Let $ S $
be a symbol with $ \omega \notin S $.
3 KB (455 words) - 08:11, 6 June 2020
...ays regular (cf. [[Maximal torus|Maximal torus]]). In general, a torus $ S \subset G $
is regular if and only if its centralizer $ C _{G} (S) $
2 KB (286 words) - 15:07, 17 December 2019
...s the same as the [[Voronoi diagram|Voronoi diagram]] of that set $S$. If $S$ is a [[Lattice|lattice]], it is also called the Dirichlet–Voronoi tiling
509 bytes (70 words) - 19:53, 29 April 2014
...special conditions: a right translation of a [[Semi-group|semi-group]] $ S $
for any $ x, y \in S $;
4 KB (612 words) - 08:26, 6 June 2020
''of a non-cooperative game $ \Gamma = \langle J , \{ S _ {i} \} _ {i \in J } , \{ H _ {i} \} _ {i \in J } \rangle $''
...on-cooperative game]] $ \widetilde \Gamma = \langle J , \{ \widetilde{S} {} _ {i} \} _ {i \in J } , \{ \widetilde{H} {} _ {i} \} _ {i \in J } \
4 KB (563 words) - 08:09, 6 June 2020
...$ there exist antipodes with a common image; 2) Any mapping of the sphere $
S^n$ into itself in which the images of antipodes are antipodes is an [[essen
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> K. Borsuk, "Drei
Sätze über die $n$-dimensionale euklidische Sphäre" ''Fund. Math.'' , '''
1 KB (163 words) - 06:23, 28 October 2017
...om mappings are those for which $\mathsf{P}\{\sigma=s\} = n^{-n}$ for all $s \in\Sigma_n$. A realization of such a random mapping is the result of a sim
782 bytes (121 words) - 17:57, 22 November 2016
In order that a surface $ S $
with metric $ d s ^ {2} $
1 KB (165 words) - 08:11, 6 June 2020
A measurable, in general complex-valued, function $ K (x, s) $
satisfying the conditions: 1) $ \overline{ {K (x, s) }}\; = K (s, x) $
873 bytes (124 words) - 11:32, 30 May 2020
$#C+1 = 15 : ~/encyclopedia/old_files/data/S083/S.0803210 Sample variance,
S _ {n} ( x) = \
2 KB (247 words) - 08:12, 6 June 2020
be independent random variables, let $ S _ {k} = \sum_{i=1}^ {k} X _ {i} $
{\mathsf P} \left \{ \max _ {1\leq k \leq n } ( S _ {k} - m ( S _ {k} -
2 KB (317 words) - 10:43, 20 January 2024
...ow \mathcal{P}S$ is a ''closure operation'' if for all $A,B \in \mathcal{P}S$:
A pair $(S,\mathrm{Cl})$ is a ''closure space'' if and only if $\mathrm{Cl}$ satisfies
2 KB (285 words) - 17:42, 13 October 2023
\sum_{n=1}^\infty \frac{1}{n^s} = \prod_p \left({1 - \frac{1}{p^s} }\right)^{-1}
...prime numbers $p$. The Euler identity also holds for all complex numbers $s = \sigma + it$ with $\sigma > 1$.
2 KB (279 words) - 19:13, 14 December 2015
...sitive integers with greatest common divisor $1$. The Frobenius number of $S$ is the largest natural number that cannot be written as a linear integer c
314 bytes (50 words) - 15:24, 10 August 2014
...Hilb}_{X/S}(S^*)=\Hom_S(S^*,\operatorname{Hilb}(X/S))$. In particular, if $S$ is the spectrum of a field $k$ (cf. [[Spectrum of a ring|Spectrum of a rin
...$. For any connected ground scheme $S$ the scheme $\operatorname{Hilb}^P(X/S)$ is also connected [[#References|[2]]].
3 KB (484 words) - 05:48, 17 April 2024
...ng to $S$. The Aitken $\Delta ^ { 2 }$ process consists of transforming $( S _ { n } )$ into the new sequence $( T _ { n } )$ defined, for $n = 0,1 , \d
...} + S _ { n } } = S _ { n } - \frac { \Delta S _ { n } } { \Delta ^ { 2 } S _ { n } }, \end{equation*}
9 KB (1,390 words) - 20:20, 25 January 2024
...ut its mean surface by a [[Conjugate net|conjugate net]] of lines. Let $ S $
...aucour congruence. Then there is a family of surfaces corresponding to $ S $
2 KB (305 words) - 08:11, 6 June 2020
...rity) $\phi_i(v+u)=\phi_i(v)+\phi_i(u)$. These axioms were introduced by L.S. Shapley [[#References|[1]]] for an axiomatic definition of the expected pa
$$\phi_i(v)=\sum_{i\in S}\frac{(|S|-1)!(n-|S|)!}{n!}[v(S)-v(S\setminus\{i\})].$$
2 KB (304 words) - 12:43, 19 August 2014
..., is an extension of the Darboux pencil. A (non-developable) hypersurface $S$ degenerates into a hyper-quadric if and only if its generalized [[Darboux
<TR><TD valign="top">[1]</TD> <TD valign="top"> S.P. Finikov, "Projective-differential geometry" , Moscow-Leningrad (1937)
2 KB (240 words) - 08:52, 8 April 2023
...eory of canonical correlations the random variables $ X _ {1} \dots X _ {s} $
and $ X _ {s+1} \dots X _ {s + t } $,
2 KB (363 words) - 06:29, 30 May 2020