$#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
...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
#REDIRECT [[Homology of a complex]]
35 bytes (5 words) - 14:22, 11 July 2018
...ollowing property: For any $S \in T(F)$, $F \in \mathcal{K}$, there exists a unique continuous linear operator $R:E_1 \tilde\otimes E_2 \to F$ such that
...(y)$. If in this case the topological tensor product exists, then there is a dense subspace in $E_1 \tilde\otimes E_2$ that can be identified with the a
5 KB (896 words) - 23:16, 10 April 2019
1) If $a/b$ and $a'/b'$ are two consecutive terms of the Farey series of order $n$, then
2) If $a/b$, $a'/b'$, $a''/b''$ are three consecutive terms of the Farey series of order $n$, then t
1 KB (206 words) - 11:54, 2 January 2021
i) Studying spaces with cells in a small range of dimensions, for example $r$-connected $n$-dimensional spaces
...py theory. A further aspect is that "deformation" methods are essential in a variety of subjects for the purposes of classification, and the comparison
9 KB (1,441 words) - 17:45, 1 July 2020
...et (e.g. the points of a sphere, unlike those of a plane, cannot be put in a continuous one-to-one correspondence with pairs of numbers), and one then i
...Apollonius' coordinates did not have numerical values. By the 2nd century A.D., however, Ptolemy was already using numerical coordinates as latitude an
7 KB (980 words) - 17:09, 11 April 2014
...xamples of complex systems are: the nervous system, the brain, a computer, a control system in human society, etc.
...otion is that of a complex [[Control system|control system]]. As a result, a number of special disciplines have also arisen, including the word "system
4 KB (532 words) - 17:22, 7 February 2011
...cated by the subscript on $-$). In many situations, $H$ is the gradient of a functional to be minimized.
...a _ { n }$ is a non-negative non-increasing sequence, typically $1 / n$ or a constant, $X_n$ is the "somehow stationary" observed sequence and $\theta
8 KB (1,242 words) - 15:31, 1 July 2020
...a unary [[relation symbol]] for being an element of the valuation ring, or a binary relation symbol for valuation divisibility $v(x)\leq v(y)$ (cf. [[St
...ecidability is one ingredient in the proof that Hilbert's 10th problem has a positive solution for the ring of all algebraic integers (see [[Algebraic D
12 KB (1,846 words) - 09:28, 26 November 2016
A function $(x,s)\mapsto K_n(x,s)$ that is formed from the given kernel $K$ o
$$A\phi(x)=\int\limits_a^bK(x,t)\phi(t)dt,$$
2 KB (292 words) - 19:24, 9 October 2014
$#A+1 = 33 n = 0
The simplest form of an algebraic expression, a [[Polynomial|polynomial]] containing only one term.
2 KB (376 words) - 08:01, 6 June 2020
...n equivalence relation on a family of sets" — As for me, a "family" means, a mapping from an "index" set (to something). Here I'd say, on the class of a
...of a family of topologies]]" I see that "family" is just another name for a set. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|
1 KB (183 words) - 20:17, 10 January 2015
...ne of the five regular polyhedra (Platonic solids); if the edge length is $a$, then the volume of the octahedron is
$$v=\frac{a^3\sqrt 2}{3}\approx0.4714a^3.$$
2 KB (244 words) - 14:08, 30 July 2014
...ral languages a particularly hard case for a formal language approach (for a survey of linguistic research, cf. [[#References|[a2]]]):
...r of lexical items has up to now (2000) prevented linguists from providing a reasonably complete grammar for any natural language. Even worse, natural l
18 KB (2,627 words) - 17:03, 1 July 2020
$#A+1 = 469 n = 2
A family $ \{ T \} $
34 KB (5,024 words) - 09:12, 21 January 2024
''distance on a [[set]] $X$ ''
A function $\rho$ with non-negative real values, defined on the [[Cartesian p
5 KB (793 words) - 09:16, 7 June 2016
...system]] of functions. The system $\left\{{\psi_n}\right\}$ is said to be a Bessel system if, for any function $f \in L_2$, the series
.... If the system $\left\{{\psi_n}\right\}$ is a Bessel system, there exists a constant $M$ such that for any $f \in L_2$
1 KB (233 words) - 05:56, 14 January 2017
...ith respect to the plane) points and locally cuts the plane (at one point $a$ at least).
A similar characterization of closed $(n-1)$-dimensional sets in the $n$-dime
941 bytes (170 words) - 11:48, 19 November 2018
$#A+1 = 15 n = 0
..., the crossing of which alters the law governing the motion of the system. A turbulent system in $ \mathbf R ^ {n} $
4 KB (557 words) - 08:26, 6 June 2020
...empotent semi-ring]] (i.e. a [[semi-ring]] with idempotent addition). Let $A$ be an idempotent semi-ring with operations $\oplus$ (addition) and $\odot$
...if one has an important and interesting numerical algorithm, then there is a good chance that its semi-ring analogues are important and interesting as w
7 KB (1,079 words) - 20:39, 16 November 2023
$#A+1 = 51 n = 0
A theorem stating that the Cauchy problem has a (unique) analytic solution locally if the functions occurring in the differ
7 KB (987 words) - 15:35, 4 June 2020
...hed by G. Fano (1892). It consists in the fact that the diagonal points of a quadrangle are not collinear. The Fano postulate is equivalent to the fact
...iagonal points of any quadrangle are collinear, is a projective plane over a field (of characteristic 2).
1 KB (167 words) - 08:56, 13 April 2017