$#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
...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
''operation $ {\mathcal A} $''
A set-theoretical operation, discovered by P.S. Aleksandrov [[#References|[1]
3 KB (432 words) - 16:59, 1 July 2020
$#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 = 14 n = 0
$#C+1 = 14 : ~/encyclopedia/old_files/data/B017/B.0107320 Boundary (of a manifold)
1 KB (204 words) - 06:28, 30 May 2020
$#A+1 = 6 n = 0
$#C+1 = 6 : ~/encyclopedia/old_files/data/S091/S.0901530 Swerve of a curve,
1 KB (206 words) - 05:43, 9 April 2023
$#A+1 = 72 n = 0
From a purely mathematical point of view, the Golay codes are the most interesting
5 KB (772 words) - 11:10, 23 March 2023
$#A+1 = 64 n = 0
''of a family of curves in the plane''
8 KB (1,211 words) - 19:37, 5 June 2020
$#A+1 = 2 n = 0
A diffeomorphism generating a [[Y-system| $ Y $-
459 bytes (65 words) - 08:29, 6 June 2020
$#A+1 = 9 n = 0
...n table of an arbitrary finite [[Groupoid|groupoid]]. Heading the table is a list of symbols denoting all elements of the groupoid (in any order); these
2 KB (300 words) - 16:43, 4 June 2020
$#A+1 = 55 n = 0
...the largest sure result in different situations implies the formulation of a great variety of maximin problems.
9 KB (1,423 words) - 08:07, 6 June 2020
A canonical decomposition theorem (due to Jordan) for [[Function of bounded
...e pair is unique up to addition of a constant, i.e. if $g^+$ and $g^-$ is a second pair with the same property, then $g^+-f^+=g^--f^-\equiv {\rm const
2 KB (301 words) - 14:05, 10 December 2012
$#A+1 = 30 n = 0
A set-theoretic inclusion $ V \subset W $
2 KB (292 words) - 22:11, 5 June 2020
''of a homomorphism $\phi : A \rightarrow A'$ of algebraic systems''
...\in \theta \}$, is an isomorphism of the quotient system $A/\theta$ onto $A'$.
764 bytes (124 words) - 07:39, 13 November 2016
...^{\pi i/12}\eta(z)$ and $\eta(-1/z)=\sqrt{-iz}\eta(z)$. So, $\eta^{24}$ is a [[modular form]] of weight $12$ (cf. also [[Modular group]]).
...es now called [[Dedekind sum]]s. See [[#References|[a2]]], Chapt. IV, for a further discussion.
1 KB (196 words) - 19:54, 12 April 2017
$#A+1 = 51 n = 0
is a [[Singular point|singular point]] of the differential equation . The rank o
6 KB (861 words) - 13:02, 6 January 2024
...ral transform|integral transform]] which maps holomorphic functions $f$ of a complex variable onto complex solutions $u$ of linear second-order partial
Then the transform is realized by a complex line integral (cf. [[Curvilinear integral|Curvilinear integral]]) a
4 KB (623 words) - 15:18, 14 February 2020
...iant. For $x \in X$ and $g \in G$, $g.x$ denotes the action of $g$ on $X$. A family $\mathcal{K}$ of compact subsets of $X$ is said to have the Pompeiu
A typical example occurs when $X = \mathbf{R} ^ { n }$, $\mu$ is the [[Lebesg
9 KB (1,368 words) - 20:29, 10 January 2021
...premium to cover its liability. The company is furthermore assumed to have a certain initial capital $u$ at its disposal. One important problem in risk
i) the [[Stochastic point process|stochastic point process]] is a [[Poisson process|Poisson process]] with intensity $\lambda$;
4 KB (698 words) - 13:17, 3 October 2014
A definition that is meaningful only when the object to be defined is assumed
...uch that the object to be defined falls within its range of applicability. A property is called predicative if it contains no such bound variables.
4 KB (713 words) - 17:07, 14 February 2020
$#A+1 = 125 n = 0
...f a function of several variables. There are several different concepts of a multiple integral (Riemann integral, Lebesgue integral, Lebesgue–Stieltje
11 KB (1,648 words) - 16:53, 20 January 2024
$#A+1 = 100 n = 2
The group of all permutations (self-bijections) of a set $ X $
7 KB (1,003 words) - 08:24, 6 June 2020
A formula for the logarithm $\ln\phi(\lambda)$ of the [[Characteristic functi
...istics $\gamma$ and $G$ are such that $\gamma$ is a real number and $G$ is a non-decreasing left-continuous [[Function of bounded variation|function of
2 KB (252 words) - 17:46, 10 October 2014
$#A+1 = 38 n = 0
...e probability distribution concentrated on a set of points of the form $ a + nh $,
4 KB (622 words) - 22:15, 5 June 2020
''in a category''
...ght). An equivalent definition of a monomorphism is: For any object $X$ of a category $\mathfrak{K}$ the mapping of sets induced by $\mu$,
2 KB (279 words) - 05:35, 12 January 2017
A [[Graph|graph]] in which multiple edges are allowed.
...pp. Chapt. 9</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> J.A. Bondy, U.S.R. Murthy, "Graph theory with applications" , Macmillan (1
866 bytes (122 words) - 20:09, 15 March 2023