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- $#A+1 = 302 n = 0 $#C+1 = 302 : ~/encyclopedia/old_files/data/A110/A.1100010 A priori and a posteriori bounds in matrix computations30 KB (4,205 words) - 18:47, 5 April 2020
- ...lpha = 0$ 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 manifold7 KB (1,066 words) - 06:29, 26 March 2023
- $#A+1 = 26 n = 0 ...data/C021/C.0201550 Character of a finite\AAhdimensional representation of a semi\AAhsimple Lie algebra2 KB (326 words) - 07:50, 21 January 2022
- ...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 C6 KB (978 words) - 17:44, 1 July 2020
- $#A+1 = 34 n = 0 ...cyclopedia/old_files/data/P075/P.0705030 Product of a family of objects in a category3 KB (545 words) - 08:07, 6 June 2020
- ...{ r }$ 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 algebra5 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 group6 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 by940 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\AAhsystem3 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 continuous2 KB (327 words) - 14:21, 15 August 2023
- ...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) a6 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 dens2 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
- ...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
- ...e $X$ is said to be of the first category in $X$ if it can be expressed as a finite or countable union of [[nowhere-dense set|nowhere dense sets]] in $X ...h sets is residual (or comeager), cp. again with Chapter 9 of {{Cite|Ox}}. A non-empty closed set of real numbers, in particular an interval, is not of2 KB (291 words) - 19:06, 7 December 2023
- A concept of classical measure theory generalized further in [[Geometric meas ===Lebesgue density of a set===10 KB (1,662 words) - 09:58, 16 August 2013
Page text matches
- $#A+1 = 310 n = 4 can be made terms of a sequence33 KB (4,248 words) - 08:17, 21 March 2022
- $#A+1 = 3 n = 0 ...tural parametrization (see [[Natural parameter|Natural parameter]]) is, in a neighbourhood of that point,1 KB (210 words) - 08:02, 6 June 2020
- ...to a certain form of the concept of infinity in mathematics — the idea of a potential infinity. ...al realizability to the example given above is tantamount to assuming that a unit can be added to any natural number, that it is possible to form the su1 KB (196 words) - 17:15, 7 February 2011
- $#A+1 = 38 n = 0 A set that is not a [[Measurable set|measurable set]]. In more detail: A set $ X $4 KB (623 words) - 08:03, 6 June 2020
- $#A+1 = 66 n = 0 A vector subbundle $ \pi : P \rightarrow M $5 KB (750 words) - 08:06, 6 June 2020
- A unimodal [[probability distribution]] on the circle with probability densit ...um value at $\phi = \theta_1$, so that $\theta_1$ is the mode; $\kappa$ is a concentration parameter. The normalising factor $I_0(\kappa)$ is an incomp1,000 bytes (132 words) - 19:47, 13 December 2016
- $#A+1 = 52 n = 0 ...component systems and relations of syntactic subordination. The notion of a component system can be defined in the following way. Let $ x $10 KB (1,545 words) - 08:24, 6 June 2020
- $#A+1 = 180 n = 2 ...ation of elliptic curves (cf. [[Elliptic curve|Elliptic curve]]), that is, a morphism $ \pi : X \rightarrow B $15 KB (2,046 words) - 05:46, 13 June 2022
- $#A+1 = 24 n = 0 A method for adding sequences of positive integers; created by L.G. Shnirel'm3 KB (458 words) - 19:05, 20 November 2023
- ...prove the [[Bolzano–Weierstrass theorem|Bolzano–Weierstrass theorem]] and a number of other theorems in analysis. ...on assumes its maximum at some point, but not to specify this point within a given degree of accuracy.3 KB (522 words) - 16:49, 6 August 2014
- $#A+1 = 17 n = 0 $#C+1 = 17 : ~/encyclopedia/old_files/data/P072/P.0702420 Perturbation of a linear system3 KB (437 words) - 07:39, 26 February 2022
- ...n unhealthy interest in proving this theorem was stimulated at one time by a large international prize, which was abolished at the end of the First Worl ...e theorem was proved by L. Euler (1770), for $n=5$ by P.G.L. Dirichlet and A. Legendre (1825), and for $n=7$ by G. Lamé (1839) (see [[#References|[2]]]16 KB (2,596 words) - 09:27, 13 February 2024
- $#A+1 = 19 n = 0 ...illation]] of the system, the amplitude of the forced oscillation may have a rather large value, and will be the larger the lower the resistance of the6 KB (850 words) - 19:39, 5 June 2020
- ...erved data, the missingness is independent of the unobserved measurements. A process that is neither MCAR nor MAR is termed ''non-random'' (MNAR). ...le simplification in the analysis (Verbeke and Molenberghs 2000). There is a strong trend, nowadays, to prefer this kind of analyses, in the likelihood5 KB (739 words) - 11:38, 31 March 2016
- ...ssive particle ($m>0$) the little group is the group $\mathrm{SU}(2)$. For a particle with mass zero the little group is the Euclidean group of the plan <TR><TD valign="top">[2]</TD> <TD valign="top"> I.M. Gel'fand, R.A. Minlos, Z.Ya. Shapiro, "Representations of the rotation and the Lorent2 KB (347 words) - 19:55, 12 January 2017
- $#A+1 = 289 n = 0 ...erentiable manifold, that can locally be described by definite rules using a certain function, usually called the symbol of the pseudo-differential oper29 KB (4,077 words) - 04:02, 4 January 2022
- $#A+1 = 14 n = 0 A method for solving linear differential equations for given boundary value o4 KB (526 words) - 22:12, 5 June 2020
- ...to construct ab initio a non-traditional continuum, but where it is simply a question of classical real numbers that are computable in some sense or oth571 bytes (88 words) - 16:54, 7 February 2011
- $#A+1 = 70 n = 0 A [[Significance test|significance test]] for the mean value of a [[Normal distribution|normal distribution]].6 KB (791 words) - 20:10, 10 January 2024
- ...one has a game of survival for player II, while if $h_\infty = 1$ one has a game of survival for player I. ...e [[#References|[2]]]). Differential games of survival can be looked at as a generalization of the games under discussion to the case of continuous time2 KB (397 words) - 16:58, 18 October 2014