S _ {n} ^ {2} = \
{\mathsf E} \{ S _ {n} ^ {2} \} = \
3 KB (400 words) - 10:59, 29 May 2020
F_n(x) = \sum_{s=1}^\infty f(x^s) s^{-n} \ .
f(x) = \sum_{s=1}^\infty \mu(s) F_n(x^s) s^{-n} \ ,
2 KB (340 words) - 17:15, 30 April 2016
in a time interval $ [ s, t] $:
p _ {ij} ( s, t) = {\mathsf P} \{ \xi ( t) = j \mid \xi ( s) = i \} ,\ s< t.
5 KB (751 words) - 02:57, 4 March 2022
A surface $ S ^ \prime $
is superposed on a surface $ S $(
3 KB (529 words) - 08:08, 6 June 2020
H ^ {s} ( F, A) \times H ^ {s + 1 } ( B, A)
where $ \delta : H ^ {*} ( F, A) \rightarrow H ^ {s + 1 } ( E, F, A) $
3 KB (536 words) - 09:05, 8 April 2023
$#C+1 = 30 : ~/encyclopedia/old_files/data/S090/S.0900490 Strip (generalized),
by an equation $ \mathbf r = \mathbf r ( s) $,
2 KB (389 words) - 08:23, 6 June 2020
1) if $ S _ {p} \subset S _ {q} $,
then $ F ( S _ {p} ) \subset F ( S _ {q} ) $;
3 KB (417 words) - 08:08, 6 June 2020
...roup]] into a [[group]]. A semi-group $S$ is imbeddable in a group $G$ if $S$ is isomorphic to a sub-semi-group of $G$. Necessary and sufficient conditi
([[cancellation law]]s);
3 KB (457 words) - 12:04, 7 July 2024
\zeta ( s) = \sum_{n=1} ^ \infty \frac{1}{n ^ {s} }
L( s, \chi ) = \sum_{n=1} ^ \infty \frac{\chi ( n, k) }{n ^ {s} },
4 KB (642 words) - 13:03, 6 January 2024
...ubmodule $S$ is '''superfluous''' if it is not a summand of $M$: that is, $S + L = M$ implies $L = M$.
480 bytes (76 words) - 14:23, 12 November 2023
...with an identity, equipped with an automorphism $\def\s{\sigma}a\mapsto a^\s$, is a mapping $q:E\times E\to A$, $(x,y)\mapsto q(x,y)$, linear in $x$ for
...E\times F\to G$, where $E$, $F$, $G$ are $A$-modules. In the case when $a^\s = a$ ($a\in A$), one obtains the notion of a
3 KB (572 words) - 13:14, 7 April 2023
be a commutative ring, let $ S $
modules. A homomorphism of $ S $-
5 KB (785 words) - 19:35, 5 June 2020
...An equivalent definition is: A function $ \phi : \mathbf R \rightarrow S $,
where $ S $
3 KB (414 words) - 08:10, 6 June 2020
...quations consists of an approximation which replaces the kernel $ K ( x, s) $
K ( x, s) \phi ( s) ds = f ( x)
3 KB (401 words) - 17:32, 5 June 2020
...modynamical system, one describes any one of the pairs of parameters $ ( s, v) $,
$ ( s, p) $,
4 KB (556 words) - 08:25, 6 June 2020
...araboloid and the surface are all zero at $(x_0,y_0)$, where $P=p(x_0,y_0)=
s(x_0,y_0)$.
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> R.
S. Millman, G.D. Parker, "Elements of differential geometry" , Prentice-H
2 KB (287 words) - 13:35, 29 April 2014
\int\limits _ { a } ^ { b } | f ( x) - S _ {n} ( f , x ) | ^ {2} d x
S _ {n} ( f , x ) = \
2 KB (317 words) - 12:37, 6 January 2024
Abel's theorem on algebraic equations: Formulas expressing the solution of an arbi
The theorem was proved by N.H. Abel in 1824 . Abel's theorem may also be obtained as a corollary of [[Galois theory|Galois theor
6 KB (894 words) - 06:14, 26 March 2023
\sum _ {s = 1 } ^ { {T } - t }
( x _ {s} - \overline{x}\; )
4 KB (586 words) - 17:31, 5 June 2020
...They are block linear codes which are a special case of [[alternant code]]s.
...' of length $n$ and parameter $s$ over $GF(q)$ is defined by an $n \times s$ [[parity check matrix]] $H$ of [[alternant matrix|alternant]] form
851 bytes (132 words) - 07:25, 14 November 2023