$#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
$#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
''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
...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
...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
...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
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41 bytes (7 words) - 14:43, 11 July 2018
$#A+1 = 74 n = 0
$#C+1 = 74 : ~/encyclopedia/old_files/data/E036/E.0306980 Extension of a group
6 KB (917 words) - 20:29, 17 January 2024
The phrase "quantum group" is more or less a synonym for "Hopf algebra" . More precisely, the category of quantum groups
...nslate the definition of a group into the language of algebras: instead of a space $ G $
18 KB (2,674 words) - 19:09, 16 December 2019
$#A+1 = 24 n = 0
A projective space of odd dimension, $ P _ {2n-} 1 $,
3 KB (441 words) - 08:09, 6 June 2020
A partially resolving operator $L_m^h$, uniformly bounded in $h$ and $m$, des
...[[#References|[6]]]). There are also other definitions of the stability of a computational algorithm (cf. e.g. [[#References|[1]]], [[#References|[3]]])
2 KB (295 words) - 14:06, 14 August 2014
A non-linear integral equation of the type
$$\phi(x)+\int\limits_a^bK(x,s)f[s,\phi(s)]ds=0,\quad a\leq x\leq b,$$
2 KB (338 words) - 11:07, 24 August 2014
...enerated field. The terminology was introduced by Serge Lang to enunciate a [[Lang conjecture on analytically hyperbolic varieties|range of conjectures
...Characteristic of a field|characteristic zero]]: hence $X$ is defined over a finitely generated field $E$. If the set of points $X(F)$ is finite for an
2 KB (277 words) - 18:16, 2 October 2023
...example of a uniserial ring is the ring of upper-triangular matrices over a skew-field.
731 bytes (117 words) - 16:40, 1 May 2014
$#A+1 = 115 n = 0
$#C+1 = 115 : ~/encyclopedia/old_files/data/A011/A.0101690 Algebraic systems, variety of
10 KB (1,438 words) - 16:10, 1 April 2020
$#A+1 = 92 n = 0
An integral equation with a real symmetric kernel (cf. [[Kernel of an integral operator|Kernel of an in
13 KB (1,912 words) - 16:30, 6 January 2024
$#A+1 = 44 n = 0
An algebra $ A $
5 KB (706 words) - 09:14, 28 June 2022
...stochastic process]] $X=(X_t(\omega),\mathcal F_t)$ that is measurable (as a mapping $(\omega,t)\to X(\omega,t)=X_t(\omega)$) with respect to the [[Pred
<TR><TD valign="top">[a1]</TD> <TD valign="top"> C. Dellacherie, P.A. Meyer, "Probabilities and potential" , '''B''' , North-Holland (1982)
901 bytes (132 words) - 14:08, 15 April 2023
$#A+1 = 10 n = 0
For a partial differential equation, written in normal form with respect to a distinguished variable $ t $,
2 KB (288 words) - 22:12, 5 June 2020
$#A+1 = 98 n = 0
$#C+1 = 98 : ~/encyclopedia/old_files/data/A110/A.1100160 Acceleration methods
12 KB (1,681 words) - 06:15, 28 March 2023
$#A+1 = 27 n = 0
...with multiplication having a two-sided homotopy identity. More precisely, a pointed topological space $ ( X , e) $
3 KB (410 words) - 19:42, 5 June 2020
...full matrix ring of a [[local ring]]. This holds, in particular, if $J$ is a [[nil ideal]].
915 bytes (144 words) - 16:49, 17 October 2014
$#A+1 = 164 n = 0
$#C+1 = 164 : ~/encyclopedia/old_files/data/A014/A.0104140 Automaton, finite
19 KB (2,906 words) - 07:33, 26 March 2023
$#A+1 = 25 n = 0
A finite-dimensional real [[Lie algebra|Lie algebra]] $ \mathfrak g $
3 KB (378 words) - 22:16, 5 June 2020
The [[characteristic subgroup]] of a [[P-group|$p$-group]] generated by all Abelian subgroups of maximal order.
...valign="top"> J.G. Thompson, "A replacement theorem for $p$-groups and a conjecture" ''J. Algebra'' , '''13''' (1969) pp. 149–151 {{ZBL|0194.0
724 bytes (97 words) - 14:51, 8 April 2023
$#A+1 = 26 n = 0
$#C+1 = 26 : ~/encyclopedia/old_files/data/R082/R.0802490 Risk of a statistical procedure
3 KB (411 words) - 08:11, 6 June 2020
''of a topological space''
...itrary spaces in which the concept of a complex is used everywhere, but in a situation which is more involved than that of triangulation. There are two
9 KB (1,350 words) - 11:39, 25 October 2014
...hat $U = \cup_i f_i[U_i]$ are taken as coverings and so in $X_{\text{et}}$ a topology is introduced.
...es (that is, sheaves on $X_{\text{et}}$). For example, if $f : X \to Y$ is a morphism of schemes and $\mathcal{F}$ is an étale sheaf on $X$, then by pu
3 KB (538 words) - 20:07, 3 June 2017