(1) \qquad
\frac{\partial^{2} u(t,x)}{\partial t^{2}} + L[u(t,x)] = f(t,x), \qquad x \in \mathbf{R}^{n}, ~ t > 0,
3 KB (464 words) - 06:54, 3 March 2017
$$\operatorname{Si}(0)=0,\qquad\operatorname{Si}(\infty)=\frac\pi2,\qquad\operatorname{si}(\infty)=0.$$
$$\operatorname{Si}(-x)=-\operatorname{Si}(x);\qquad\operatorname{si}(x)+\operatorname{si}(-x)=-\pi;$$
2 KB (327 words) - 21:27, 1 January 2019
\frac{\ln (a_n)^{-1}}{\ln n} \geq 1 + \alpha \qquad \forall n\geq N
\frac{\ln (a_n)^{-1}}{\ln n} \leq 1 \qquad \forall n \geq N
727 bytes (124 words) - 10:35, 10 December 2013
...rtial x_1} (y) & \frac{\partial \Phi^1}{\partial x_2} (y)&\qquad \ldots \qquad & \frac{\partial \Phi^1}{\partial x_n} (y)\\
...rtial x_1} (y) & \frac{\partial \Phi^2}{\partial x_2} (y)&\qquad \ldots \qquad & \frac{\partial \Phi^2}{\partial x_n} (y)\\
3 KB (384 words) - 14:28, 14 December 2012
Y_\nu (z) = \frac{J_\nu (z) \cos \nu \pi - J_{-\nu} (z)}{\sin \nu \pi} \qquad \mbox{for}\; \nu\not\in \mathbb Z
Y_n (z) = \lim_{\nu\to n} Y_\nu (z) \qquad \mbox{for}\; n\in \mathbb Z\,
2 KB (361 words) - 11:28, 14 June 2019
...^{3})}_{x},\underbrace{(y^{0},y^{1},y^{2},y^{3})}_{y} \in \mathbb{R}^{4}: \qquad
...\beta} x^{\alpha} y^{\beta} = x^{0} y^{0} - \sum_{k = 1}^{3} x^{k} y^{k}, \qquad \text{where} \quad
1 KB (187 words) - 23:29, 14 December 2016
\forall E \in M, ~ \forall g \in G: \qquad
\forall E \in M, ~ \forall g \in G: \qquad
6 KB (971 words) - 20:18, 23 April 2017
L(a)=A\alpha,\qquad R(a)=\alpha A,\qquad J(\alpha)=A\alpha A\ .
$$L(\alpha)=S^1\alpha,\qquad R(\alpha)=\alpha S^1,\qquad L(\alpha)=S^1\alpha S^1,$$
3 KB (484 words) - 20:54, 28 November 2014
\phi' (t) \leq C \phi (t) \qquad \mbox{for all } t\in [0,T]\, .
\phi (t) \leq e^{C t} \phi (0) \qquad \mbox{for all } t\in [0, T]\, .
4 KB (716 words) - 11:40, 30 November 2013
...}{\partial x_1} (y) & \frac{\partial f^1}{\partial x_2} (y)&\qquad \ldots \qquad & \frac{\partial f^1}{\partial x_n} (y)\\
...{\partial x_1} (y) & \frac{\partial f^2}{\partial x_2} (y)&\qquad \ldots \qquad & \frac{\partial f^2}{\partial x_n} (y)\\
4 KB (631 words) - 08:46, 18 November 2012
[k] \equiv k (x^0 + 0) - k(x^0 - 0) \ne 0, \qquad [c \rho] \ne 0.
[T] = 0, \qquad [w] = 0, \qquad t \ge 0
5 KB (735 words) - 03:06, 15 February 2024
...)\qquad \mbox{for all } y \mbox{ such that } g_i (x^\star)= g_i (y) = b_i \qquad \forall i\in \{1, \ldots , m\}\, .
\frac{\partial F}{\partial x_j} (x^\star, \lambda^\star) = 0 \qquad \forall j\in \{1, \ldots , n\}
11 KB (1,859 words) - 23:04, 27 June 2014
...k ) e ^ { i k x } ,} & {x \xrightarrow{\qquad\qquad\qquad\qquad\qquad\qquad }+\infty .} \end{array} \right. \end{equation}
t_{+}(k) e^{-ikx}, & x \xrightarrow{\qquad\qquad\qquad\qquad\qquad\qquad } +\infty, \\
12 KB (1,851 words) - 04:43, 15 February 2024
\delta (f(x), f(y)) \leq M d (x,y) \qquad\qquad \forall x,y\in X\, .
2 KB (257 words) - 16:49, 9 November 2013
a_n := \frac{1}{2^k n} \qquad \mbox{ for } N_k+1\leq n \leq N_{k+1}\, .
a_n = \frac{2^k}{n^2} \qquad \mbox{ for } N_k+1\leq n \leq N_{k+1}\, .
2 KB (288 words) - 11:28, 22 March 2023
d (x_n, x_m) < \varepsilon \qquad \forall m,n\geq N\, .
(x_\alpha, x_\beta)\in U \qquad \forall \alpha, \beta \geq \alpha_0\, .
2 KB (274 words) - 10:12, 9 December 2013
$$||B\vee C||=||B||\cup||C||,\qquad ||B\supset C||=\overline{||B||}\cup||C||,$$
$$||\neg B||=\overline{||B||},\qquad \forall xB(x) = \bigcap_{a\in\fM} ||B(a)||,$$
3 KB (439 words) - 22:34, 16 June 2014
$$d x_1 = \dot \phi_1(t) \, dt_1, \qquad d x_2 = \dot \phi_2(t) \, dt_2$$
F = 0, \qquad F_{\dot x} = 0.
9 KB (1,496 words) - 08:59, 13 February 2024
\limsup_{n\to\infty}\, x_n\qquad \liminf_{n\to\infty}\,\, x_n
...minf_n\,\, x_n\qquad \limsup_n\, (\lambda x_n) = \lambda\, \limsup_n\, x_n\qquad \mbox{when } \lambda > 0
8 KB (1,481 words) - 09:55, 16 August 2013
{F_{\alpha}}(A \phi) = \lambda_{\alpha} {F_{\alpha}}(\phi), \qquad \alpha \in \mathfrak{A},
...t_{\Bbb{R}} e^{i s x} \tilde{f}(s) ~ \mathrm{d}{s}, \qquad x \in \Bbb{R}, \qquad f,\tilde{f} \in {L^{2}}(\Bbb{R}),
3 KB (517 words) - 00:44, 16 September 2015
\a!&=\a_1!\cdots\a_n!\qquad\text{(as usual, }0!=1!=1),
...a}{\b}=\binom{\a_1}{\b_1}\cdots\binom{\a_n}{\b_n}=\frac{\a!}{\b!(\a-\b)!},\qquad \text{if}\quad \a\geqslant\b.
3 KB (512 words) - 06:16, 13 June 2022
i^{p+1} H^{(1)}_p (ix) \qquad \mbox{and} \qquad i^{-(p+1)} H^{(2)}_p (-ix)
2 KB (376 words) - 16:10, 2 April 2014
L (f) = \int_X f\, d\mu \qquad \forall f\in C (X)\, .
L (f) = \int_X fg\, d\mu\qquad \forall f\in C(X)\, .
3 KB (451 words) - 17:37, 18 August 2012
...\gamma^{\beta} \gamma^{\alpha} = - 2 \eta^{\alpha \beta} \mathsf{I}_{4}, \qquad \forall \alpha,\beta \in \{ 0,1,2,3 \}.
..._{2} & \mathbf{0}_{2} \\ \mathbf{0}_{2} & - \mathsf{I}_{2} \end{bmatrix}; \qquad
2 KB (328 words) - 16:06, 15 December 2016
\[\delta(-x)=\delta(x);\qquad\delta(cx)=|c|^{-1}\delta(x),\quad c=\mathrm{const},\]
\[x\delta(x)=0;\qquad\delta(x)+x\delta'(x)=0,\]
2 KB (390 words) - 22:12, 31 December 2018
$$|\{f,z\}|\leq\frac6{{(1-|z|^2)}^2},\qquad|z|<1.$$
$$|\{f,z\}|\leq\frac2{{(1-|z|^2)}^2},\qquad|z|<1,$$
3 KB (443 words) - 11:10, 30 December 2018
\left<\cdot,\cdot\right>:\Gamma(E)\times\Gamma(E^*)\to C^\infty(B),\qquad (s,s^*)\mapsto \left< s,s^*\right>(b)=\left< s(b),s^*(b)\right>.
585 bytes (112 words) - 13:20, 20 May 2012
$$\cos x=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\dotsb,\qquad-\infty<x<\infty.$$
2 KB (283 words) - 12:43, 14 February 2020
\forall A \subseteq \mathfrak{P}: \qquad
960 bytes (147 words) - 04:53, 24 April 2017
$$\Spin_3\simeq \def\SL{ {\rm SL}}\SL_2,\qquad \Spin_2 \simeq \SL_2\times \SL_2,$$
$$\Spin_5 \simeq \def\Sp{ {\rm Sp}}\Sp_4,\qquad \Spin_6 \simeq \SL_4.$$
4 KB (648 words) - 13:16, 7 April 2023
\int_\Gamma f(z)\, dz = 0\, \qquad\qquad \mbox{for any}\, \Gamma \in \mathcal{P}\, ,
2 KB (358 words) - 17:23, 12 January 2014
\mu (D) = \inf\; \{ \mu (C): D\subset {\rm int}\, (C)\} \qquad \forall D\in \mathcal{C}\, .
\mu (D) = \inf\;\{\mu (C) : D\subset C \mbox{ and } C \mbox{ is open}\} \qquad \forall D\in \mathcal{C}
5 KB (751 words) - 09:47, 16 August 2013
g \circ f & = \mathsf{Id}_{X} \quad \text{on} ~ M, \qquad (1) \\
f \circ g & = \mathsf{Id}_{Y} \quad \text{on} ~ f[M], \qquad (2)
4 KB (752 words) - 03:29, 9 January 2017
{\rm ap}\,\limsup_{x\to x_0}\, f(x) \qquad \mbox{and}\qquad {\rm ap}\, \liminf_{x\to x_0}\, f(x)
...\downarrow 0} \frac{\lambda (G\cap ]x_0, x_0+r[)}{r} = 1 \qquad \mbox{and}\qquad \lim_{r\downarrow 0} \frac{\lambda (G\cap ]x_0-r, x_0[)}{r} = 1\,
5 KB (745 words) - 17:18, 18 August 2012
\mu (B)= \sup \{\mu(K): K\subset B, K \mbox{ compact}\} \qquad \forall B\in \mathcal{B}\,.
\mu (N) = \inf \{\mu (U): U\supset N,\, U \mbox{ open}\}\, \qquad \forall N\in \mathcal{B},
4 KB (498 words) - 22:40, 31 December 2017
H\circ i_A=i_B\circ h,\qquad i_A:A\to X,\ i_B:B\to Y.
X=\bigsqcup_x G(x),\quad Y=\bigsqcup_y G(y),\qquad G(x)=\{g\cdot x:~g\in G\},\quad G(y)=\{g\cdot y:~g\in G\}.
5 KB (894 words) - 09:02, 12 December 2013
...^q a_n b_n = \sum_{n=p}^{q-1} B_n (a_q - a_{n+1}) + B_q a_q - B_{p-1} a_p \qquad \forall 1\leq p < q\, .
860 bytes (157 words) - 20:29, 9 December 2013
\forall x \in \mathbb{R}: \qquad
\mathsf{P}(S_{n} = m) = \binom{n}{m} p^{m} (1 - p)^{n - m}, \qquad \text{where} ~ m \in \mathbb{Z} \cap [0,n],
5 KB (692 words) - 19:33, 7 July 2016
...mathrm{d}{s} \stackrel{\text{df}}{=} \int_{0}^{s} F(x(s)) ~ \mathrm{d}{s} \qquad (1)
\int_{\gamma} F(x) ~ \mathrm{d}{x_{k}}, \qquad k \in \{ 1,\ldots,n \}
9 KB (1,447 words) - 06:40, 1 December 2016
\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} \qquad
\frac{\partial u}{\partial s} = \frac{\partial v}{\partial n} \qquad
7 KB (1,063 words) - 12:51, 22 March 2023
{\rm dist}\, (x, Z_f)^\alpha \leq C |f(x)| \qquad \qquad \forall x \in K.
|f(x)-f(y)|^\theta \leq C |\nabla f (y)| \qquad \qquad \forall y\in V\, .
7 KB (1,088 words) - 21:21, 14 January 2021
f (x_0) \geq \limsup_{x\to x_0}\; f(x) \qquad \left(\mbox{resp. }\quad f(x_0)\leq \liminf_{x\to x_0}\; f(x)\right)\, .
F(x):= \inf_{f\in\mathcal{F}}\; f(x) \qquad \left(\mbox{resp.}\; \sup_{f\in\mathcal{F}}\; f(x)\right)
8 KB (1,260 words) - 15:29, 5 January 2017
\rd R\cdot v=KR,\qquad K=K(x,y)\in\R[x,y].
H(x,y)=R_1^{\lambda_1}(x,y)\cdots R_k^{\lambda_k}(x,y),\qquad \lambda_1,\dots,\lambda_k\in\C,
5 KB (809 words) - 09:08, 12 December 2013
K_n := c_n \frac{a_n}{a_{n+1}} - c_{n+1} \geq \delta \qquad \forall n\geq N\, ,
1,017 bytes (170 words) - 11:25, 10 December 2013
$$ D_t = (20n)^{n(n + 1)t/2}, \qquad b_t = nt + \left[{\frac{n(n + 1)}{4} + 1}\right], $$
2 KB (248 words) - 21:55, 14 January 2017
...\le t \le 1} |f(t) - S_n(t, f)| \le 12 \omega\left(\frac{1}{n}, f\right), \qquad n = 1, 2, \ldots.$$
$$\|f - S_n(f)\|_{L_p[0, 1]} \le 24 \omega_p \left(\frac{1}{n}, f\right), \qquad n = 1, 2, \ldots.$$
6 KB (1,003 words) - 05:01, 23 July 2018
1\qquad\text{if }t=s,\\
0\qquad\text{if }t\neq s.
3 KB (550 words) - 10:36, 23 May 2017
\mathsf{E} {F_{n}}(x) = F(x), \qquad
\forall z \in \mathbf{R}_{> 0}: \qquad
5 KB (778 words) - 04:08, 22 June 2017
b(u,v) = \overline{\langle Bu, v\rangle}, \qquad \forall u,v \in V, \\
b(B^{-1} l,v) = \overline{\langle l,v \rangle}, \qquad \forall v \in V, l\in V',
5 KB (784 words) - 03:17, 15 February 2024
...$ (\alpha + \beta) + \gamma = \alpha + (\beta + \gamma) \qquad \text{and} \qquad \alpha + 0 = \alpha = 0 + \alpha, $$ where $ 0 $ is the order type of the e
...gamma), \qquad \alpha \cdot 1 = \alpha = 1 \cdot \alpha \qquad \text{and} \qquad \alpha \cdot 0 = 0 = 0 \cdot \alpha, $$ where $ 1 $ is the order type of a
6 KB (1,008 words) - 17:31, 5 January 2017
D (\lambda f + \mu g) = \lambda Df + \mu Dg \qquad \forall \lambda, \mu \in \mathbb R, \forall f,g\in C^1 (M)\, ,
(f+g)' = f' + g' \qquad \mbox{and} \qquad (fg)' = fg' + gf'\, .
5 KB (757 words) - 10:34, 11 December 2013
\dot x=y,\quad \dot y=-x, \qquad (x,y)\in(\R^2,0),
\dot x=x+\cdots,\qquad \dot y=-y+\cdots,\qquad (x,y)\in(\C^2,0)
5 KB (706 words) - 09:05, 12 December 2013
D\in T_a M\iff D:C^\infty(M)\to\R,\qquad D(f\pm g)=Df\pm Dg,\ D(\lambda f)=\lambda Df,\ D(f\cdot g)=f(a)\cdot Dg+g(a
1 KB (196 words) - 08:55, 12 December 2013
f(z) = \sum_{k=-m}^\infty c_k (z-a)^k,\qquad a \neq \infty, c_{-m} \neq 0, z \in V,
f(z) = \sum_{k=-m}^\infty \frac{c_k}{z^k},\qquad a = \infty, c_{-m} \neq 0, z \in V',
3 KB (549 words) - 09:10, 18 January 2014
\frac{|a_{n+1}|}{|a_n|} \geq 1 - \frac{1}{n} \qquad \forall n \geq N\, ,
1 KB (228 words) - 10:49, 10 December 2013
...wnarrow 0} \frac{\lambda (B_r (x)\cap E)}{\omega_n r^n} \qquad \mbox{and} \qquad \liminf_{r\downarrow 0} \frac{\lambda (B_r (x)\cap E)}{\omega_n r^n}\, ,
\qquad \mbox{and}\qquad \theta^\alpha_* (\mu, x) =\liminf_{r\downarrow 0} \frac{\mu (B_r (x))}{\ome
10 KB (1,662 words) - 09:58, 16 August 2013
\sup\; \{\mu (C):C\subset E\mbox{ is closed}\} = \mu (E) \qquad \mbox{for any Borel set } E.
\sup\; \{\mu (C):C\subset E\mbox{ is compact}\} = \mu (E) \qquad \mbox{for any Borel set } E
5 KB (764 words) - 09:39, 16 August 2013
\mathbf{r} = \mathbf{r}(u,v) \qquad (1)
...hbf{r}}{\partial u},\frac{\partial \mathbf{r}}{\partial u} \right\rangle, \qquad
11 KB (1,911 words) - 18:57, 1 December 2016
...t(x^{k+1}, \dots, x^n \right) dx^\alpha dx^\beta,$$$$i,j = 1, \dots, k ; \qquad \alpha, \beta = k+1 , \dots , n.$$Otherwise the space is called irreducible
8 KB (1,254 words) - 14:07, 2 January 2014
f^{(\a)}=\p^\a f\in C^{m-|\a|}(U),\qquad 0\le |\a|\le m,\ f^{(0)}=f,
...\a(a,x)=f^\a(x)-\sum_{|\b|\le m-|\a|}\frac1{\b!}f^{\a+\b}(a)\cdot(x-a)^\b,\qquad x,a\in K,
5 KB (913 words) - 12:24, 12 December 2020
$$\dot z=A(t)z,\qquad z\in\CC^n,\quad t\in (\CC,t_*)\tag {LS}$$
...0(t)\partial^n+a_{n-1}(t)\partial^{n-1}+\cdots+a_{n-1}(t)\partial +a_n(t),\qquad \partial =\frac d{dt},\tag L
7 KB (1,237 words) - 11:48, 23 November 2023
$$f:K\times[0,1]\to Y, \qquad F_0:K=K\times\{0\}\to X$$
1 KB (187 words) - 22:36, 24 November 2013
...{\mu (B_r (x))} \int_{B_r (x)} |f(y)-f(x)|\, d\mu (y) = 0\qquad \mbox{and}\qquad \lim_{r\downarrow 0} \frac{\nu_s (B_r (x))}{\mu (B_r (x))}= 0\, .
4 KB (532 words) - 13:29, 30 November 2012
$$\beta(x_1, x_2) = b(x_1 \tensor x_2), \qquad x_1 \in V_1, \qquad x_2 \in V_2.$$
$$x_1, y \in V_1, \qquad x_2, z \in V_2, \qquad c \in A;$$
11 KB (1,992 words) - 03:52, 23 July 2018
S_n(f; x) = \frac1\pi \int_{-\pi}^\pi f(x+t) D_n() \, dt, \qquad n=0,1,\ldots,
(\vb{x}, \vb{y}) = x_1y_1 + \cdots + x_N y_N, \qquad |\vb{x}| = \sqrt{(\vb{x}, \vb{x})}.
6 KB (1,047 words) - 11:37, 13 February 2024
F (t) := \frac{1}{t} \int_0^t \left(f(x+u)+f(x-u) - 2 f(x)\right)\, du \qquad \mbox{for } t>0
1 KB (216 words) - 20:45, 16 October 2012
\bigcup_{i=1}^\infty A_i \in \mathcal{A} \qquad \mbox{whenever } \{A_i\}_{i\in \mathbb N}\subset \mathcal{A}\, .
2 KB (231 words) - 09:47, 16 August 2013
\frac{x^2}{p}-\frac{y^2}{q}=2z, \qquad\text{where}\;p,q>0.
2 KB (252 words) - 11:12, 25 May 2016
\qquad \forall x\in E\, .
\qquad \forall x\in E\, .
6 KB (865 words) - 22:40, 17 August 2013
$$x=\frac{2at^2}{t^2+1},\qquad y=\frac{2at^3}{t^2+1}.$$
2 KB (300 words) - 09:39, 26 March 2023
|f(x)-f(y)|\leq C|x-y|\qquad \mbox{for every } x,y\in U\, .
2 KB (249 words) - 14:09, 2 May 2014
$$\sin x=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\dotsb,\qquad-\infty<x<\infty.$$
3 KB (441 words) - 13:51, 14 February 2020
F'. H = F_n, \qquad G'. H = G_n,
2 KB (288 words) - 04:27, 15 February 2024
\forall i \in J, ~ \forall \mu_{i} \in M_{i}: \qquad
2 KB (296 words) - 06:03, 8 April 2023
...^{\eta_{1}} \cdot \beta_{1} + \cdots + \gamma^{\eta_{n}} \cdot \beta_{n}, \qquad (1) \\
\eta > \eta_{1} > \ldots > \eta_{n}, \qquad 0 \leq \beta_{i} < \gamma, \qquad (2)
9 KB (1,404 words) - 18:33, 4 December 2017
\partial x_n^{\alpha_n}},\qquad D^{0}f=f,
\qquad (1\leq p< \infty).
8 KB (1,334 words) - 17:47, 30 November 2012
\forall f \in C(X): \qquad
\forall f \in {C_{0}}(X): \qquad
5 KB (819 words) - 17:08, 6 January 2017
f(z) = \frac{p(z)}{q(z)} \qquad \mbox{for every}\qquad z\in U\cap C\, .
5 KB (819 words) - 10:11, 18 January 2014
A, ~ 2^{A}, ~ 2^{2^{A}}, ~ 2^{2^{2^{A}}}, ~ \ldots \qquad (1)
\sum_{t \in T} \alpha_{t} < \prod_{t \in T} \beta_{t}. \qquad (2)
9 KB (1,402 words) - 11:57, 10 April 2018
A^{*} = A, \qquad
B^{*} B = A - A^{2} + c \mathbf{1}, \qquad
5 KB (814 words) - 07:12, 24 January 2024
n _ {j}\qquad \textrm{ if }i \neq j ,\qquad\qquad \atop n _ {j} - 1 \ \ \textrm{ if } \ i = j,\ i,\ j = 1 \dots m,}
9 KB (1,344 words) - 16:08, 6 February 2020
F(x) = G(x,F \uparrow x), \qquad (\star)
2 KB (351 words) - 21:15, 29 January 2017
f(x) = l(x),\qquad f(y) \ge l(y),\qquad y \in G. \tag{4}
...m\limits_{i = 1}^{n} \frac{\partial f(x)}{\partial x^i} (y^i - x^i) \ge 0,\qquad x, y \in G.
9 KB (1,555 words) - 08:20, 25 July 2013
f^{\pm} (x_1, \ldots, x_n) \leq f^{\pm} (y_1, \ldots, y_n) \qquad \mbox{if } x_i\leq y_i \, \forall i\, .
2 KB (323 words) - 09:38, 16 August 2013
|f(x)-f(x')| \leq M|x-x'|\qquad \forall x,x'\in [a,b]\, .
|f(x)-f(x')|\leq M |x-x'|^\alpha \qquad \forall x,x'\in \mathbb R
5 KB (736 words) - 09:19, 17 June 2014
\left|\int_A f (x) \rd\lambda (x)\right| < \varepsilon \qquad \mbox{for every measurable set}\, A \mbox{ with } \lambda (A)< \delta\, .
\nu (A) = \int_A f\, \rd\mu \qquad \text{for every } A\in\mathcal{B}.
9 KB (1,407 words) - 11:50, 4 February 2021
Y_\nu (z) = \frac{J_\nu (z) \cos \nu \pi - J_{-\nu} (z)}{\sin \nu \pi} \qquad \mbox{for}\; \nu\not\in \mathbb Z
Y_n (z) = \lim_{\nu\to n} Y_\nu (z) \qquad \mbox{for}\; n\in \mathbb Z\,
22 KB (3,786 words) - 06:49, 24 February 2024
...l y^{\alpha}}{\partial x^{i}} \frac{\partial y^{\alpha}}{\partial x^{j}}, \qquad (\star)
..._{1} \ldots i_{s - 1} k i_{s + 1} \ldots i_{p}}_{j_{1} \ldots j_{q}}}(x), \qquad k,i_{\alpha},j_{\beta} \in \mathbb{N}_{\leq n}.
6 KB (941 words) - 05:04, 11 December 2016
\gamma^{\alpha} \frac{\partial \psi}{\partial x^{\alpha}} - \mu \psi = 0, \qquad \alpha \in \{ 0,1,2,3 \},
...ial^{2} \psi}{\partial x^{\alpha} \partial x^{\beta}} + \mu^{2} \psi = 0, \qquad \alpha,\beta \in \{ 0,1,2,3 \}.
9 KB (1,306 words) - 18:13, 17 March 2023
|f (x_1, t) - f (x_2, t)|\leq M |x_1-x_2| \qquad \forall (x_1, t), (x_2, t)\in U \times [0,T]\,
e^{-Mt} |x_1-x_2| \leq |\Phi_t (x_1)-\Phi_t (x_2)| \leq e^{Mt} |x_1-x_2| \qquad \forall x_1, x_2\in \mathbb R^n\, .
5 KB (851 words) - 11:10, 30 November 2013
\exists n \in \omega_{0}: \qquad (p_{n} \Vdash \phi) \lor (p_{n} \Vdash \neg \phi).
* The relation $$ p \Vdash \phi(c_{1},\ldots,c_{n}), \qquad (\text{where } c_{1},\ldots,c_{n} \text{ are constants in } \mathcal{L}) $$
13 KB (2,070 words) - 12:25, 6 February 2021
...d} \quad \hat{r}_{i} = - \frac{\hbar}{i} \frac{\partial}{\partial p_{i}}; \qquad i \in \{ 1,\ldots,N \}.
6 KB (937 words) - 09:15, 14 December 2016
$$-y'' = q(x)y = \lambda y, \qquad a < x < b. \tag{1}$$
$$-y'' + q(x)y = \lambda y + f(x), \qquad a < x < b, \tag{2}$$
8 KB (1,288 words) - 05:22, 23 July 2018
J_{1/2} (x) = \sqrt{\frac{2}{\pi x}} \sin x \qquad J_{-1/2} (x) = \sqrt{\frac{2}{\pi x}} \cos x\, .
&& P_n (-x) = (-1)^n P_n (x) \qquad Q_n (-x) = (-1)^n Q_n (x)
6 KB (1,108 words) - 07:54, 26 March 2023
$$ \{f,gh\}=\{f,g\}h+g\{f,h\},\qquad \forall f,g,h\in C^\infty(M).$$
...s N}(x,y):=\{f(\cdot,y),g(\cdot,y)\}_M(x)+\{f(x,\cdot),g(x,\cdot)\}_N(y), \qquad \forall (x,y)\in M\times N.$$
6 KB (1,109 words) - 13:50, 12 December 2013
\omega\in\varLambda^2(M),\qquad \rd \omega=0,\qquad \forall v\in T_p M\quad \exists w\in T_p M:\ \omega_p(v,w)\ne0.
5 KB (856 words) - 05:41, 24 February 2022
$$H_{\text{dR}}^p (X/k) \cong H^p (X^\text{an}, \mathbf{C}), \qquad p \ge 0,$$
2 KB (380 words) - 01:16, 23 July 2018
\forall x \in \mathbf{R}: \qquad
\forall x \in \mathbf{R}, ~ \forall \omega \in \Omega: \qquad
9 KB (1,419 words) - 05:52, 15 June 2017
f(x) = \sum_n a_n (x-x_0)^n \qquad \forall x\in J
f(x) = \sum_n P_n (x-x_0)\qquad \forall x\in V\, .
6 KB (1,048 words) - 21:19, 14 January 2021
...{ 1 } , M _ { 2 } ) = \mathbf{v} ( M _ { 1 } ) \mathbf{v} ( M _ { 2 } ) , \qquad M _ { 1 } , M _ { 2 } \in \Gamma. \end{equation}
\begin{equation} \tag{a3} f | _ { k } ^ { \mathbf{v} } M = f , \qquad \forall M \in \Gamma. \end{equation}
13 KB (1,993 words) - 07:12, 15 February 2024