$#A+1 = 302 n = 0
$#C+1 = 302 : ~/encyclopedia/old_files/data/A110/A.1100010 A priori and a posteriori bounds in matrix computations
30 KB (4,205 words) - 18:47, 5 April 2020
...lpha = 0$ 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 = 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
...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
''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
''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
...t of [[AMS-LaTeX]] markup, a superset of [[LaTeX]] markup which is in turn a superset of [[TeX]] markup, for mathematical formulae. It generates either
...usual text, and with short TeX elements usually replaced by html parts. As a consequence, in many cases TeX-elements, e.g. vector symbols, "stick out" b
78 KB (11,584 words) - 08:19, 1 June 2011
...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
...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
...a triangle is proportional to its area. The maximum value of the defect of a triangle equals two right angles if all the vertices of the triangle are po
For a triangle in [[spherical geometry]] one has the opposite effect that the sum
1 KB (162 words) - 11:52, 13 December 2015
...scillations, theory of]]). The term "auto-oscillation" was introduced by A.A. Andronov (see [[#References|[1]]]).
...ng system, and the oscillating system itself. An essential feature of such a system is its feedback nature: on the one hand, the regulating mechanism co
9 KB (1,404 words) - 16:55, 15 April 2012
$#A+1 = 23 n = 0
...J.H.C. Whitehead, which asks for a characterization of Abelian groups $ A $
4 KB (665 words) - 08:29, 6 June 2020
...set]] in a dyadic space is dyadic, but not all closed $G_\delta$ sets are. A dyadic space which satisfies the first axiom of countability is metrizable,
<TR><TD valign="top">[2]</TD> <TD valign="top"> B.A. Efimov, "On dyadic spaces" ''Soviet Math. Dokl.'' , '''4''' (1963) pp
1 KB (202 words) - 20:40, 2 January 2021
|[[Norm on a field]]
|[[Potential of a mass distribution]]
5 KB (641 words) - 11:27, 6 June 2020
...L_0)$, if these spaces are finite-dimensional. The index of an operator is a homotopy invariant that characterizes the solvability of the equation $Ax=b
The index defined above is also called the analytic index of $A$, cf. [[Index formulas|Index formulas]].
1 KB (181 words) - 18:19, 21 November 2018
$#A+1 = 25 n = 0
...1 = 25 : ~/encyclopedia/old_files/data/P075/P.0705300 Projective object of a category
4 KB (597 words) - 08:08, 6 June 2020
$#A+1 = 30 n = 0
A projective $ n $-
2 KB (353 words) - 13:52, 8 April 2023
...ould be a σ-algebra. If you mean rather a ring etc., then you have to make a reservation. Any objections? I'll wait some days, and if no one will object
...unions. Therefore the (measurable) sets of finite Lebesgue measure are not a σ-ring. --[[User:Boris Tsirelson|Boris Tsirelson]] 18:28, 20 December 2011
750 bytes (116 words) - 18:02, 20 December 2011
$#A+1 = 58 n = 0
A fundamental operation in the [[Exterior algebra|exterior algebra]] of tenso
3 KB (535 words) - 19:38, 5 June 2020
$#A+1 = 30 n = 0
...erential equations, the original problem is reduced to the minimization of a functional:
4 KB (578 words) - 19:54, 12 January 2024
...also [[Principal G-object|Principal $G$-object]]) with base space $M$ for a compact connected [[Lie group|Lie group]] $G$. For $G$ simply connected, e.
...rname { Tr } ( A \bigwedge d A + \frac { 2 } { 3 } A \bigwedge A \bigwedge A ) \operatorname { mod } 2 \pi , \end{equation*}
4 KB (628 words) - 16:58, 1 July 2020
...v space|Sobolev space]]). Then $f$ is said to be quasi-regular if there is a number $K \in [ 1 , \infty )$ such that the inequality
is satisfied almost everywhere (a.e.) in $G.$ Here, $f ^ { \prime } ( x )$ denotes the formal derivative of $
9 KB (1,309 words) - 17:02, 1 July 2020
$#A+1 = 92 n = 3
a critical point of order $ m $
9 KB (1,400 words) - 11:09, 26 March 2023
The same as a [[Dilatation|dilatation]]. See also [[Expanding mapping|Expanding mapping]]
119 bytes (17 words) - 17:13, 7 February 2011
population or a part of it, such as the residents of a country or the
patients of a hospital. Giving birth, dying, shifting usual place of
20 KB (2,970 words) - 20:18, 12 March 2016
$#A+1 = 30 n = 0
$#C+1 = 30 : ~/encyclopedia/old_files/data/A010/A.0100700 Additive relation
2 KB (377 words) - 20:50, 4 April 2020
$#A+1 = 12 n = 0
...stability for systems of linear time-invariant differential equations. For a system of linear differential equations (cf. [[Differential equation, ordin
5 KB (695 words) - 22:14, 5 June 2020
$#A+1 = 209 n = 2
There are a number of theorems named after Karl Theodor Wilhelm Weierstrass (1815-1897)
22 KB (3,120 words) - 01:51, 24 February 2022
...12/a012980/a012980122.png, https://www.encyclopediaofmath.org/legacyimages/a/a013/a013720/a01372013.png, https://www.encyclopediaofmath.org/legacyimages
...a014/a014320/a0143209.png, https://www.encyclopediaofmath.org/legacyimages/a/a014/a014320/a0143208.png, https://www.encyclopediaofmath.org/legacyimages/
51 KB (6,659 words) - 19:37, 7 April 2019
...)$ of $\textbf{Q}^{\text{ab}}$ (cf. also [[Galois group|Galois group]]) is a free [[Profinite group|profinite group]] of countable rank. Here, $\textbf{
...ery $H$-Galois field extension of $\textbf{Q}^{\text{ab}}$ is dominated by a $G$-Galois field extension of $\textbf{Q}^{\text{ab}}$.
11 KB (1,686 words) - 18:54, 6 February 2021