(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