$#A+1 = 302 n = 0
$#C+1 = 302 : ~/encyclopedia/old_files/data/A110/A.1100010 A priori and a posteriori bounds in matrix computations
30 KB (4,205 words) - 18:47, 5 April 2020
$#A+1 = 76 n = 1
...1 = 76 : ~/encyclopedia/old_files/data/A010/A.0100550 Action of a group on a manifold
7 KB (1,066 words) - 06:29, 26 March 2023
...lpha = 0$ can be uniquely represented as $\phi = \psi \, \mu$. A kernel of a morphism $\alpha$ is denoted by $\ker \alpha$.
...of $\alpha$. Thus, the kernels of a morphism $\alpha$ form a subobject of $A$, denoted by $\operatorname{Ker} \alpha$.
3 KB (482 words) - 13:57, 26 December 2017
$#A+1 = 26 n = 0
...data/C021/C.0201550 Character of a finite\AAhdimensional representation of a semi\AAhsimple Lie algebra
2 KB (326 words) - 07:50, 21 January 2022
...following classical assertion is well known. Let $D \subset \mathbf{C}$ be a simply connected bounded domain with smooth boundary $\partial D$, and $f \
if and only if $f ( z )$ extends into the domain $D$ as a [[Holomorphic function|holomorphic function]] of the class $H ( D ) \cap C
6 KB (978 words) - 17:44, 1 July 2020
$#A+1 = 34 n = 0
...cyclopedia/old_files/data/P075/P.0705030 Product of a family of objects in a category
3 KB (545 words) - 08:07, 6 June 2020
...{ r }$ generate $\mathfrak{m}$, and in that case $( A , \mathfrak m )$ is a regular local ring.
...s of finite length; in that case $y _ { 1 } , \dots , y _ { s }$ is called a system of parameters of $M$.
3 KB (406 words) - 17:45, 1 July 2020
$#A+1 = 95 n = 0
...~/encyclopedia/old_files/data/W097/W.0907540 Weight of a representation of a Lie algebra
5 KB (778 words) - 02:00, 4 January 2022
$#A+1 = 62 n = 1
...ncyclopedia/old_files/data/C021/C.0201570 Character of a representation of a group
6 KB (828 words) - 09:30, 26 March 2023
''operation $ {\mathcal A} $''
A set-theoretical operation, discovered by P.S. Aleksandrov [[#References|[1]
3 KB (432 words) - 16:59, 1 July 2020
...ummable ones. A measurable function $f(x)$ is called $A$-integrable over $[a,b]$ if
The number $I$ is called the $A$-integral. It is denoted by
940 bytes (157 words) - 11:01, 31 March 2017
$#A+1 = 27 n = 0
$#C+1 = 27 : ~/encyclopedia/old_files/data/A010/A.0100080 \BMI A\EMI\AAhsystem
3 KB (440 words) - 18:48, 5 April 2020
''analytic set, in a complete separable metric space''
A continuous image of a [[Borel set]]. Since any Borel set is a continuous
2 KB (327 words) - 14:21, 15 August 2023
...n is actually observed. The a posteriori probability is connected with the a priori probability by the [[Bayes formula|Bayes formula]].
638 bytes (101 words) - 12:04, 27 October 2014
...sumption on its existence is not sufficiently founded). For the use of the a priori distribution, see [[Bayesian approach]].
1 KB (204 words) - 19:22, 21 April 2024
...posteriori probability|a posteriori probability]]. This terminology is, as a rule, used in connection with the [[Bayes formula|Bayes formula]].
328 bytes (49 words) - 17:22, 7 February 2011
...riable, to be contrasted with its unconditional or [[A priori distribution|a priori distribution]].
...$ when $\Theta=\theta$; then the a posteriori distribution of $\Theta$ for a given $X=x$, according to the [[Bayes formula|Bayes formula]], has the dens
2 KB (248 words) - 21:34, 1 January 2019
...id $R$ if for any $\lambda \in R$ and $a \in A$ the product $\lambda a \in A$ is defined, such that
\lambda (\mu a) = (\lambda\mu) a
6 KB (1,055 words) - 05:59, 22 April 2023
...$. In a wider sense, a section of any morphism in an arbitrary category is a right-inverse morphism.
If $U \subset Y$ is a subset of $Y$, a section over $U$ of $p$ is a mapping $s : U \rightarrow X$ such that $p(s(u)) = u$ for all $u \in U$.
769 bytes (149 words) - 18:13, 15 November 2014
''$M_0=(x_0,y_0)$ relative to a circle''
$$(x-a)^2+(y-b)^2=R^2$$
2 KB (298 words) - 06:25, 12 October 2023
$#A+1 = 3 n = 0
A [[Net (in differential geometry)|net (in differential geometry)]] on a surface $ V _ {2} $
882 bytes (119 words) - 08:28, 6 June 2020
$#A+1 = 22 n = 0
''on the finiteness of the area of a continuous surface given by an explicit equation''
4 KB (530 words) - 08:25, 6 June 2020
''for a series $\sum_{n=0}^\infty u_n(x)$ of functions''
...e series $\sum_{n=0}^\infty\lambda_nu_n(x)$ converges almost-everywhere on a measurable set $X$, where the $u_n(x)$ are numerical functions defined on $
896 bytes (152 words) - 16:01, 17 July 2014
...clopediaofmath.org/legacyimages/b/b110/b110090/b11009027.png" /> is called
a left- (respectively right-) invariant mean if
.../b/b110/b110090/b11009034.png" />. The existence of Banach limits above is
a special case of an invariant mean, where <img align="absmiddle" border="0"
10 KB (1,395 words) - 06:44, 9 October 2016
A method for constructing a compound formula from given formulas, such that the [[Truth value|truth val
429 bytes (55 words) - 17:23, 7 February 2011
The same as a half-line (cf. [[Half-line (ray)]]).
171 bytes (22 words) - 13:47, 8 April 2023
$#A+1 = 20 n = 0
Consider a regular [[Martingale|martingale]] $ ( X _ {n} , {\mathcal F} _ {n} ) $,
3 KB (442 words) - 06:29, 30 May 2020
$#A+1 = 40 n = 1
A one-to-one continuously-differentiable mapping $ f : M \rightarrow N $
8 KB (1,074 words) - 11:43, 26 March 2023
A pre-$\lambda$-ring is a commutative ring $R$ with identity element $1$ and a set of mappings $\lambda^n : R \rightarrow R$, $n = 0,1,2,\ldots$ such that
...representation ring $R(G)$ of a finite group $G$ (cf. [[Representation of a compact group]]). In all these cases the $\lambda^n$ are induced by taking
10 KB (1,721 words) - 07:44, 23 March 2016
$#A+1 = 41 n = 0
A (phrase-structure) grammar (cf. also [[Grammar system|Grammar system]]) $
6 KB (867 words) - 14:14, 31 December 2020
$#A+1 = 62 n = 1
...ncyclopedia/old_files/data/C021/C.0201570 Character of a representation of a group
6 KB (828 words) - 09:30, 26 March 2023
$#A+1 = 29 n = 0
A quantum-mechanical system consisting of a nucleus of mass $ M $
5 KB (757 words) - 19:32, 22 March 2024
==Upper and lower limit of a real sequence==
The upper and lower limit of a sequence of real numbers $\{x_n\}$ (called also limes superior and limes in
8 KB (1,481 words) - 09:55, 16 August 2013
...f success, while 0 denotes the occurrence of a failure. The probability of a given sequence of successful or unsuccessful events, e.g.
has a [[Binomial distribution|binomial distribution]]. As $ n \rightarrow \inft
4 KB (636 words) - 13:12, 6 February 2020
In every convex quadrangle inscribed in a circle, the product of the lengths of the diagonals is equal to the sum of
...ducts of the lengths of its opposite sides, the four vertices are lying on a circle.
1 KB (176 words) - 21:35, 30 April 2014
...t element of $S$, and similarly the left [[annihilator]] of any element is a principal left ideal on an idempotent element of $S$.
Examples include the monoid of [[binary relation]]s on a set $A$ under composition of relations, with the empty relation as zero element.
714 bytes (106 words) - 16:43, 23 November 2023
...order $4n$, obtained as the extension of the cyclic group of order $2$ by a cyclic group of order $2n$. It has the presentation $\langle n,2,2 \rangle
A^n = B^2 = (AB)^2 \ .
601 bytes (92 words) - 20:50, 23 November 2023
''$n$-ary operation, on a set $A$''
A mapping
1 KB (216 words) - 05:53, 15 April 2023
...nvergent is called a $\mathcal K$-space; a complete metric linear space is a $\mathcal K$-space, but there are examples of normal $\mathcal K$-spaces th
...a$ is uniformly bounded on $\mathcal K$-bounded subsets of $E$. If $E$ is a complete metric linear space, this statement generalizes the classical unif
3 KB (545 words) - 12:08, 3 August 2014
$#A+1 = 11 n = 1
...e form of a confluent hypergeometric function of the second kind $ \Psi (a, b, x) $:
2 KB (257 words) - 07:39, 26 March 2023