$#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
...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
...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
...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
...ly one fixes a quotient module $X/A$, that is, an extension of the module $A$ by the module $B$ is an [[exact sequence]]
0 \rightarrow A \rightarrow X \rightarrow B \rightarrow 0 \ .
2 KB (354 words) - 21:55, 30 October 2016
A side of a face of a [[Polyhedron|polyhedron]].
142 bytes (22 words) - 16:55, 7 February 2011
$#A+1 = 36 n = 0
A [[Lie algebra|Lie algebra]] whose elements are smooth functions on a smooth real [[Manifold|manifold]] $ M $(
6 KB (836 words) - 22:16, 5 June 2020
$#A+1 = 51 n = 0
A system of information transmission (transformation) using a quantum-mechanical object as the carrier of the information.
6 KB (890 words) - 08:08, 6 June 2020
A [[Topological group|topological group]] (in particular, a [[Lie group|Lie group]]) for which the underlying topological space is simp
...a certain simply-connected group (called the universal covering of $G$) by a discrete central subgroup isomorphic to $\pi_1(G)$.
2 KB (324 words) - 08:48, 8 April 2023
...otent elements. For any scheme $\left({ X,\mathcal{O}_X }\right)$ there is a largest closed reduced subscheme $\left({ X_{\mathrm{red}},\mathcal{O}_{X_{
...ents of the ring $\mathcal{O}_{X,x}$. A [[Group scheme|group scheme]] over a field of characteristic 0 is reduced [[#References|[3]]].
2 KB (310 words) - 07:40, 19 March 2023
$#A+1 = 13 n = 0
...lex plane: the set of values of every non-constant holomorphic function on a domain $ D \subset \mathbf C $
3 KB (457 words) - 08:07, 6 June 2020
$#A+1 = 61 n = 0
A connected non-oriented [[Graph|graph]] $G$ which does not contain cycles. A tree has no multiple edges and no loops. Since they are the simplest possib
6 KB (1,006 words) - 06:20, 30 March 2023
...ry values on the circumference and with its zeros and poles. Let $f(z)$ be a meromorphic function in the disc $\lvert z\rvert\leq R$; let $a_\mu$, $\lve
...\lvert z\rvert<R$; formula (1) was obtained by J.L. Jensen in {{Cite|Je}}. A small modification is necessary to adapt (1) to the case $f(0)=0$.
7 KB (1,197 words) - 20:51, 19 April 2012
''of a metric space $(X,d)$''
Given a [[Metric space|metric space]] $(X,d)$, a completion of $X$ is a triple $(Y,\rho,i)$ such that:
2 KB (340 words) - 15:24, 18 October 2014
$#A+1 = 119 n = 0
be a compact [[Hausdorff space|Hausdorff space]] (cf. also [[Compact space|Compa
8 KB (1,167 words) - 11:37, 12 January 2021
* A [[BCH-algebra]]
149 bytes (22 words) - 16:39, 21 December 2015
$#A+1 = 37 n = 0
is the harmonic measure of a boundary set $ \alpha $
3 KB (478 words) - 19:43, 5 June 2020
...not a topological group with respect to this topology and therefore is not a compact group.
...logical manifold, while every infinite zero-dimensional compact group with a countable base is homeomorphic to the perfect Cantor set.
8 KB (1,117 words) - 20:03, 27 February 2021
...tions, explicitly given by R.M. Vogt, [[#References|[a12]]]. The result is a homotopy coherent diagram in $T o p$, cf. [[#References|[a7]]].
...py-coherent diagrams that arise in other ways and to other settings having a suitable notion of homotopy, such as the categories of chain complexes, dif
9 KB (1,449 words) - 00:50, 15 February 2024
$#A+1 = 140 n = 0
...of a large number of independent or weakly-dependent random variables have a probability distribution close to the [[Normal distribution|normal distribu
20 KB (2,992 words) - 07:15, 21 March 2023
...nilpotent torsion-free groups $G_1$ and $G_2$ can be uniquely extended to a homomorphism $f^* : G_1^* \rightarrow G_2^*$.
<TR><TD valign="top">[1]</TD> <TD valign="top"> A.G. Kurosh, "The theory of groups" , '''1–2''' , Chelsea (1955–1956)
1 KB (227 words) - 18:28, 5 April 2018
$#A+1 = 38 n = 0
A continuous [[probability distribution]] concentrated on $ (0, 1) $
5 KB (641 words) - 08:58, 8 April 2023
$#A+1 = 50 n = 0
dimensional integral manifold passes through each point of a certain domain in the space $ \mathbf R ^ {n} $.
5 KB (702 words) - 17:45, 4 June 2020
$#A+1 = 228 n = 0
A queue for which the algorithm provides for the calls to form a queue if the system is busy at the time of their arrival; here the service
18 KB (2,750 words) - 19:29, 16 January 2024
The same as a [[Ramified prime ideal|ramified prime ideal]].
60 bytes (10 words) - 16:57, 7 February 2011
$#A+1 = 4 n = 0
...m field theory]], states in its generalized form [[#References|[a2]]] that a canonical quantum field which for fixed $ t $
2 KB (291 words) - 19:42, 5 June 2020