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\sum_{i=1}^m X_i>T | \sum_{i=1}^{m}X_{i}>T | synthetic | 0043dcfce37f0566 | mathwriting-2024/synthetic/0043dcfce37f0566.inkml |
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XEF | XEF | synthetic | dc61de3182778966 | mathwriting-2024/synthetic/dc61de3182778966.inkml |
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R_M = \frac{R_\infty}{1+m_{\text{e}}/M}, | R_{M}=\frac{R_{\infty}}{1+m_{e}/M}, | synthetic | 1443b7e420419f63 | mathwriting-2024/synthetic/1443b7e420419f63.inkml |
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\Psi_x(x_1,x_2) = \delta(x - x_1) g(x_2) | \Psi_{x}(x_{1},x_{2})=\delta(x-x_{1})g(x_{2}) | synthetic | 24e6b0da46fa7244 | mathwriting-2024/synthetic/24e6b0da46fa7244.inkml |
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f(L \cap R) ~\supseteq~ f(L) \cap f(R) | f(L\cap R)\supseteq f(L)\cap f(R) | synthetic | b96f5fabf42cd059 | mathwriting-2024/synthetic/b96f5fabf42cd059.inkml |
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L(0) = 0 | L(0)=0 | synthetic | 8f1e1bd29025ebb4 | mathwriting-2024/synthetic/8f1e1bd29025ebb4.inkml |
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\Psi_{c*}= \frac{load}{strength} = \frac{u_{*c}^2}{\Delta g d} | \Psi_{c*}=\frac{load}{strength}=\frac{u_{*c}^{2}}{\Delta gd} | synthetic | 761b9bf18d1dad88 | mathwriting-2024/synthetic/761b9bf18d1dad88.inkml |
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(x,y)\mapsto (x+c,y) | (x,y)\mapsto(x+c,y) | synthetic | 6439076a1242757b | mathwriting-2024/synthetic/6439076a1242757b.inkml |
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f\colon U\to Y, | f:U\rightarrow Y, | synthetic | bd24ac062a73970e | mathwriting-2024/synthetic/bd24ac062a73970e.inkml |
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A,B,C \in M | A,B,C\in M | synthetic | bb4a09c75c4d58f4 | mathwriting-2024/synthetic/bb4a09c75c4d58f4.inkml |
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gW = gW^T-f(U-U^*)+\lambda gP^\text{ex}. | gW=gW^{T}-f(U-U^{*})+\lambda gP^{ex}. | synthetic | fc80c0ea336e86d3 | mathwriting-2024/synthetic/fc80c0ea336e86d3.inkml |
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a_1a_2a_3\cdots a_n = d^n\prod_{k=0}^{n-1} \left(\frac{a_1}{d}+k\right) = d^n \frac{\Gamma \left(\frac{a_1}{d} + n\right) }{\Gamma \left( \frac{a_1}{d} \right)} | a_{1}a_{2}a_{3}\cdot\cdot\cdot a_{n}=d^{n}\prod_{k=0}^{n-1}(\frac{a_{1}}{d}+k)=d^{n}\frac{\Gamma(\frac{a_{1}}{d}+n)}{\Gamma(\frac{a_{1}}{d})} | synthetic | 0d688b7aeff9158a | mathwriting-2024/synthetic/0d688b7aeff9158a.inkml |
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f(z) = \sum_{n=-m}^\infty a_n e^{2i\pi nz}. | f(z)=\sum_{n=-m}^{\infty}a_{n}e^{2i\pi nz}. | synthetic | 6dbe3b176b0d92ca | mathwriting-2024/synthetic/6dbe3b176b0d92ca.inkml |
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\log K_2 = 2.05 | logK_{2}=2.05 | synthetic | fb6ce0d35c7b3888 | mathwriting-2024/synthetic/fb6ce0d35c7b3888.inkml |
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b_{15}+c_{13} | b_{15}+c_{13} | synthetic | e2da167b69fa2f6b | mathwriting-2024/synthetic/e2da167b69fa2f6b.inkml |
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\Delta_{n+1} \equiv \Omega_{n+1} - \Omega_n = \frac{f(u_n)}{u_n} \delta_n\Omega_n = \frac{f(u_n)(1+u_{n-1})}{f(u_{n-1})u_n}\Delta_n, | \Delta_{n+1}\equiv\Omega_{n+1}-\Omega_{n}=\frac{f(u_{n})}{u_{n}}\delta_{n}\Omega_{n}=\frac{f(u_{n})(1+u_{n-1})}{f(u_{n-1})u_{n}}\Delta_{n}, | synthetic | aa154505778ce121 | mathwriting-2024/synthetic/aa154505778ce121.inkml |
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[X,E^\bullet] = i^![V] | [X,E^{\bullet}]=i^{!}[V] | synthetic | afc8b81bb48d0cb3 | mathwriting-2024/synthetic/afc8b81bb48d0cb3.inkml |
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W_1 := \max{W/2, 2\mathrm{AREA}(\mathcal{I'})/H} | W_{1}:=maxW/2,2AREA(I^{\prime})/H | synthetic | 2a69ad346ed13f94 | mathwriting-2024/synthetic/2a69ad346ed13f94.inkml |
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\frac{\frac{\frac{6.5477518}{15.1470445}}{u}}{\frac{\frac{12.29}{111111100666}}{\frac{333111111666}{38.28}}} | \frac{\frac{\frac{6.5477518}{15.1470445}}{u}}{\frac{\frac{12.29}{111111100666}}{\frac{333111111666}{38.28}}} | synthetic | 8abe7b99e4f05874 | mathwriting-2024/synthetic/8abe7b99e4f05874.inkml |
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C(\alpha)_{n+1} = C(\alpha)_n \cup \{\beta_1+\beta_2,\beta_1\beta_2,{\beta_1}^{\beta_2}: \beta_1,\beta_2\in C(\alpha)_n\} \cup \{\psi(\beta): \beta\in C(\alpha)_n \land \beta<\alpha\} | C(\alpha)_{n+1}=C(\alpha)_{n}\cup\{\beta_{1}+\beta_{2},\beta_{1}\beta_{2},{\beta_{1}}^{\beta_{2}}:\beta_{1},\beta_{2}\in C(\alpha)_{n}\}\cup\{\psi(\beta):\beta\in C(\alpha)_{n}\wedge\beta<\alpha\} | synthetic | c302a4463624888d | mathwriting-2024/synthetic/c302a4463624888d.inkml |
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p_{R} \approx 0 | p_{R}\approx0 | synthetic | 17dddcb422959e96 | mathwriting-2024/synthetic/17dddcb422959e96.inkml |
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X_{H \circ \phi} | X_{H\circ\phi} | synthetic | ab74326d732c737b | mathwriting-2024/synthetic/ab74326d732c737b.inkml |
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\log(1+x) = \sum_{n = 0}^\infty a_n T_n(x)~. | log(1+x)=\sum_{n=0}^{\infty}a_{n}T_{n}(x). | synthetic | 1f7d640dacab4f23 | mathwriting-2024/synthetic/1f7d640dacab4f23.inkml |
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\left( 2(n+r-1)(n+r-2) + 3 (n+r-1) - 1\right) a_{n-1}(r) = \left( 2 (n+r-1)(n+r) + 3 (n+r) \right)a_{n}(r) | (2(n+r-1)(n+r-2)+3(n+r-1)-1)a_{n-1}(r)=(2(n+r-1)(n+r)+3(n+r))a_{n}(r) | synthetic | f30f488fad610968 | mathwriting-2024/synthetic/f30f488fad610968.inkml |
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c_n \sim 1/n | c_{n}\sim1/n | synthetic | aff03e5017a24960 | mathwriting-2024/synthetic/aff03e5017a24960.inkml |
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\tan(20)\cdot\frac{2 \tan(20)}{1-\tan^2(20)}/\sqrt{3} = \frac{\tan(20)}{1+\sqrt{1+\tan^2(20)}} | tan(20)\cdot\frac{2tan(20)}{1-tan^{2}(20)}/\sqrt{3}=\frac{tan(20)}{1+\sqrt{1+tan^{2}(20)}} | synthetic | f72c4b1ea5d46571 | mathwriting-2024/synthetic/f72c4b1ea5d46571.inkml |
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\cot(\arcsin x) = \frac{1}{\tan(\arcsin x)} = \frac{1}{\frac{x}{\sqrt{1 - x^2}}} = \frac{\sqrt{1 - x^2}}{x} | cot(arcsinx)=\frac{1}{tan(arcsinx)}=\frac{1}{\frac{x}{\sqrt{1-x^{2}}}}=\frac{\sqrt{1-x^{2}}}{x} | synthetic | f1d9259a4e536916 | mathwriting-2024/synthetic/f1d9259a4e536916.inkml |
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a+b=(x+y)^{n} | a+b=(x+y)^{n} | synthetic | a9acdd26fdd7215c | mathwriting-2024/synthetic/a9acdd26fdd7215c.inkml |
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\frac{d\omega}{d\Omega} = \left(\frac{Z_1Z_2e^2}{4E_0}\right)^2 \frac{1}{\left(\sin{\theta/2}\right)^4}, | \frac{d\omega}{d\Omega}=(\frac{Z_{1}Z_{2}e^{2}}{4E_{0}})^{2}\frac{1}{(sin\theta/2)^{4}}, | synthetic | 5d0e34e2bb5b4b57 | mathwriting-2024/synthetic/5d0e34e2bb5b4b57.inkml |
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v_\mathcal{D}:\mathcal{D}^\mathbb{N}\rightarrow\mathbb{T} | v_{D}:D^{\mathbb{N}}\rightarrow\mathbb{T} | synthetic | 96ed38016bb273a1 | mathwriting-2024/synthetic/96ed38016bb273a1.inkml |
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\oint{dl} | \oint dl | synthetic | b0dfbdbdb1ddd6a8 | mathwriting-2024/synthetic/b0dfbdbdb1ddd6a8.inkml |
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-\frac{\mathrm{d}}{\mathrm{d}x} \bigg[ \tau(x) \frac{\mathrm{d}\rho(x)}{\mathrm{d}x} \bigg]+v(x)\rho(x) = \omega^2\sigma(x)\rho(x) | -\frac{d}{dx}[\tau(x)\frac{d\rho(x)}{dx}]+v(x)\rho(x)=\omega^{2}\sigma(x)\rho(x) | synthetic | 46d57cab426d6f0d | mathwriting-2024/synthetic/46d57cab426d6f0d.inkml |
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10^{-2} | 10^{-2} | synthetic | 3a73bb36d4beeb1c | mathwriting-2024/synthetic/3a73bb36d4beeb1c.inkml |
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p_y(x,y) = \textstyle \sum\limits_{i=0}^3 \sum\limits_{j=1}^3 \frac{a_{ij} x^i j y^{j-1}}{\Delta y}, | p_{y}(x,y)=\sum_{i=0}^{3}\sum_{j=1}^{3}\frac{a_{ij}x^{i}jy^{j-1}}{\Delta y}, | synthetic | ea4600ab5b12a852 | mathwriting-2024/synthetic/ea4600ab5b12a852.inkml |
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1-p=\frac{m}{m+r} | 1-p=\frac{m}{m+r} | synthetic | 6a66c688f4515785 | mathwriting-2024/synthetic/6a66c688f4515785.inkml |
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\mathcal A \models_{\{\emptyset\}}^- \phi | A\models_{\{\emptyset\}}^{-}\phi | synthetic | 50f946dd9b82d207 | mathwriting-2024/synthetic/50f946dd9b82d207.inkml |
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\operatorname{ker} R | kerR | synthetic | e86265a5ccea4247 | mathwriting-2024/synthetic/e86265a5ccea4247.inkml |
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\operatorname{vec} (X) | vec(X) | synthetic | ced68d869e49367f | mathwriting-2024/synthetic/ced68d869e49367f.inkml |
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\mathcal{C} = \binom{n}{2i} | C=(\begin{matrix}n\\ 2i\end{matrix}) | synthetic | dd2c422131e10b66 | mathwriting-2024/synthetic/dd2c422131e10b66.inkml |
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A_\text{r} | A_{r} | synthetic | 4069610e22d8d857 | mathwriting-2024/synthetic/4069610e22d8d857.inkml |
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\chi^{3} | \chi^{3} | synthetic | 8ce145e9a51c4ab6 | mathwriting-2024/synthetic/8ce145e9a51c4ab6.inkml |
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Y_1 \subseteq Y_2. | Y_{1}\subseteq Y_{2}. | synthetic | 0239e0ec4ba8cf0e | mathwriting-2024/synthetic/0239e0ec4ba8cf0e.inkml |
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\mathbf x_{i+1} = \mathbf x_i + \left(\mathbf x_i - \mathbf x_{i-1}\right) \frac{\Delta t_i}{\Delta t_{i-1}} + \mathbf a_i \Delta t_i^2. | x_{i+1}=x_{i}+(x_{i}-x_{i-1})\frac{\Delta t_{i}}{\Delta t_{i-1}}+a_{i}\Delta t_{i}^{2}. | synthetic | fc9948057fc2f87c | mathwriting-2024/synthetic/fc9948057fc2f87c.inkml |
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(2)_t^2(3)_t\cdot (6)_{t}\cdot (6)_t \cdot (2)_{t^2}^2(3)_{t^2}\cdot (6)_{t^2} \cdot (2)_{t^3}(6)_{t^3}\cdot (2)_{t^3}^2(3)_{t^3} | (2)_{t}^{2}(3)_{t}\cdot(6)_{t}\cdot(6)_{t}\cdot(2)_{t^{2}}^{2}(3)_{t^{2}}\cdot(6)_{t^{2}}\cdot(2)_{t^{3}}(6)_{t^{3}}\cdot(2)_{t^{3}}^{2}(3)_{t^{3}} | synthetic | 2c524b3b1f8aa1ec | mathwriting-2024/synthetic/2c524b3b1f8aa1ec.inkml |
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0<N(q)<1 | 0<N(q)<1 | synthetic | e5c05d592a52252a | mathwriting-2024/synthetic/e5c05d592a52252a.inkml |
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n \in N. | n\in N. | synthetic | edfc1188530ec246 | mathwriting-2024/synthetic/edfc1188530ec246.inkml |
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\eta_H(C[V_{Y_0}]) \geq g(|Y_0|), | \eta_{H}(C[V_{Y_{0}}])\ge g(|Y_{0}|), | synthetic | f38df741d0f0feef | mathwriting-2024/synthetic/f38df741d0f0feef.inkml |
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\partial_t q = (s_r+ i s_i) \,\Delta^2 q + (d_r+ i d_i) \,\Delta q + \ell_r q + (c_r + i c_i)|q|^2 q + (q_r + i q_i) |q|^4 q. | \partial_{t}q=(s_{r}+is_{i})\Delta^{2}q+(d_{r}+id_{i})\Delta q+l_{r}q+(c_{r}+ic_{i})|q|^{2}q+(q_{r}+iq_{i})|q|^{4}q. | synthetic | 2f72e2c7405c2334 | mathwriting-2024/synthetic/2f72e2c7405c2334.inkml |
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\alpha_i/\alpha_0 | \alpha_{i}/\alpha_{0} | synthetic | f288589ae54fdf90 | mathwriting-2024/synthetic/f288589ae54fdf90.inkml |
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\hat{L} = - i\frac{\partial H(x, p)}{\partial p} \frac{\partial}{\partial x} + i\frac{\partial H(x, p)}{\partial x} \frac{\partial}{\partial p}, | \hat{L}=-i\frac{\partial H(x,p)}{\partial p}\frac{\partial}{\partial x}+i\frac{\partial H(x,p)}{\partial x}\frac{\partial}{\partial p}, | synthetic | 5f9de36d33134078 | mathwriting-2024/synthetic/5f9de36d33134078.inkml |
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\cos\tfrac{A}{3} + 2\cos\tfrac{B}{3} \cos\tfrac{C}{3} | cos\frac{A}{3}+2cos\frac{B}{3}cos\frac{C}{3} | synthetic | f29c84c8fdc006f0 | mathwriting-2024/synthetic/f29c84c8fdc006f0.inkml |
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E \simeq pc | E\simeq pc | synthetic | 2a4ddb4fc2ec0c91 | mathwriting-2024/synthetic/2a4ddb4fc2ec0c91.inkml |
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\frac{\langle E \rangle}{A}= -\frac {\hbar c \pi^2}{720 a^3}\,. | \frac{\langle E\rangle}{A}=-\frac{\hbar c\pi^{2}}{720a^{3}}. | synthetic | f12cacdedaa67e6c | mathwriting-2024/synthetic/f12cacdedaa67e6c.inkml |
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H_{ij}=\beta e^{-\left({r_{ij} \over r_0}\right)^\eta} | H_{ij}=\beta e^{-(\frac{r_{ij}}{r_{0}})^{\eta}} | synthetic | ebfa71d3cf87d115 | mathwriting-2024/synthetic/ebfa71d3cf87d115.inkml |
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\int_{0}^{1}{{{B}_{2n-1}}\left( x \right)\cot \left( \pi x \right)dx}=\frac{2\left( 2n-1 \right)!}{{{\left( -1 \right)}^{n-1}}{{\left( 2\pi \right)}^{2n-1}}}\zeta \left( 2n-1 \right) | \int_{0}^{1}B_{2n-1}(x)cot(\pi x)dx=\frac{2(2n-1)!}{{(-1)}^{n-1}{(2\pi)}^{2n-1}}\zeta(2n-1) | synthetic | 219b59b75e54e896 | mathwriting-2024/synthetic/219b59b75e54e896.inkml |
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h_\text{PR} | h_{PR} | synthetic | 84b36169b852d150 | mathwriting-2024/synthetic/84b36169b852d150.inkml |
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M(x) - L(x) | M(x)-L(x) | synthetic | 2a725e19caa9454e | mathwriting-2024/synthetic/2a725e19caa9454e.inkml |
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t_X \sim \frac{1}{\left(\dot{N}\dot{G}^3\right)^{1/4}}, | t_{X}\sim\frac{1}{(\dot{N}\dot{G}^{3})^{1/4}}, | synthetic | b54a6f3fc0f5d707 | mathwriting-2024/synthetic/b54a6f3fc0f5d707.inkml |
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\{I, R\} | \{I,R\} | synthetic | de504ae35416e8d3 | mathwriting-2024/synthetic/de504ae35416e8d3.inkml |
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\frac{\sqrt 2 (a\!+\!b\!-\!2c)(2a\!-\!b\!-\!c)(a\!-\!2b\!+\!c)}{5(a^2\!+\!b^2\!+\!c^2\!-\!ab\!-\!ac\!-\!bc)^\frac{3}{2}} | \frac{\sqrt{2}(a+b-2c)(2a-b-c)(a-2b+c)}{5(a^{2}+b^{2}+c^{2}-ab-ac-bc)^{\frac{3}{2}}} | synthetic | 1aa6d46aefe13b10 | mathwriting-2024/synthetic/1aa6d46aefe13b10.inkml |
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\sigma = \oint_{4\pi} \frac{\mathrm d \sigma}{\mathrm d \Omega} \, \mathrm d \Omega = \int_0^{2\pi} \int_0^\pi \frac{\mathrm d \sigma}{\mathrm d \Omega} \sin \theta \, \mathrm d \theta \, \mathrm d \varphi. | \sigma=\oint_{4\pi}\frac{d\sigma}{d\Omega}d\Omega=\int_{0}^{2\pi}\int_{0}^{\pi}\frac{d\sigma}{d\Omega}sin\theta d\theta d\varphi. | synthetic | 08d4880f246bb8fe | mathwriting-2024/synthetic/08d4880f246bb8fe.inkml |
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\frac{555599977777}{10} | \frac{555599977777}{10} | synthetic | a3831863e195d494 | mathwriting-2024/synthetic/a3831863e195d494.inkml |
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f_y(x,y) = 1-e^y = 0 \Rightarrow y = 0 | f_{y}(x,y)=1-e^{y}=0\Rightarrow y=0 | synthetic | b829351c927e3122 | mathwriting-2024/synthetic/b829351c927e3122.inkml |
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\textstyle f=\prod_v f_v | f=\prod_{v}f_{v} | synthetic | e6320b6a8a59569a | mathwriting-2024/synthetic/e6320b6a8a59569a.inkml |
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\frac{\frac{73.07}{x}}{111144222299} | \frac{\frac{73.07}{x}}{111144222299} | synthetic | 5d2a3fefdef02371 | mathwriting-2024/synthetic/5d2a3fefdef02371.inkml |
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n_i = 5 \times 10^{6} | n_{i}=5\times10^{6} | synthetic | d1a017d7935c0211 | mathwriting-2024/synthetic/d1a017d7935c0211.inkml |
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f = \sum_n \left( f_n - f_{n-1}\right), | f=\sum_{n}(f_{n}-f_{n-1}), | synthetic | 79c01be283652cf2 | mathwriting-2024/synthetic/79c01be283652cf2.inkml |
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G(k) = {1 \over i\omega - {k^2\over 2m} }. \, | G(k)=\frac{1}{i\omega-\frac{k^{2}}{2m}}. | synthetic | b2550d04a5596e2b | mathwriting-2024/synthetic/b2550d04a5596e2b.inkml |
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\Delta^\bullet([n]) | \Delta^{\bullet}([n]) | synthetic | 3c0ac2c9523d9dbe | mathwriting-2024/synthetic/3c0ac2c9523d9dbe.inkml |
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\kappa(x, y) := \textrm{Tr}( \textrm{ad}\,x\, \textrm{ad}\, y )\ \forall x,y \in \mathfrak{g} | \kappa(x,y):=Tr(adxady)\forall x,y\in g | synthetic | dc0d900242e0c10c | mathwriting-2024/synthetic/dc0d900242e0c10c.inkml |
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b = a / 2, | b=a/2, | synthetic | 4bb34ddbc04e6d1b | mathwriting-2024/synthetic/4bb34ddbc04e6d1b.inkml |
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\scriptstyle f\in L^1([0,\infty[) | f\in L^{1}([0,\infty[) | synthetic | 2b29c3bac1e9247f | mathwriting-2024/synthetic/2b29c3bac1e9247f.inkml |
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\sqrt{2} = 1.414... | \sqrt{2}=1.414... | synthetic | 39ddbbe5bc2d759b | mathwriting-2024/synthetic/39ddbbe5bc2d759b.inkml |
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p^+ + p^+ \to p^+ + p^+ + \pi^0 | p^{+}+p^{+}\rightarrow p^{+}+p^{+}+\pi^{0} | synthetic | b0d57f83950f71d7 | mathwriting-2024/synthetic/b0d57f83950f71d7.inkml |
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OR = {4/96 \over 5/895} = 7.46 | OR=\frac{4/96}{5/895}=7.46 | synthetic | cf2be42d11db1e86 | mathwriting-2024/synthetic/cf2be42d11db1e86.inkml |
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\geq,> | \ge,> | synthetic | 4c3a8782611c4d8a | mathwriting-2024/synthetic/4c3a8782611c4d8a.inkml |
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w_h = N_h/N | w_{h}=N_{h}/N | synthetic | 7329abf5c45872e5 | mathwriting-2024/synthetic/7329abf5c45872e5.inkml |
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x = y^2 | x=y^{2} | synthetic | f9909cd659fb3596 | mathwriting-2024/synthetic/f9909cd659fb3596.inkml |
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\gamma \colon [0, r] \to X | \gamma:[0,r]\rightarrow X | synthetic | 9494d8b5713e3232 | mathwriting-2024/synthetic/9494d8b5713e3232.inkml |
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x^{s_0-c-1/2}\,f_2(x) | x^{s_{0}-c-1/2}f_{2}(x) | synthetic | 6d79ae115047bf4f | mathwriting-2024/synthetic/6d79ae115047bf4f.inkml |
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\nabla \times \mathbf{B} = \mu \mathbf{J} + \mu \epsilon \frac{\partial \mathbf{E}}{\partial t}. | \nabla\times B=\mu J+\mu\epsilon\frac{\partial E}{\partial t}. | synthetic | 316a753b3f3a7e01 | mathwriting-2024/synthetic/316a753b3f3a7e01.inkml |
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\pi_0(x) = \sum_{n=1}^\infty \frac{\ \mu(n)\ }{n}\ \Pi_0\bigl(x^{1/n}\bigr)\ , | \pi_{0}(x)=\sum_{n=1}^{\infty}\frac{\mu(n)}{n}\Pi_{0}(x^{1/n}), | synthetic | db91206e1be6a8e4 | mathwriting-2024/synthetic/db91206e1be6a8e4.inkml |
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f_t(\cdot) | f_{t}(\cdot) | synthetic | 71fedebe6a652577 | mathwriting-2024/synthetic/71fedebe6a652577.inkml |
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df = \frac{\left(\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2}\right)^2} {\dfrac{\left(\dfrac{s_1^2}{n_1}\right)^2}{n_1-1} + \dfrac{\left(\dfrac{s_2^2}{n_2}\right)^2}{n_2-1}} | df=\frac{(\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}})^{2}}{\frac{(\frac{s_{1}^{2}}{n_{1}})^{2}}{n_{1}-1}+\frac{(\frac{s_{2}^{2}}{n_{2}})^{2}}{n_{2}-1}} | synthetic | 5f4a662b8f191ae9 | mathwriting-2024/synthetic/5f4a662b8f191ae9.inkml |
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G_0 = \frac { \beta i_B} {i_S} \ . | G_{0}=\frac{\beta i_{B}}{i_{S}}. | synthetic | 09fa4cd7c02647cf | mathwriting-2024/synthetic/09fa4cd7c02647cf.inkml |
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x_{p+r_0}\leq x_{p+r_1}\leq ... \leq x_{p+r_{d_x-1}} | x_{p+r_{0}}\le x_{p+r_{1}}\le...\le x_{p+r_{d_{x}-1}} | synthetic | 9c612c0ab6ce6dac | mathwriting-2024/synthetic/9c612c0ab6ce6dac.inkml |
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f(X_i, \beta) | f(X_{i},\beta) | synthetic | d9677a0e1b5e92b7 | mathwriting-2024/synthetic/d9677a0e1b5e92b7.inkml |
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m'\leq n' | m^{\prime}\le n^{\prime} | synthetic | 92229d77ad0c2289 | mathwriting-2024/synthetic/92229d77ad0c2289.inkml |
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s \ge t | s\ge t | synthetic | c68484465c780606 | mathwriting-2024/synthetic/c68484465c780606.inkml |
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B=SAS^T | B=SAS^{T} | synthetic | 4eb6fd3404f3d7ad | mathwriting-2024/synthetic/4eb6fd3404f3d7ad.inkml |
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e^{i \mathbf k \cdot \mathbf r} | e^{ik\cdot r} | synthetic | 16593c680fdc84a7 | mathwriting-2024/synthetic/16593c680fdc84a7.inkml |
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A_{\{\varphi\}} | A_{\{\varphi\}} | synthetic | c6f00a063fe1dac2 | mathwriting-2024/synthetic/c6f00a063fe1dac2.inkml |
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\alpha\cdot X = (-1)^{|\alpha||X|}X\cdot\alpha. | \alpha\cdot X=(-1)^{|\alpha||X|}X\cdot\alpha. | synthetic | 8cdbee1ba989d6ce | mathwriting-2024/synthetic/8cdbee1ba989d6ce.inkml |
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\sigma = E\left(L-Lo\right)/Lo | \sigma=E(L-Lo)/Lo | synthetic | 4b64714cc3b07815 | mathwriting-2024/synthetic/4b64714cc3b07815.inkml |
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\hat{r}=r_x \cdot \hat{x} +r_y \cdot \hat{y} +r_z \cdot \hat{z} | \hat{r}=r_{x}\cdot\hat{x}+r_{y}\cdot\hat{y}+r_{z}\cdot\hat{z} | synthetic | f3bda70a786adf3c | mathwriting-2024/synthetic/f3bda70a786adf3c.inkml |
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\lambda_0 = \frac{v}{f_0} | \lambda_{0}=\frac{v}{f_{0}} | synthetic | f0ccbf7b36ec6908 | mathwriting-2024/synthetic/f0ccbf7b36ec6908.inkml |
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f^{-1}(y) s\subseteq A. | f^{-1}(y)s\subseteq A. | synthetic | 12729e3729c0b28d | mathwriting-2024/synthetic/12729e3729c0b28d.inkml |
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{\frac{{f^2}\cdot {k}}{E_v\cdot t}}=S | \frac{f^{2}\cdot k}{E_{v}\cdot t}=S | synthetic | 9f48b0699bec194f | mathwriting-2024/synthetic/9f48b0699bec194f.inkml |
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m^{7/8} < n < m^{8/7} | m^{7/8}<n<m^{8/7} | synthetic | 2a2049c6cc9d0173 | mathwriting-2024/synthetic/2a2049c6cc9d0173.inkml |
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\overline{\Gamma(1)} | \overline{\Gamma(1)} | synthetic | 774f0779173aa159 | mathwriting-2024/synthetic/774f0779173aa159.inkml |
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