\right)^{\frac{1}{2}}d r\int_{3}^{\epsilon}\epsilon d\epsilon\\ =\frac{\pi^{2}E c\epsilon^{2}}{12\left(1-\sigma^{2}\right)}\end{array}\]

\[\begin{array}{l}I_{2}^{M}:=\frac{\{\boldsymbol{\theta}\cdot\boldsymbol{\theta}\}_{2}}{M}\cdot I_{3}^{M}:\cdot\frac{\left\{\boldsymbol{\theta}^{3}\cdot\mathbf{t}\right\}_{6}}{M^{2}}\cdot I_{4}^{M}:\cdot\frac{\left\{\boldsymbol{\theta}^{4}\cdot\{\mathbf{t}\cdot\mathbf{t}\}_{2}\right\}_{8}}{M^{3}}\\ =\left\{\{\boldsymbol{\theta}\cdot\mathbf{f}\}_{1}\cdot\{\mathbf{t}\cdot\mathbf{t}\}_{2}\right\}_{8}\frac{\left\{\boldsymbol{\theta}^{6}\cdot\mathbf{j}\right\}_{12}}{M^{6}}\\ =\left(\frac{36\left\{\boldsymbol{\theta}^{2}\mathbf{f}\cdot\mathbf{j}\right\}_{12}}{M^{2}}-\frac{28\left\{\left\{\boldsymbol{\theta}^{2}\cdot\mathbf{f}\right\}_{3}\cdot\mathbf{t}\right\}_{6}}{5M}\right)\frac{\left\{\boldsymbol{\theta}^{6}\cdot\mathbf{j}\right\}_{12}}{M^{5}}\\ =\frac{2\left\{\mathbf{f}\boldsymbol{\theta}^{3}\cdot\mathbf{t}\{\mathbf{t}\cdot\mathbf{t}\}_{2}\right\}_{14}}{M^{3}}+\frac{2M\left\{\left\{\mathbf{f}\cdot\boldsymbol{\theta}^{3}\right\}_{1}\cdot\mathbf{j}\right\}_{12}}{7M^{3}}-\frac{7q\left\{\left\{\mathbf{f}\cdot\boldsymbol{\theta}^{3}\right\}_{4}\cdot\mathbf{t}\right\}_{6}}{99M^{2}}\end{array}\]

\[\begin{aligned}\left[\begin{array}{l l}K_{11}&K_{12}\\ K_{21}&K_{22}\end{array}\right]\left[\begin{array}{l}x_{1}\\ x_{2}\end{array}\right]=\left[\begin{array}{l}F_{1}\\ F_{2}\end{array}\right]\end{aligned}\]

\[\begin{array}{l}\mathbf{E}_{1}=\mathbf{F}_{1}b\frac{\pi\mathbf{D}}{\mathbf{N}t}1i-8\\ =\mathbf{F}_{2}b\frac{\pi\mathbf{D}}{\mathbf{N}t}1Q-8\\ =\mathbf{F}_{3}b\frac{\pi\mathbf{D}}{\mathbf{N}t}1r-8\end{array}\]

\[\begin{aligned}&p(x)=\sum_{x^{\prime}\in\mathcal{X}}p\left(x\mid x^{\prime}\right)p\left(x^{\prime}\right)\\ &p\left(x\mid x^{\prime}\right)=\mathbb{E}_{z\sim p(z)}\left[p_{\mathrm{edit~}}\left(x\mid x^{\prime},z\right)\right]\end{aligned}\]

\[\begin{aligned}U_{e,-1}=\frac{1}{\sqrt{E_{e}+m_{e}}}\left(\begin{array}{c}0\\ E_{e}+m_{e}\\ 0\\ -p_{e z}\end{array}\right)\end{aligned}\]

\[\begin{array}{l}\kappa_{g}=\frac{8k^{2}\zeta^{2}\Theta}{3\pi h}\left(\frac{D}{\zeta}\right)^{2}\left(\frac{T}{\Theta}\right)^{2}\Sigma\Lambda_{j}P_{j,4},\\ \Im_{g}=\sqrt{2}k\left(\frac{D}{\zeta}\right)^{\frac{3}{2}}\left(\frac{T}{\Theta}\right)^{3}\sum_{j}P_{j,5}\end{array}\]

\[\begin{array}{l}T(x\cdot z)=T_{11}\cdot-Y z\kappa+e\partial_{3}P_{3}\\ =-\partial_{3}\phi\cdot a_{33}P(x\cdot z)+(e-\mu)\kappa\end{array}\]

\[\begin{aligned}\left.\begin{array}{r}\left\{c_{11}l^{2}+c_{44}\left(m^{2}+n^{2}\right)-\rho V_{i}^{2}\right\}A_{i}+\left(c_{12}+c_{44}\right)\left(\operatorname{lm}B_{i}+n l C_{i}\right)=0\\ \left\{c_{11}m^{2}+c_{44}\left(l^{2}+n^{2}\right)-\rho V_{i}^{2}\right\}B_{i}+\left(c_{12}+c_{44}\right)\left(\operatorname{lm}A_{i}+m n C_{i}\right)=0\\ \left\{c_{11}n^{2}+c_{44}\left(l^{2}+m^{2}\right)-\rho V_{i}^{2}\right\}C_{i}+\left(c_{12}+c_{44}\right)\left(\ln A_{i}+m n B_{i}\right)=0\end{array}\right\}\end{aligned}\]

\[\begin{aligned}b_{b}T=\left[\begin{array}{c c c c}c_{\phi_{i}}&-s_{\phi_{i}}&0&-r_{b}\left(c_{\phi_{i}}\right)\\ s_{\phi_{i}}&c_{\phi_{i}}&0&-r_{b}\left(s_{\phi_{i}}\right)\\ 0&0&1&0\\ 0&0&0&1\end{array}\right]\end{aligned}\]

\[\begin{array}{c}\frac{\mathrm{LN}-\mathrm{M}^{2}}{\mathrm{EG}-\mathrm{F}^{2}}=\frac{1}{\rho_{1}\rho_{2}}\cdot\mathrm{K}\\ =4\mathrm{~V}^{2}\mathrm{H}\left(w^{\prime}\right)\end{array}\]

\[\begin{aligned}\mu&=\mu_{\max}\cdot\operatorname{EXP}\left(-\frac{2.3}{15}\cdot\left|T-T_{o p t}\right|\right.\\ &\times)\cdot\frac{I}{I+K_{I}}\cdot\frac{C_{n}}{C_{n}+K_{N}}\cdot\frac{C_{p}}{C_{p}+K_{P}}\cdot f\left(u_{w}\right)\end{aligned}\]

\[\begin{aligned}H_{A}&=F_{h}\\ &=\frac{F_{v}\cdot a}{a+b+c}\\ &=F_{v}-V_{C}\end{aligned}\]

\[\begin{aligned}\mathbb{J}_{N}=\left(\begin{array}{l l l l}0&0&0&1\\ 0&0&1&0\\ 0&.\cdot&0&0\\ 1&0&0&0\end{array}\right),\end{aligned}\]

\[\begin{aligned}\operatorname{diag}_{2}=\left(\begin{array}{c c c}\sqrt{\rho}&0&0\\ 0&\mathrm{i}\sqrt{2\eta}&0\\ 0&0&\mathrm{i}\sqrt{2\eta}\end{array}\right)\end{aligned}\]

\[\begin{array}{l}\mathrm{~low-frequency:~}\frac{\partial\rho_{3}^{\prime}}{\partial t}=-\frac{\alpha\beta c^{4}\tau_{\nu}}{c_{p}\rho_{0}}\left(\frac{\partial\rho_{1}}{\partial x}\right)^{2}+\frac{\alpha c}{2\rho_{0}}\frac{\partial\rho_{1}^{\prime2}}{\partial x}\\ \mathrm{~high-frequency:~}\frac{\partial\rho_{3}^{\prime}}{\partial t}=-\frac{\alpha\beta c^{2}}{\tau_{\nu}c_{p}\rho_{0}}\rho_{1}^{\prime2}\end{array}\]

\[\begin{array}{l}p^{i}:\mathrm{u}_{f}(t)=e^{-t}\\ =\mathrm{u}_{8}(t)\int_{M}^{t}\frac{t^{2}}{2e^{(t+s)}}H_{L}(s)d s\\ =\mathrm{u}_{l}(t)\int_{7}^{t}\frac{t^{2}}{2e^{(t+s)}}H_{1}(s)d s+\mathrm{u}_{1}(t)\int_{F}^{t}\frac{t^{2}}{2e^{(t+s)}}H_{b}(s)d s\end{array}\]

\[\begin{aligned}\mathrm{d}\ln A_{n}/\mathrm{d}t&=\nabla_{\perp}\cdot\boldsymbol{c}\\ &=\nabla\boldsymbol{k}:\Omega_{k k}+\operatorname{tr}\left(\Omega_{k x_{\perp\perp}}\right)\\ &=\nabla_{\perp}\boldsymbol{n}:\left(k\Omega_{k k}\right)+\operatorname{tr}\left(v_{n x_{\perp\perp}}\right)\end{aligned}\]

\[\begin{array}{l}E_{g}=\frac{1240}{\lambda_{\mathrm{peak~}}}\\ E_{g}=E_{g}^{b}+\frac{h}{8D^{2}}\left(\frac{1}{m_{e}}+\frac{1}{m_{h}}\right)\end{array}\]

\[\begin{aligned}f(\operatorname{Re})=\left\{\begin{array}{l l}\frac{24}{\operatorname{Re}}\left(1+\frac{3}{16}\operatorname{Re}\right)\mathrm{Re}<0.01\\ \frac{24}{\operatorname{Re}}\left(1+0.1315\mathrm{Re}^{0.82-0.05\log_{10}\operatorname{Re}}\right)0.01\leq\operatorname{Re}\leq20\end{array}\right.\end{aligned}\]

\[\begin{aligned}\mu_{1}\left(z_{1}b_{1}^{\vee}\right)&=\mu_{1}\left(z_{2}b_{2}^{\vee}\right)\cdot j\\ &=P_{j-1}\left(A_{1}\cdot\ldots\cdot A_{j-1}\right)w_{j}P_{n-j}\left(A_{j+1}^{\prime}\cdot\ldots\cdot A_{n}^{\prime}\right)b_{1}^{\vee}\\ &=-v_{1}\left(T_{1}^{\prime}\right)^{-1}b_{1}^{\vee}\\ &=\mu_{1}\left(v_{2}x_{2}^{\vee}\right)\end{aligned}\]

\[\begin{array}{c}\left(u_{0e}^{\prime}+a_{0e}^{\prime}\right)\left\{\left(u_{0e}+a_{0e}\right)-\tan\theta\right\}=0\\ \left(u_{0e}^{\prime}-a_{0e}^{\prime}\right)\left\{\left(u_{0e}-a_{0e}\right)-\tan\theta\right\}=0\\ u_{0e}^{\prime}=\mathrm{d}u_{0e}/\mathrm{d}\theta,\quad\mathrm{~etc}\end{array}\]

\[\begin{aligned}\boldsymbol{B}(x\cdot W)&=\boldsymbol{b}(x)\cdot\boldsymbol{B}\left(x\cdot R^{+}\right)\cdot\boldsymbol{B}\left(x\cdot m^{-}\right)\\ &=-\boldsymbol{i}_{x}l\cdot\boldsymbol{B}(x\cdot a)-\boldsymbol{B}(x\cdot-a)\cdot-\boldsymbol{i}_{y}2a\\ &=\nabla\boldsymbol{B}(g\cdot y)\cdot\nabla\boldsymbol{B}(x\cdot-a)\cdot\nabla\boldsymbol{B}(x\cdot a)\end{aligned}\]

\[\begin{aligned}\bar{\mathbf{C}}=\left[\begin{array}{l l}2\xi_{h0}\omega_{h0}&\\ &2\xi_{\alpha0}\omega_{\alpha0}\end{array}\right],\bar{\mathbf{K}}=\left[\begin{array}{l l}\omega_{h0}^{2}&\\ &\omega_{\alpha0}^{2}\end{array}\right],\quad\mathbf{C}_{s e}=\left[\begin{array}{l l}H_{1}&H_{2}\\ A_{1}&A_{2}\end{array}\right],\quad\mathbf{K}_{s e}=\left[\begin{array}{c c}H_{4}&H_{3}\\ A_{4}&A_{3}\end{array}\right](6)\end{aligned}\]

\[\begin{aligned}W^{-1}(\tau)=\mathrm{e}^{F(\tau)}\left(\begin{array}{c c}w_{22}(\tau)&-w_{12}(\tau)\\ -w_{21}(\tau)&w_{11}(\tau)\end{array}\right)\end{aligned}\]

\[\begin{array}{c}\frac{d^{2}A}{d t^{2}}=-2\left[\left(c^{2}+\frac{1}{3}\bar{u^{2}}\right)k^{2}-4\pi G\bar{\rho}\right]A\\ k^{2}<\frac{4\pi G\bar{\rho}}{c^{2}+\frac{1}{3}\bar{u^{2}}}\end{array}\]

\[\begin{array}{c}\mathcal{S}^{\prime}=\left\{s_{a}:a\in\Delta_{\mathrm{aff}}^{\prime}\right\}\\ =\left\{w\in\mathcal{W}_{\chi_{C}}:w\left(\mathcal{A}^{\prime}\right)\cdot\mathcal{A}^{\prime}\right\}\end{array}\]

\[\begin{array}{l}\mathrm{~Eswirl~}(\%)=\left[\frac{1}{\left(1+\frac{F S}{m}\right)}\right]*100\\ A E(\%)=\left[1-\frac{1+\frac{F S}{m}}{1+F S}\right]*100\end{array}\]

\[\begin{aligned}S=\left[\begin{array}{l}r-i\\ -g h\frac{\partial Z}{\partial x}-g\frac{n^{2}u\sqrt{u^{2}+v^{2}}}{h^{1/3}}\\ -g h\frac{\partial Z}{\partial x}-g\frac{n^{2}u\sqrt{u^{2}+v^{2}}}{h^{1/3}}\end{array}\right]\end{aligned}\]

\[\begin{array}{l}\quad x+2y+2(x+y-1)t+(x-2)t^{2}-\frac{2t^{3}}{3}=\frac{\theta_{p}}{\beta u_{y}}\\ \mathrm{~where~}t=\left(\frac{x}{2}-1\right)+\left(\frac{x^{2}}{4}+y\right)^{\frac{1}{2}}\end{array}\]

\[\begin{aligned}&F_{\theta}=F_{\alpha}-F_{\mathrm{frame~}}\\ &m\frac{d v}{d\theta}=m\frac{d v}{d\alpha}-m\frac{d v}{d t}\end{aligned}\]

\[\begin{array}{c}\Phi_{\Xi}\left(g_{2}\right)=\int_{K_{2}}f_{\Xi}\left(k_{2}g_{2}\right)d k_{2}\cdot\Phi_{\xi}\left(g_{W}\right)\cdot\int_{K_{C}}f_{\xi}\left(k_{i}g_{X}\right)d k_{2}\\ =\int_{L\left(\mathfrak{o}_{F}\right)}\omega_{\psi}\left(h g_{s}\right)\mathbf{1}_{L^{*}\left(\mathfrak{o}_{F}\right)}(x)d x\end{array}\]

\[\begin{array}{l}\rho_{G L}=\left(1+e^{\alpha_{G L}\left(\Theta_{G L}-V_{L}+V_{R}\right)}\right)^{-1}\\ =\left(1+e^{\alpha_{G R}\left(\Theta_{G R}-V_{R}+V_{L}\right)}\right)^{-1}\end{array}\]

\[\begin{aligned}\frac{\mathrm{d}}{\mathrm{d}t}E(Y I)&=\alpha E\left(I^{2}\right)-(\xi+\delta)E(Y I)+\frac{\beta V}{H}E\left(Y^{2}\right)\\ &-\frac{\alpha}{H}E\left(Y I^{2}\right)-\frac{\beta}{H}E\left(Y^{2}I\right)\end{aligned}\]

\[\begin{aligned}\left(\begin{array}{c}Z\\ Z^{\prime}\end{array}\right)=\left(\begin{array}{c c}c_{\phi}&s_{\phi}\\ -s_{\phi}&c_{\phi}\end{array}\right)\left(\begin{array}{l}Z_{0}\\ Z_{1}\end{array}\right)\end{aligned}\]

\[\begin{aligned}&\left\langle q\left|T_{1}\right|q^{\prime}\right\rangle=\sum_{s,s^{\prime}\geqslant1}^{\infty}\frac{\mathrm{i}}{\omega_{s,s^{\prime}}}\varphi_{s}(q)\varphi_{s^{\prime}}^{*}\left(q^{\prime}\right)\\ &\left\langle q\left|T_{M}\right|q^{\prime}\right\rangle=\sum_{s,s^{\prime}\geqslant1}^{\infty}\sum_{r,r^{\prime}\geqslant1}^{M}\frac{\mathrm{i}}{\omega_{s,s^{\prime}}}\varphi_{s,r}(q)\varphi_{s^{\prime},r^{\prime}}^{*}\left(q^{\prime}\right)\end{aligned}\]

\[\begin{aligned}&\mathrm{Mo}-\mathrm{Mo}=2\cdot79\mathrm{~A}\\ &\mathrm{~and~}=3\cdot71\mathrm{~A}\end{aligned}\]

\[\begin{array}{l}\mathcal{D}^{+}=\left\{\boldsymbol{x}\in\mathcal{D}\mid h_{\mathcal{P}}(\boldsymbol{x})>Z\right\}\\ =\left\{\boldsymbol{x}\in\mathcal{D}\mid h_{\mathcal{P}}(\boldsymbol{x})\cdot D\right\}\\ =\left\{\boldsymbol{x}\in\mathcal{D}\mid h_{\mathcal{P}}(\boldsymbol{x})<E\right\}\end{array}\]

\[\begin{aligned}A_{\mathrm{m}}&=s^{2}a^{2}E(k)+\left(a^{2}-a^{2}s^{2}\right)K(k)+\left(a^{2}s^{2}+s^{2}b^{2}-2a^{2}\right)\Pi\left(s^{2}k^{2}\cdot k\right)\\ &=\left(a^{4}-s^{4}a^{2}b^{2}\right)E(k)+\left(s^{4}a^{2}b^{2}-2s^{2}a^{2}b^{2}+a^{2}b^{2}\right)K(k)\\ &+\left(-a^{4}-s^{4}a^{2}b^{2}+4s^{2}a^{2}b^{2}-a^{2}b^{2}-s^{4}b^{4}\right)\Pi\left(s^{2}k^{2}\cdot k\right)\end{aligned}\]

\[\begin{aligned}\frac{\partial\rho(u\cdot v\cdot t)}{\partial t}&=\frac{\partial}{\partial u}\left(\gamma_{u}u\rho\right)+\frac{\partial}{\partial v}\left(\gamma_{v}v\rho\right)+\sigma(t)\left\{\rho\left(u-h_{u}\cdot v\right)-\rho(u\cdot v)\right\}\\ &+\sigma(t)\delta(u)\int_{1-h_{u}}^{1}d u^{\prime}\rho\left(u\cdot v-h_{v}\cdot t\right)d u^{\prime}+\sigma(t)\delta(u)\delta(v)\\ &\times\int_{1-h_{u}}^{1}d u^{\prime}\int_{1-h_{v}}^{1}d v^{\prime}\rho\left(u^{\prime}\cdot v^{\prime}\cdot t\right)\end{aligned}\]

\[\begin{aligned}&\frac{1}{v_{\mathrm{p}}}\frac{\partial I_{\mathrm{p}}}{\partial t}+\mu\frac{\partial I_{\mathrm{p}}}{\partial x}\\ &=\frac{(1/2)\int_{-1}^{1}I_{\mathrm{p}}d\mu-I_{\mathrm{p}}}{\Lambda_{\mathrm{p}}}-\frac{G}{2}\left(\frac{1}{C_{\mathrm{p}}v_{\mathrm{p}}}\int_{-1}^{1}I_{\mathrm{p}}d\mu-\frac{1}{C_{\mathrm{e}}v_{\mathrm{e}}}\int_{-1}^{1}I_{\mathrm{e}}d\mu\right)\end{aligned}\]

\[\begin{aligned}P_{X}(z)&:=1\cdot Q_{M}(z):\cdot1\\ &=P_{k}(z)+z^{2^{k}}Q_{k}(z)\\ &=P_{k}(z)-z^{2^{k}}Q_{k}(z)\end{aligned}\]

\[\begin{aligned}\left(\begin{array}{l l}A&B\\ C&D\end{array}\right)=\left(\begin{array}{l l}A&0\\ C&1\end{array}\right)\left(\begin{array}{c c}1&A^{-1}B\\ 0&D-C A^{-1}B\end{array}\right)\end{aligned}\]

\[\begin{aligned}y_{v_{r}v_{s}}\left(\omega_{\mathrm{e}}\right)&=\int_{t}^{l}\int_{u}^{l}\left\{\int_{-\infty}^{\infty}y_{v}(x:\xi\cdot\tau)\mathrm{e}^{-\mathrm{i}\omega_{\mathrm{e}}\tau}d\tau\right\}v_{r}(\xi)v_{s}(x)\mathrm{d}x\mathrm{~d}\xi\\ &=\int_{Z}^{l}\int_{J}^{l}y_{v}\left(x:\xi\cdot\omega_{\mathrm{e}}\right)v_{r}(\xi)v_{s}(x)\mathrm{d}x\mathrm{~d}\xi\\ &=y_{v_{r}v_{s}}^{R}\left(\omega_{\mathrm{e}}\right)+\mathrm{i}y_{v_{r}v_{s}}^{I}\left(\omega_{\mathrm{e}}\right)\end{aligned}\]

\[\begin{aligned}\left(\begin{array}{c c}m_{1}&\\ &m_{2}\end{array}\right)=\sqrt{m_{1}m_{2}}e^{-\xi\sigma_{3}},\quad\xi=\frac{1}{2}\ln\left(m_{2}/m_{1}\right)\end{aligned}\]

\[\begin{array}{r}Z\left(x_{P}+V t\cdot t\right)=\frac{1}{4\pi^{2}\left(x_{R}+V t\right)}\int_{\mathrm{i}\sigma-\infty}^{\mathrm{i}\sigma+\infty}\int_{-\infty}^{\infty}\boldsymbol{B}^{\mathrm{R}}\left(x_{O}+V t\cdot\omega+V k\right)\\ \times\left[\mathrm{i}k\boldsymbol{I}-\boldsymbol{A}^{\mathrm{R}}(\omega+V k)\right]^{-2}\left[\boldsymbol{B}^{\mathrm{R}}(8\cdot\omega+V k)\right]^{-1}\\ \times\boldsymbol{D}^{\mathrm{R}}(\omega+V k)H(\omega+V k)\mathrm{e}^{\mathrm{i}\left(k x_{M}-\omega t\right)}\mathrm{d}k\mathrm{~d}\omega.\end{array}\]

\[\begin{aligned}\left.\begin{array}{l}\mathrm{A}\frac{d\omega_{1}}{d t}-(\mathrm{B}-\mathrm{C})\omega_{2}\omega_{3}=\mathrm{X}_{1}\\ \mathrm{~B}\frac{d\omega_{2}}{d t}-(\mathrm{C}-\mathrm{A})\omega_{3}\omega_{1}=\mathrm{Y}_{1}\\ \mathrm{C}\frac{d\omega_{3}}{d t}-(\mathrm{A}-\mathrm{B})\omega_{1}\omega_{2}=\mathrm{Z}_{1}\end{array}\right\}\end{aligned}\]

\[\begin{aligned}\left.\begin{array}{r l}\sigma_{x}=\frac{E}{1-\mu^{2}}\left(e_{x}+\mu e_{\theta}\right)\\ \sigma_{x,}=E e_{x}\\ e_{x}=E_{x}-z X_{x}=e_{x_{\imath}}\\ e_{\theta}=E_{\theta}-z X_{\theta}\end{array}\right\}\end{aligned}\]

\[\begin{aligned}\mathbf{I}_{\mathbf{s}}=\left[\begin{array}{c c c}941.129&0.477&0.061\\ 0.477&864.456&43.457\\ 0.061&43.457&918.303\end{array}\right]\mathrm{kg}\cdot\mathrm{m}^{2}\end{aligned}\]

\[\begin{aligned}N_{1}&=\left(\Gamma\left(\frac{c}{a}\right)\right)^{3}\Gamma\left(\frac{4+c}{a}\right)-4\Gamma\left(\frac{1+c}{a}\right)\left(\Gamma\left(\frac{c}{a}\right)\right)^{2}\Gamma\left(\frac{3+c}{a}\right)\\ &=6\left(\Gamma\left(\frac{1+c}{a}\right)\right)^{2}\Gamma\left(\frac{c}{a}\right)\Gamma\left(\frac{c+2}{a}\right)-3\left(\Gamma\left(\frac{1+c}{a}\right)\right)^{4}\\ &=\left(\Gamma\left(\frac{c+2}{a}\right)\Gamma\left(\frac{c}{a}\right)-\left(\Gamma\left(\frac{1+c}{a}\right)\right)^{2}\right)^{2}.\end{aligned}\]

\[\begin{aligned}\left.\begin{array}{l}F_{\mathrm{A}}^{\mathrm{IV}}=-6\pi\mu r_{\mathrm{A}}\left\{v_{\mathrm{A}}^{\mathrm{IV}}f_{1}^{\mathrm{IV}}(k,\epsilon)+v_{\mathrm{B}}^{\mathrm{IV}}f_{2}^{\mathrm{IV}}\left(k^{-1},\epsilon k^{-1}\right)\right\},\\ F_{\mathrm{B}}^{\mathrm{IV}}=-6\pi\mu r_{\mathrm{B}}\left\{v_{\mathrm{A}}^{\mathrm{I}}f_{2}^{\mathrm{IV}}(k,\epsilon)+v_{\mathrm{B}}^{\mathrm{I}}f_{1}^{\mathrm{IV}}\left(k^{-1},\epsilon k^{-1}\right)\right\}\end{array}\right\}\end{aligned}\]

\[\begin{array}{l}\mathrm{~1.~}\mathcal{Y}_{0}=\left\{x_{0}\right\}\\ \mathrm{~2.~For~}i\geq0,\quad\mathcal{Y}_{i+1}=\mathcal{Y}_{i}\cup w_{0}\left(\mathcal{Y}_{i}\right)\cup w_{1}\left(\mathcal{Y}_{i}\right)\quad\left(\mathrm{~Note:~}\mathcal{Y}_{i+1}\supseteq\mathcal{Y}_{i}\right)\\ \mathrm{~3.~}\mathcal{A}_{0}=\lim_{i\rightarrow\infty}\mathcal{Y}_{i}\end{array}\]

\[\begin{array}{l}\frac{\partial u}{\partial t}=D\frac{\partial^{2}u}{\partial x^{2}}+\lambda(r)u-\omega(r)v\\ =D\frac{\partial^{2}v}{\partial x^{2}}+\omega(r)u+\lambda(r)v\end{array}\]

\[\begin{aligned}\left.\begin{array}{l}a_{r}^{\dagger}a_{r}\Psi_{N}=0\\ a_{-r}^{\dagger}a_{-r}\Psi_{N}=\Psi_{N}\end{array}\right\}\quad r>N\end{aligned}\]

\[\begin{aligned}k^{2}E_{x}&=-\frac{\mathrm{d}}{\mathrm{d}z}\left[\mathrm{i}k\sin\theta(1/l+1)E_{z}\right]\\ &=-\mathrm{i}k\sin\theta\alpha\vartheta\left(\frac{1-v}{\sin^{2}\theta}E_{z}\right)\\ &=\frac{1}{\mathrm{i}h\sin\theta}\vartheta\left[(1-v)E_{z}\right]\end{aligned}\]

\[\begin{aligned}\left.\begin{array}{l}U_{m}=\int_{0}^{\pi}\left\{\cos\left(\frac{\alpha}{\sin\phi}\right)+\sin\left(\frac{\alpha}{\sin\phi}\right)\right\}\frac{\cos m\phi}{(\sin\phi)^{3/2}}d\phi\\ \mathrm{V}_{m}=\int_{0}^{\pi}\left\{\cos\left(\frac{\alpha}{\sin\phi}\right)-\sin\left(\frac{\alpha}{\sin\phi}\right)\right\}\frac{\sin m\phi}{(\sin\phi)^{3/2}}d\phi\end{array}\right\}\end{aligned}\]

\[\begin{aligned}\left.\begin{array}{c}\epsilon_{\lambda\beta}^{(3)}s^{\lambda\beta}=\epsilon\rho\epsilon_{\lambda\beta}s^{(2)}d d_{\alpha}^{\lambda}\\ \partial s^{(3)}/\partial\rho=-\left.s^{\alpha\beta}\right|_{\alpha}+\epsilon d_{\alpha}^{\beta}{}^{(2)}s^{\alpha3}\\ \partial s^{*33}/\partial\rho=-d_{\alpha\beta}{}^{(3)}s^{\alpha\beta}-\left.(\delta/\epsilon)s^{\alpha3}\right|_{\alpha}\end{array}\right\}\end{aligned}\]

\[\begin{array}{l}p\left(v_{n+1\cdot m}^{(h)}-v_{n\cdot m}^{(h)}\right)+u_{n+1\cdot m}^{(h)}v_{n\cdot m}^{(h)}=U_{n\cdot m}^{(h)}(1\cdot-1)\\ =q\left(v_{n\cdot m+1}^{(h)}-v_{n\cdot m}^{(h)}\right)+u_{n\cdot m+1}^{(h)}v_{n\cdot m}^{(h)}\\ =u_{n+1\cdot m}^{(h)}v_{n\cdot m}^{(h)}\end{array}\]

\[\begin{aligned}&p_{x x}-p_{0}=-\frac{4}{675}\frac{1}{2h}\mathrm{C}_{0}c_{x x}\sum_{0}^{\infty}\left(\nu_{1}\gamma_{r}+\nu_{2}\gamma_{-r}\right)\\ &p_{x y}=-\frac{4}{675}\frac{1}{2h}\mathrm{C}_{0}c_{x y}\sum_{0}^{\infty}\left(\nu_{1}\gamma_{r}+\nu_{2}\gamma_{-r}\right)\end{aligned}\]

\[\begin{aligned}\left\{\begin{array}{c}M=J\frac{d\omega_{1}}{d t}\\ M=F_{1}r_{2}\cos\theta-F_{2}r_{3}\\ r_{1}=f(\varphi)=f\left(\omega_{1}t\right)\\ v_{1}=\frac{d r_{1}}{d t}\\ v_{1y}=v_{1}\cos\alpha_{1}\\ \omega_{2}=\frac{v_{1y}\cos\alpha_{2}}{l_{1}}=\frac{v_{2}\cos\alpha_{2}}{t_{2}}\\ \omega_{3}=\frac{v_{2}\cos\beta_{1}}{l_{3}}=\frac{v_{3}\cos\beta_{2}}{t_{4}}\\ s=\int_{0}^{t}v_{3}d t\end{array}\right.\end{aligned}\]

\[\begin{aligned}q_{i j}(h)&=\frac{1}{\gamma+\eta\omega_{i}}\left(\alpha+\frac{\eta}{\gamma}\omega_{i}p_{j}\right)-\frac{1}{\gamma}p_{i j}(h)\\ &=\frac{1}{\gamma}\left[P_{j}+\frac{\gamma\left(\alpha-P_{j}\right)}{\gamma+\eta\omega_{i}}-p_{i j}(h)\right]\\ &=\frac{1}{\gamma}\left[\bar{h}_{j}-p_{i j}(h)\right]\end{aligned}\]

\[\begin{aligned}\frac{\partial e_{2}}{h\partial x_{2}}&=-\left[\frac{\mathrm{d}h}{h\mathrm{~d}z}\right]e_{3}\\ &=\left[\frac{\mathrm{d}h}{h\mathrm{~d}z}\right]e_{2}\end{aligned}\]

\[\begin{aligned}\left.\begin{array}{r l}p=\left(\chi_{i}\right)_{1}\left(\chi_{f}\right)_{1}^{*}+\left(\chi_{i}\right)_{2}\left(\chi_{f}\right)_{2}^{*}+\left(\chi_{i}\right)_{3}\left(\chi_{f}\right)_{3}^{*}+\left(\chi_{i}\right)_{4}\left(\chi_{f}\right)_{4}*\\ j_{x}=\left(\chi_{i}\right)_{1}\left(\chi_{f}\right)_{4}^{*}+\left(\chi_{i}\right)_{2}\left(\chi_{f}\right)_{3}*+\left(\chi_{i}\right)_{3}\left(\chi_{f}\right)_{2}^{*}+\left(\chi_{i}\right)_{4}\left(\chi_{f}\right)_{1}*\\ j_{y}=i\left(\chi_{i}\right)_{1}\left(\chi_{f}\right)_{4}^{*}-i\left(\chi_{i}\right)_{2}\left(\chi_{f}\right)_{3}^{*}+i\left(\chi_{i}\right)_{3}\left(\chi_{f}\right)_{2}^{*}-i\left(\chi_{i}\right)_{4}\left(\chi_{f}\right)_{1}*\\ j_{2}=\left(\chi_{i}\right)_{1}\left(\chi_{f}\right)_{3}^{*}-\left(\chi_{i}\right)_{2}\left(\chi_{f}\right)_{4}^{*}+\left(\chi_{i}\right)_{3}\left(\chi_{f}\right)_{1}^{*}-\left(\chi_{i}\right)_{4}\left(\chi_{f}\right)_{2}^{*}\end{array}\right\}\end{aligned}\]

\[\begin{aligned}G^{*}&=\frac{1}{B D^{2}-A^{2}}[C(C D+A)+(A B C D)]+\frac{1}{2\left(B D^{2}-A^{2}\right)^{2}}\\ &{\left[B D(C D+A)+A(C D+A)(B D-A C)+D^{2}(B D-A C)\right]}\end{aligned}\]

\[\begin{array}{l}\alpha_{u}=k_{\mathrm{u}}\left(\frac{K_{\mathrm{u}}+K_{\mathrm{c}}}{2K_{\mathrm{c}}}\right)\\ =k_{1}\left(\frac{K_{1}+K_{\mathrm{c}}}{2K_{\mathrm{c}}}\right)\end{array}\]

\[\begin{aligned}\delta_{y}&={\left[\frac{3k^{2}-4k-3}{(k+1)^{2}}\left(\frac{\alpha_{1}}{t}+\alpha_{2}\right)^{2}-\frac{2k\alpha_{1}}{(k+1)t^{2}}\right]}\\ &={\left[\frac{2(k-1)\alpha_{1}}{(k+1)t^{2}}-\frac{(3k+1)(k-1)}{(k+1)^{2}}\left(\frac{\alpha_{1}}{t}+\alpha_{2}\right)^{2}\right]}\\ &\times\left\{3\left[\eta_{1}\left(\frac{\alpha_{1}}{t}+\alpha_{2}\right)-\frac{\eta_{2}\alpha_{1}}{t^{2}}+\frac{2\alpha_{1}\eta_{3}}{3t^{2}\left(\alpha_{1}+\alpha_{2}t\right)}\right]\right\}^{-1}\end{aligned}\]

\[\begin{array}{l}u=\frac{F(y)}{r^{\frac{1}{2}}}+\frac{F_{1}(y)}{r^{\frac{3}{2}}}+\ldots\\ =\frac{G(y)}{r^{\frac{1}{2}}}+\frac{G_{1}(y)}{r^{\frac{3}{2}}}+\ldots\end{array}\]

\[\begin{aligned}&(1+2\lambda\cos\theta)\left(x^{\prime\prime}-2y^{\prime}\right)=p x\\ &(1+2\lambda\cos\theta)\left(y^{\prime\prime}+2x^{\prime}\right)=q y\\ &\mathrm{~stitute~}\quad\sum_{-\infty}^{\infty}\mathrm{A}_{n}e^{i(k+n)\theta},\quad y=\sum_{-\infty}^{\infty}\mathrm{B}_{n}e^{i(k+n)\theta}\end{aligned}\]

\[\begin{aligned}\tau_{z_{1}}\left(z_{1}\cdot z_{2}\right)&:=x_{2}-x_{1}+y_{2}\left(y_{2}-y_{1}\right)\\ &=x_{2}-x_{1}+y_{1}\left(y_{2}-y_{1}\right)\end{aligned}\]

\[\begin{array}{l}\kappa_{x l_{i}}=l_{i}\Delta\kappa_{x}\cdot\kappa_{z l_{i}}\cdot l_{i}\Delta\kappa_{z}l_{i}\cdot q\cdot1\cdot\mathrm{~K}\cdot N_{i}-1\\ =\kappa_{x u}/N_{1}\cdot\Delta\kappa_{z}\cdot\kappa_{z u}/N_{2}\end{array}\]

\[\begin{aligned}&\{1-2v+\varpi(1+2v)\sin\phi\}\dot{\sigma}_{r}+2\{1-2v-\varpi\sin\phi\}\dot{\sigma}_{\theta}\\ &=E\left\{(1+\varpi\sin\phi)\frac{\partial v}{\partial r}+2(1-\varpi\sin\phi)\frac{v}{r}\right\}\end{aligned}\]

\[\begin{aligned}\eta&=\sqrt{}\left(2\log_{\theta}\nu T-2\log_{\theta}\xi\right)\\ &=\sqrt{\left[2\log\nu T\left(1-\frac{\log\xi}{\log\nu T}\right)\right]}\\ &=\sqrt{}(2\log\nu T)-\frac{\log\xi}{\sqrt{}(2\log\nu T)}-\frac{1}{2}\frac{\log^{2}\xi}{\sqrt{}(2\log\nu T)^{3}}+\ldots\end{aligned}\]

\[\begin{array}{c}g_{2^{\prime}4}=\frac{1}{2}a^{2}\left(t^{\prime2}+t^{2}-\gamma\right)\\ =\frac{1}{2}a^{2}\left(x-x^{\prime}\right)\left[\left(t^{\prime}+t\right)^{2}-\gamma\right]^{\frac{1}{2}}\\ =\frac{1}{2}a^{2}\left(x^{\prime}-x\right)\left[\left(t^{\prime}+t\right)^{2}-\gamma\right]^{\frac{1}{2}}\\ =\frac{1}{2}a^{2}\left(x^{\prime}-x\right)\left(y-y^{\prime}\right)\\ =\frac{1}{2}a^{2}\left(x^{\prime}-x\right)\left(x-x^{\prime}\right)-a^{2}t^{\prime}t\\ =V_{\mu\alpha^{\prime}}\left(x\cdot x^{\prime}\right)\\ =V_{\left(\alpha^{\prime}\beta^{\prime}\right)(\mu\nu)}\cdot V_{\mu\nu\alpha^{\prime}\beta^{\prime}}\left(x\cdot x^{\prime}\right)\end{array}\]