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Write the LaTeX representation for this image.
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{\mathrm{E}}[\widehat{s}]=\sum_{i=1}^{n}{\mathrm{E}}[\psi_{i}X_{i}^{\prime }(\widehat{\beta }-\beta )]=\mathcal{I}_{1}+\mathcal{I}_{2},
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Write the LaTeX representation for this image.
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\mathcal{C}_{\Gamma}(x,v)=[g'(x)]^{-1}\mathcal{C}_K(g(x),\lambda) \quad{\rm for\ each}\ \lambda\in\mathcal{M}_{x}(v).
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Provide the LaTeX formula.
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R(X,Y,Z,W)=\overline{R}(X,Y,Z,W)+\langle B(X,Z),B(Y,W)\rangle-\langle B(X,W),B(Y,Z)\rangle,
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f | _ { r = \infty } = m | _ { r = \infty } = l | _ { r = \infty } = 1 \ .
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Write the LaTeX representation for this image.
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|a_n|^2 & \le |a_n^2 -ta_{2n-1}| + t|a_{2n-1}|\\ & \le n^2 -t(2n-1) + C t (2n-1)\\ & = n^2 + t (C-1) (2n-1)\\ & \le C n^2\,.
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Provide the LaTeX formula.
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-Lw_{n}=f(\cdot, w_{n})+ n(w_{n}-h_{1})^{-}-k(w_{n}-h_{2})^{+}+ \mu-\beta_{n},
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Write the LaTeX representation for this image.
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\{a_{2i-1}, a_{2i}, b_{2i-1}, b_{2i} \} \subset G_{\Gamma( \mathcal{B}_{\sum_{i=1}^{2n} \varepsilon_{i} 2^{i-1}})}
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Write the LaTeX representation for this image.
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\phi _ { \cal M ^ { * } } = \lim _ { x _ { 0 } \to 0 } { \frac { \phi _ { A d S } } { \mu ^ { \lambda } } } .
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
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一位留着棕色长发的年轻女性独自站在灰色背景前，她身穿黑色无袖连衣裙，露出肩膀，佩戴着耳环等饰品，脚穿高跟鞋。从背后看去，她的裙装简约而精致，展现出时尚模特的气质。整体造型优雅且具有设计感。
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Provide the LaTeX formula.
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(a_{3n+\varepsilon}\,,a_{3n+\varepsilon+1})=A(\varepsilon)\left(\begin{matrix}a_n\\a_{n+1}\end{matrix}\right)
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
- 推测图片边缘被裁剪掉的元素
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一位身穿黑色丝袜和高跟鞋的女性正摆出姿势。她的搭配凸显了修长的腿部线条，展现出成熟与性感的魅力。
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Provide the LaTeX formula.
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|\xi(x^s(y_0),y_0)|=|\xi(x^s(y_0),y_0)-\xi(x^s(y_1),y_1)|\leq C|y_0-y_1|^2.
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Provide the LaTeX formula.
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\Sigma _{CS}=-\frac{1}{4}\int dx^{4}\epsilon ^{\mu \nu \alpha \beta }c_{\mu}A_{\nu }F_{\alpha \beta },
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Provide the LaTeX formula.
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\frac{d}{ds}F(A+sB)|_{s=0}=\dot{F}^{ij}|_AB_{ij}\\begin{align*}5pt]\frac{d^2}{ds^2}F(A+sB)|_{s=0}=\ddot{F}^{ij,kl}|_AB_{ij}B_{kl}
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
- 推测图片边缘被裁剪掉的元素
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一位身穿黑色丝袜和高跟鞋的女性，这样的搭配凸显了她的修长腿型，尽显优雅与性感魅力。
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Provide the LaTeX formula.
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k=\frac{ \sqrt{2ME_{k}}}{\hbar}\; ,\; \; \; \; \; \; \; \; \; \; \; \; {\bf R}={\bf r} - {\bf r}'\; ,
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
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一位留着长发的年轻女性独自站在简约的白背景下，黑色长发垂落，身着优雅连衣裙，搭配精致首饰。她化着淡妆，脚踩高跟凉鞋，双手插兜，展现出随性又时尚的态度。整体造型精致而富有细节感，突显了她的独特气质。
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Write the LaTeX representation for this image.
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-\frac{\overline{F}}{2F}\,F_a+\frac 12F^c \overline{g}_{ca}=\overline{F}\psi_a\,.
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Describe the content of the image.
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This is a photo showcasing a building with a traditional European style. The building is characterized by its pink exterior walls and red roof tiles, with a prominent spire at the top. In front of the building is a parking lot, with a blue sedan parked in the middle. The background of the photo features a clear blue sky and distant mountains, adding a natural and tranquil atmosphere to the scene.
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Provide the LaTeX formula.
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V_1\big(V_2f\big)(x) = (D_xf)\big((V_1V_2)(x)\big) + (D_x^2f)\big(V_1(x),V_2(x)\big).
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Write the LaTeX representation for this image.
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\lim_{n \to \infty}\left( \int_{0}^{\infty}(1-g_{m_n}(\lambda;x))j_n(dx) + \lambda \int_{0}^{1}G_{m_n}(x)j_n(dx)\right) = -\kappa\lambda^2.
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Provide the LaTeX formula.
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H_{(\mu_{1})_{*}}(z)=\int_{\mathbb{T}}\frac{t+z}{t-z}\,d(\mu_{1})_{*}(t)
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Write the LaTeX representation for this image.
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A(y_n...y_1x) - A(y_n...y_1x') = A(0^n 1^\infty) - A(0^\infty) = a_n - a \ .
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Write the LaTeX representation for this image.
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t {\phi}_{p,\alpha}'(t)=pt^{p}(1+\log(t))^{\alpha}+\alpha t^{p}(1+\log(t))^{\alpha-1}.
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
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一位留着黑色长发的年轻女性独自站立，身穿橙色无袖连衣裙，脚蹬高跟鞋，双手佩戴手链，耳朵戴着耳环。她回过头看向一侧，整体造型充满时尚感，展现了精致的细节和优雅气质。
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Provide the LaTeX formula.
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V(\varphi) = \left( V_{0} {k_{0}}^{-{\alpha}/2}\right){\varphi}^{-\alpha} \,,
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{1\over 1-e^{-y}\mp i\epsilon}={\cal{P}}{1\over 1-e^{-y}}\pm\pi i\delta(y),
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Provide the LaTeX formula.
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[a^{\dagger}_ia_j \pm a_ja^{\dagger}_i,a^{\dagger}_k]=(2/p) \delta_{jk}a^{\dagger}_i ,\quad \forall i,j,k =1,2,...,M .
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Provide the LaTeX formula.
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cf \left( \sum_{j=1}^n X_{1j} \alpha_j, \ldots,\sum_{j=1}^n X_{rj} \alpha_j \right) = \sum_{i=1}^n (c \alpha_i) [f]_i \in R_3.
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Introduce the content of the image.
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This is a photo showcasing modern architectural design, with the foreground featuring a green lawn and a few street lamps, while the background is a modern building with a curved roof and large glass windows. The sky is clear, with a few white clouds scattered across the blue sky.
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Provide the LaTeX formula.
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Z_j \leq \frac{D'}{Q_1} + 10 \sqrt{\frac{D'}{Q_1^2Q_2^2}} \sqrt{\log(k)} = \frac{1}{Q_1}\left( D' + 10\frac{\sqrt{D' \log k}}{Q_2} \right).
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Provide the LaTeX formula.
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A _ { 0 } ( z _ { 0 } , z _ { 1 } ) = \delta ( z _ { 0 } ) \theta ( z _ { 1 } - x _ { 1 } ) \theta ( x _ { 2 } - z _ { 1 } )
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
- 推测图片边缘被裁剪掉的元素
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一位身材火辣的亚洲女性身穿黑色内衣和高跟鞋，这样的搭配凸显了她的迷人曲线，尽显性感魅力。
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Describe the content of the image.
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This is a photo depicting a traditional handicraft production scene. In the center of the image, there is a large circular stone grinding machine, with two workers standing on either side, using wooden tools to grind the material inside the machine. The material inside the machine appears to be a brownish-yellow mixture, possibly a kind of handicraft. In the background, a cow stands quietly, seemingly observing the activities in front. The surrounding environment is a spacious workshop, with other tools and materials scattered around, creating a busy yet orderly handicraft production atmosphere.
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
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一位留着棕色长发的年轻女性独自站立，她身着黑色衬衫和裤子，脚踩高跟凉鞋，佩戴着耳环、戒指和脚链等饰品。她的妆容精致，嘴唇显得格外诱人。作为一位时尚模特，她的穿搭兼具个性与美感，整体造型既大胆又协调。
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\tilde\Omega=\bigcup_{i=1}^k \mathcal N(u_i), \mathcal N^o(u_i) \cap \mathcal N^o(\sum_{j\neq i}u_j)=\emptyset\; \forall i\;,
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Write the LaTeX representation for this image.
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\mathcal E^n(f,g):=\frac{1}{2}\sum_{x,y\in \Gamma^n}(f(x)-f(y))(g(x)-g(y))\, C^n_{xy} \qquad
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
- 推测图片边缘被裁剪掉的元素
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一位身穿白色高跟鞋和内裤的女性，这样的搭配显得大胆前卫，尽显自信与个性。
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Provide the LaTeX formula.
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r \in \Gamma \iff \exists \xi < \omega_1 \, [ r(n) = 1 \iff T(\omega\cdot \xi + n) ]
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Write the LaTeX representation for this image.
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\sum _ { i = 1 } ^ { 3 } ( 3 _ { i } , \bar { 3 } _ { i + 1 } ) + \sum _ { i = 1 } ^ { 3 } ( 8 + 1 ) _ { i }
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Write the LaTeX representation for this image.
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x_{n+1} & =x_{n}+2y_{n}-2\\y_{n+1} & =\frac{0.75x_{n}+1.5y_{n}}{3x_{n}+6y_{n}-6}
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
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一位年轻女性独自站在灰色背景前，她留着中等长度的黑发，身穿带有花卉图案的长袖衬衫，搭配高跟凉鞋。她的穿搭简约而精致，展现出时尚感，同时也突出了东方女性的独特魅力。
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Write the LaTeX representation for this image.
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-i ~\alpha ~+~ \bar{\beta} ~=~ -i ~k_{22} ~e^{i \theta _2 /2}; \hspace{.5in}-i ~\beta ~+~ \bar{\alpha} ~=~ k_{22} ~e^{-i \theta _2 /2}.
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Write the LaTeX representation for this image.
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\| \nabla \phi(t,y(t)) \|&\leq \sum\limits_{i=0}^{\infty}2 \eta_i(t) \|y(t) - x_i(t)\| \leq 4\frac{\epsilon(t)}{ \lambda(t)}.
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Write the LaTeX representation for this image.
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v ^ { i } \phi ^ { j } ( \theta \gamma ^ { i j } \theta ) ( \theta \gamma ^ { k l m } \theta ) ( \theta \gamma ^ { k l m } \theta ) ,
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Provide the LaTeX formula.
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\tilde{\mathcal{F}}(\eta,\phi_{\partial},\Sigma)=\mathcal{F}(v,\Sigma),
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
- 推测图片边缘被裁剪掉的元素
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一位身穿金色比基尼和高跟鞋的女性正姿态撩人地躺在床榻上。她大胆的穿搭展现了十足的自信与性感魅力。
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Provide the LaTeX formula.
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[u]^p_{W^{\tau,p}(B_{R/2})}&\le \frac{\mathcal{C}_1}{R^{\tau\,p}}\,\mathcal{A}_R(u,f),
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Provide the LaTeX formula.
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\frac{1}{3} {\phi}^3+ 2 \nu {\phi}{\phi}_{x}+\nu^2 {\phi}_{xx}=\mathrm{const} \, .
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
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一位留着棕色长发、身穿白色背景前独自行走的年轻女性，身着一条粉色裤装，搭配无袖连衣裙，脚穿高跟凉鞋，耳戴精致耳环。她的装扮兼具时尚感与个性，既展现了都市女性的干练风格，又不失优雅魅力。
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
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一位留着棕色长发的年轻女性独自站立，她身穿红色连衣裙，搭配高跟凉鞋，手扶髋部，面带笑容，眼睛直视观众。她的脖子上戴着项链，耳朵上挂着耳环，头上还随意地放着一副太阳镜，脸上带着一抹调皮的笑意。整体造型精致且充满细节，充分展现了她的时尚品味。
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\Psi(a)\Psi(a)^*\leq\Psi(aa^*)\leq \Psi(a^*a)=\Psi(a)^*\Psi(a)=\Psi(a)\Psi(a)^*.
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Provide the LaTeX formula.
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\begin{cases}-\Delta u=\lambda_1 |x|^av&\\-\Delta v=\lambda_2 |x|^bu&\\u=0=v&\end{cases}
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
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一位留着棕色短发的女孩站在纯白背景下，身穿一件简约的上衣和一条带有花卉图案的蓝色长裙，裙子是高跟鞋搭配的款式。她身姿挺拔，五官精致，棕色的眼睛透露出自信，双唇微微勾起。整体造型展现了修长的身材线条，时尚感十足。
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Provide the LaTeX formula.
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I_3(t;x)=\int_{0}^{t}((K_3+\phi_3)(\partial_xX)^3+3(K_2+\phi_2)(\partial_xX)(\partial^2_xX)+(K_1+\phi_1)(\partial^3_xX)(\tau;x)d\tau.
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Write the LaTeX representation for this image.
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\forall x \in E, \forall \lambda \in K_v, \ \sigma_v(x \otimes \lambda) = \sigma(x) \otimes \lambda
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Write the LaTeX representation for this image.
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\begin{cases}\partial_{t}u-\Delta u=0,\ \ & x\in\mathbb{R}^{3},\ t>0,\\u(x,0)=u_{0}(x),\ \ & x\in\mathbb{R}^{3}.\end{cases}
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Provide the LaTeX formula.
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( \bar { \Phi } \Phi , F ) ^ { a } \not \equiv ( V ^ { a } - U ^ { a } ) F ,
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
- 推测图片边缘被裁剪掉的元素
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一位身穿丝袜搭配高跟鞋的女性正站在楼梯上。她精心挑选的服饰突显了身材曲线，展现了都市女性的时尚魅力。
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Write the LaTeX representation for this image.
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\mathfrak{b}_{p^f}(F):=\prod\,\lbrace\ \mathfrak{p}\in\mathbb{P}_F\mid N_{F/\mathbb{Q}}(\mathfrak{p})=p^f\ \rbrace.
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Write the LaTeX representation for this image.
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{\rm Tr}~(-1)^F ~\equiv~\sum_E ~ n_B (E) ~-~ n_F (E) ~=~ n_B (0) ~-~ n_F (0) ~.
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Write the LaTeX representation for this image.
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{ \frac { \partial g _ { \tau } } { \partial \nu } } ( \nu ) = - k { \frac { 1 } { 1 + ( \nu + \tau ) \sp 2 } }
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Write the LaTeX representation for this image.
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(\lambda _{1}+\lambda _{2})+(\lambda _{5}+\lambda _{6})+\mu (\lambda_{1}-\lambda _{2})=0.
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Recognize all the text in the image.
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The suspect was arrested Saturday morning at around 11:35 a.m. on Girardin Street in Drummondville, roughly 150 kilometres west of Quebec City.
Oh, jolly’s the word for aye! Adieu, Doubloon! But stop; here comes little King-Post; dodge round the try-works, now, and let’s hear what he’ll have to say.
The adult stages of the majority of parasitic helminths of humans cannot be obtained routinely for direct investigation, so genetic surveys (including those investigating drug resistance) resort to sampling transmission stages, i.
Purchasing Violations:
Imprisonment
....
194/1468) Home: Molotov Lite by Eviltwin Brewing of Connecticut, U.S.A.: **1/2; 8.5% Imperial India Pale Ale; opaque with a fluffy head; off-orange; earthy and resiny with a touch of citrus to the nose; earthy, resiny flavours with a bitter astringent after taste;
101. Riddle: What does man love more than life, hate more than death or mortal strife; that which contented men desire; the poor have, the rich require; the miser spends, the spendthrift saves, and all men carry to their graves?
Args: num1 (int): The first integer to add. num2 (int): The second integer to add. Returns: int: The sum of num1 and num2. """ # Add the two input integers together using the + operator result = num1 + num2 # Return the calculated sum return result ``` Here's a detailed explanation of each part: 1.
{
Q:
1
The type you used is DateTime (on the server side as well as the client side).
Imprisonment
Zoe: hehe, thanks kevin! but that's not all. i bet i can beat you in a race too! how about that? *grins challengingly and starts pushing the sled uphill, towards another snowy slope* c'mon, let's race! loser has to do something super embarrassing!
If we to assume that $H$ is such a group, than $H$ must be normal in $S_5$ and $|H|=|S_5|/|S_4|=5$.
// ...
Should I work directly at the shader level or in javascript?
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Provide the LaTeX formula.
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\langle \phi, \psi \rangle_\eta = \langle \phi, \eta \psi \rangle_\mathcal{H} ~~~(\phi,\psi \in \mathcal{H}).
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
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一位年轻女性站在简洁的背景下，她有着黑色的长发和深邃的黑眼睛，身穿一条蓝色条纹连衣裙，脚蹬高跟凉鞋，佩戴着耳环、手链和手表等配饰。她的穿搭精致而时尚，展现了都市女性的魅力与品味。
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Write the LaTeX representation for this image.
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\dot { \nu } ( \tau ) = - { \frac { k } { ( \nu ( \tau ) + \tau ) \sp 2 + 1 + k } }
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Provide the LaTeX formula.
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\overline \tau (\rho) = \bigoplus_n \rho(n) \otimes_{k[S_n]} \tau^{\otimes n},
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Write the LaTeX representation for this image.
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\left( t_i^2 + c - c \, (U^\top U)_{i,i} \right) U^\top_{i,h} = \mu_h U^\top_{i,h}.
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Write the LaTeX representation for this image.
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f(x)=-\,\frac{1}{2}\, {\wp'(x-x_0)-\wp'(a)\over \wp(x-x_0)-\wp(a)}\, ,
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Write the LaTeX representation for this image.
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R_\mu(x,y)=\mathcal{O}\big( (1+|x-y|^2)^{-1}\big),\ \forall x, y\in\mathbb R.
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
- 推测图片边缘被裁剪掉的元素
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一位身穿高跟鞋并搭配链条装饰的女性，她的腿部线条在链条的点缀下显得格外引人注目。这种穿搭风格既前卫又充满个性，完美展现了时尚与创意的结合。
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Write the LaTeX representation for this image.
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\left[ C _ { i } , C _ { j } \right] = i \frac { \hbar c } { e B } \epsilon _ { i j }
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Provide the LaTeX formula.
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n _ { \mathrm { t h } } \sim \int d ^ { d } k \vert a ( k ) \vert ^ { 2 } \omega _ { k } \sim T a ^ { 1 - d } .
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Write the LaTeX representation for this image.
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f_q'(x) = \begin{cases} f'(x) & 1/q \leq x \leq B-1/q , \\ 0 & \end{cases}
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
- 推测图片边缘被裁剪掉的元素
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一位身穿黑色丝袜搭配高跟鞋的女性坐在沙发上，整体造型凸显出她的优雅与性感。
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Provide the LaTeX formula.
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d_q<d_{q+1}<\cdots<d_l<x\qquad\qquad\tilde{\delta}=(x,d_l,d_{l-1}\dots,d_2);
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Provide the LaTeX formula.
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k^2\varepsilon - k_\alpha k_\beta \varepsilon^{\alpha \beta} = 0~;~~~~ \varepsilon = {\varepsilon^\mu}_\mu.
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Write the LaTeX representation for this image.
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S = \int \left[-\frac{1}{4}tr F^2 -\frac{1}{2\xi }tr(\partial ^{\mu }A_\mu )^2 -i tr(\partial ^\mu \bar{C})(\nabla _\mu C)\right].
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Write the LaTeX representation for this image.
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\frac{1}{(q;q)_\infty} \sum_{n=1}^\infty (-1)^{n-1} q^{n(n-1)/2+n|k|}(1-q^n).
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Provide the LaTeX formula.
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{\cal Q}'={1\over 16\pi G_D}\int_{S^1\times S^{d-1}} *F_{q+2}=(d-2) L \Omega_{d-1} {I_{d-3}\over L}\tilde{Q}.
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Provide the LaTeX formula.
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S(z_1,z_2)&=(\bar{z_2},\bar{z_1})\\\theta(z_1,z_2)&=(e^{i\theta}z_1, e^{-i\theta}z_2)
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Write the LaTeX representation for this image.
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\det\Phi_t(x,y) = \det\left(\begin{array}{cc} & - \\t & (1-t)\end{array}\right) = 1
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Provide the LaTeX formula.
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ds^2=g_{ab} dx^a dx^b = dr^2+ a^2(r) \gamma_{\mu\nu} dx^{\mu}dx^{\nu},
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Provide the LaTeX formula.
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\widehat a(\theta)=\begin{cases} 4a(2\theta),&\theta\in[0,\pi],\\ 4a(2\theta-2\pi),&\theta\in[\pi,2\pi].\end{cases}
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Write the LaTeX representation for this image.
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(v^i \phi^i ) v^j \phi^k(\theta \gamma^{jlm} \theta ) (\theta \gamma^{klm} \theta ) ~ ,
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Recognize text in pictures.
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# US 7,985,757 A\n\nPage 3\n\n(42)\n\n**Int. C**\n\n**F59D 15/04**\n\n**F59D 7/18**\n\n**2006.01**\n\n**2006.01**\n\n(43)\n\n**References Cited**\n\n### U.S. PATENT DOCUMENTS\n\n1,251,195 A2/1919 Terry et al.\n\n1,298,058 A4/1919 Ward et al.\n\n1,409,636 A6/1919 Treutel et al.\n\n1,430,907 A7/1919 Reinger et al.\n\n1,475,408 A7/1919 Macejkovic\n\n1,602,072 A9/1919 Harvey et al.\n\n1,628,876 A10/1919 Borer et al.\n\n1,712,730 A12/1919 Rau\n\n1,723,053 A2/1920 Lueilwitz\n\n1,856,621 A4/1920 Mueller\n\n1,936,326 A6/1920 Dach\n\n2,013,353 A7/1920 Feeney\n\n2,060,935 A8/1920 Medhurst et al.\n\n2,164,965 A9/1920 Bode\n\n2,182,997 A10/1920 Green et al.\n\n2,297,107 A11/1920 Johns\n\n2,415,259 A1/1921 Gulgowski\n\n2,466,462 A2/1921 Russel\n\n2,562,129 A3/1921 Bartell\n\n2,625,963 A3/1921 Sanford et al.\n\n2,678,426 A5/1921 Schaden et al.\n\n2,823,106 A5/1921 Parker et al.\n\n2,930,397 A6/1921 Davis\n\n3,020,753 A8/1921 Schmitt\n\n3,092,758 A10/1921 Bashirian\n\n3,180,078 A11/1921 Labadie\n\n3,209,466 A12/1921 Simonis et al.\n\n3,234,264 A2/1922 Bergnaum\n\n3,348,881 A2/1922 Bruen\n\n3,435,987 A4/1922 Collier et al.\n\n3,443,299 A6/1922 Leuschke\n\n3,476,946 A8/1922 Baumbach\n\n3,544,882 A8/1922 Schinner et al.\n\n3,678,452 A9/1922 Boehm et al.\n\n3,720,381 A11/1922 Gibson et al.\n\n3,746,824 A1/1923 Stehr et al.\n\n3,833,192 A1/1923 Yundt\n\n3,912,250 A1/1923 Kohler et al.\n\n4,050,111 A3/1923 Ortiz\n\n4,096,714 A3/1923 Dickens\n\n4,121,032 A5/1923 Pouros\n\n4,152,081 A5/1923 Dicki et al.\n\n4,221,487 A7/1923 Labadie\n\n4,332,585 A7/1923 Jast et al.\n\n4,339,231 A7/1923 Graham\n\n4,452,941 A8/1923 Ryan et al.\n\n4,468,874 A8/1923 Renner-Schulist\n\n4,502,965 A9/1923 Blanda et al.\n\n4,591,614 A11/1923 Corkery\n\n4,666,598 A12/1923 Christiansen et al.\n\n4,711,580 A1/1924 Quigley\n\n4,759,556 A1/1924 Rodriguez\n\n4,836,507 A3/1924 Homenick et al.\n\n4,902,836 A5/1924 Heller et al.\n\n4,933,183 A6/1924 Wuckert et al.\n\n5,059,642 A8/1924 Fahey et al.\n\n5,077,022 A8/1924 Kris\n\n5,157,790 A8/1924 Klein et al.\n\n5,170,849 A9/1924 Bauch et al.\n\n5,198,659 A10/1924 Rowe\n\n5,249,512 A11/1924 Kemmer et al.\n\n5,261,651 A11/1924 Schuster et al.\n\n5,353,556 A1/1925 McClure et al.\n\n5,501,467 A3/1925 Kulas\n\n5,509,278 A4/1925 Goodwin\n\n5,557,201 A6/1925 Schuster\n\n5,634,458 A8/1925 Robel et al.\n\n5,753,125 A9/1925 Mitchell et al.\n\n5,815,981 A10/1925 Hahn\n\n5,880,111 A11/1925 Altenwerth\n\n5,998,360 A1/1926 Fadel et al.\n\n6,035,830 A1/1926 Champlin\n\n6,171,409 A3/1926 Dickinson\n\n6,191,941 A4/1926 Rutherford et al.\n\n6,332,717 A6/1926 Kris et al.\n\n6,389,939 A7/1926 Nicolas et al.\n\n6,489,420 A9/1926 Bahringer et al.\n\n6,581,055 A10/1926 Nolan\n\n6,704,481 A10/1926 Kulas et al.\n\n6,800,575 A10/1926 Veum et al.\n\n6,844,560 A10/1926 Huels\n\n6,920,428 A11/1926 Stark et al.\n\n6,981,049 A11/1926 Osinski et al.\n\n6,997,757 A11/1926 Crooks et al.\n\n7,139,501 A11/1926 Oberbrunner et al.\n
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Write the LaTeX representation for this image.
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\ln( P_n) \ \leq \ [(Nn+1)&(\ln(Nn + 1) - 1) + 1] - n[N(\ln(N) - 1) + 1] \\ = \ (Nn + 1)&(\ln(n + (1/N)) + \ln(N) - n.
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Write the LaTeX representation for this image.
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A ( \nu ; x , y ) = F ( \nu ; x + y ) + \int _ { x } ^ { \infty } d u A ( \nu ; x , u ) F ( \nu ; u + y )
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Write the LaTeX representation for this image.
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\gamma = \frac {n+1} 2 \left( \frac 1 2 -\frac 1 q \right) -\frac m {2 \mu_\ast (m+2)}
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Write the LaTeX representation for this image.
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g'(t) = f'\bigg(\alpha(s_2)+\frac{d(s_2)}{d(s_1)}(t-\alpha(s_1))\bigg) \leq f'(t).
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Provide the LaTeX formula.
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F_2(x) = \dfrac{\mu_1 + \dfrac{(x - \mu_0)(x^2 + 1 -2\mu_0x)}{(x^2 - 1)^3}}{x^2 - 1}
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
- 推测图片边缘被裁剪掉的元素
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一位身穿黑色丝袜和高跟鞋的女性，这样的搭配凸显了她的优雅与性感，尽显都市魅力。
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Write the LaTeX representation for this image.
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\delta V_{ij} \sim {\langle \phi_i \mid V \mid \phi_k \rangle \langle\phi_k \mid V \mid \phi_j \rangle \over \epsilon_i-\epsilon_k}\;.
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请分析这张照片的场景和人物穿着特征。重点识别以下内容：
- 整体场景氛围
- 主要人物的服装款式特征
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一位留着棕色长发、有着丰满身材的年轻女性站在纯白背景前，她面带微笑凝视着镜头，眼神温柔且充满活力。她的棕色眼睛佩戴了精致的耳环，搭配高跟凉鞋和黑色长裤，显得干练又优雅。腰间隐约可见的中腰设计与手提包相得益彰，整体造型简洁而富有细节感。作为一位时尚模特，她举手投足间流露出自信从容的魅力，展现了都市女性的独特风采。
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You are an expert radiographer. Describe accurately what you see in this image.
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Horseshoe sign.In patient with MS, postcontrast MRI image demonstrates incomplete ring of enhancement, resembling horseshoe (arrow).
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Provide the LaTeX formula.
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\partial_{ii} V=\bigg(\frac{1}{1+\lambda_i^2}-2e_i^2\bigg)V +e_i^2V\\ \partial_{ij}V=Ve_ie_j .
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Write the LaTeX representation for this image.
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\lim_{n\to\infty}\sup_{\tau\in (0,1-t_n)}\frac{1}{\tau}\int_{t_n}^{t_n+\tau}\int_0^{\infty}(\partial_sa)^2\,rdrds=0.
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Provide the LaTeX formula.
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\mathcal{G}(u)=1+\mathcal{K}u_{\sharp}^\nu-(\mathcal{K}u_{\sharp}^\nu)(0,0),
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Write the LaTeX representation for this image.
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\tilde{\theta}^{k}=\Pi_{\mathcal{K},G}\big\{\theta^{k}-G^{-1}[T(\tilde{\theta}^{k})-\beta\Lambda(y^{k}-\tilde{y}^{k})+\zeta^k]\big\}.
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