$#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
...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 = 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
$#A+1 = 34 n = 0
...cyclopedia/old_files/data/P075/P.0705030 Product of a family of objects in a category
3 KB (545 words) - 08:07, 6 June 2020
...{ r }$ 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
...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
$#A+1 = 98 n = 0
$#C+1 = 98 : ~/encyclopedia/old_files/data/D031/D.0301210 Derivation in a ring
6 KB (945 words) - 17:32, 5 June 2020
...one means the density $d(A)$ (introduced in 1930 by L.G. Shnirel'man) of $A$, namely
$$d(A)=\inf\frac{A(n)}{n},$$
3 KB (461 words) - 11:41, 14 February 2020
$#A+1 = 3 n = 0
...iquely as a union of finitely many irreducible subgerms of it. The germ of a reduced [[Complex space|complex space]] $ ( X , {\mathcal O} ) $
2 KB (303 words) - 22:13, 5 June 2020
$#A+1 = 85 n = 0
are complex constants, which arises in the solution of a class of partial differential equations by the method of separation of vari
8 KB (1,119 words) - 08:22, 6 June 2020
$#A+1 = 46 n = 0
A programmed grammar (introduced in [[#References|[a3]]]) is a construct
4 KB (620 words) - 08:10, 6 June 2020
In a mathematical setting, the Cobb–Douglas function is defined as (see [[#Ref
\begin{equation} \tag{a1} Q = A K ^ { \alpha } L ^ { 1 - \alpha }, \end{equation}
6 KB (958 words) - 15:30, 1 July 2020
A [[Complex number|complex number]] $i$ whose square is equal to minus one: $
98 bytes (17 words) - 22:37, 16 March 2014
''of a circle''
A segment joining a point of the circle (or sphere) to the centre. The length of this segment i
614 bytes (87 words) - 16:59, 7 February 2011
...Measure|measure]] $ \mu $ on the $ \sigma $-ring $ M $ of subsets $ E $ of a locally compact group $ G $ generated by the family of all compact subsets,
where $ E g = \{ x g \in G \mid x \in E \} $. Accordingly, one speaks of a left- or right-invariant Haar measure. Every Haar measure is $ \mu $-'''reg
6 KB (971 words) - 20:18, 23 April 2017
$#A+1 = 17 n = 0
...f the solution of some differential or integral equation. For instance, in a continuous-time branching process the differential equation
2 KB (356 words) - 06:29, 30 May 2020
A one-dimensional manifold properly embedded in a $3$-ball, $D^3$.
...term "arcbody" is used for a one-dimensional manifold properly embedded in a $3$-dimensional manifold.
2 KB (336 words) - 09:53, 16 March 2023
$#A+1 = 49 n = 0
...(letters of the alphabet of the language). (Here, by information one means a linear string of letters.) An example of an alphabetical coding is the cele
9 KB (1,453 words) - 18:06, 15 November 2023
''of a ring''
...with respect to the addition operation in the ring. The additive group of a ring is always Abelian.
165 bytes (31 words) - 17:21, 7 February 2011
$#A+1 = 64 n = 6
...elow: bottom-up, starting from a finite field, and top-down, starting from a [[Local field|local field]].
7 KB (1,070 words) - 19:40, 5 June 2020
A sequence $x=(\xi_i)_1^\infty$ is said to be summable to $A(x)$ by a method $A$ given by an infinite matrix $(a_{i,k})$, if
$$A(x)=\lim_i\sum_{k=1}^\infty a_{i,k}\xi_i.$$
2 KB (413 words) - 14:16, 3 August 2014
...then the statement "X is subject to the Poisson law with parameter 1" is
a simple hypothesis. See also [[Composite hypothesis|Composite hypothesis]].
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">
A.M. Mood, F.
A. Graybill, "Introduction to the theory of statistics" , McGraw-Hill (196
675 bytes (94 words) - 09:30, 27 April 2014
$#A+1 = 38 n = 0
...ial equations enabling one, in some cases, to find the general solution of a linear partial differential equation of hyperbolic type,
5 KB (738 words) - 10:08, 4 June 2020
...09---present). He is the co-author (with F.R. Hampel, P.J. Rousseeuw and W.A. Stahel) of the well known text Robust Statistics : The Approach Based on I
i.e. when the underlying distribution lies in a neighborhood of the assumed
13 KB (1,889 words) - 19:48, 13 March 2024
...players (information). Being in an information set, a player needs to take a decision (to choose an alternative of the information set, i.e. to choose o
.... Press (1953)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> A. Rapoport, "$N$-person game theory: Concepts and applications" , Univ. Mi
1 KB (186 words) - 19:40, 28 April 2014
A finite non-negative function $p$ on a [[Vector space|vector space]] $E$ (over the field of real or complex number
...lysis one also encounters topological vector spaces (including spaces with a metrizable topology) on which there exist no non-trivial semi-norms. The si
2 KB (258 words) - 07:13, 5 December 2012
...or its minimum value. The usual practice is to find the extremal values of a certain characteristic by imposing restrictions on other numerical characte
where $n=k[n/k]+r$. A complete $k$-partite graph, the cardinalities of the parts of which differ
4 KB (567 words) - 20:10, 15 March 2023
$#A+1 = 51 n = 0
be a function of a complex variable $ z $
6 KB (831 words) - 22:14, 5 June 2020