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  • ...l character'' $\chi(x,X)$ at a point $x \in X$ is the least cardinality of a [[local base]] at $x$. The character $\chi(X)$ is the least upper bound of A space satisfies the [[first axiom of countability]] if and only if it has c
    542 bytes (83 words) - 12:05, 23 November 2023
  • ...he trace of a matrix $A = [a_{ij}]$ is denoted by $\tr A$, $\Tr A$ or $\Sp A$: \tr A = \sum_{i=0}^n a_{ii}
    2 KB (389 words) - 19:21, 11 November 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
  • ...clopediaofmath.org/legacyimages/c/c025/c025850/c02585023.png" /> is called a contraction of the group <img align="absmiddle" border="0" src="https://www ...cyclopediaofmath.org/legacyimages/c/c025/c025850/c02585037.png" /> becomes a commutative ideal of <img align="absmiddle" border="0" src="https://www.enc
    10 KB (1,419 words) - 17:01, 7 February 2011
  • A [[Normal series|normal series]] all factors of which are central, that is, a series of subgroups ...upper central series have the same length, which is the minimal length of a central series of the group. This length is called the nilpotency class (or
    1 KB (185 words) - 12:34, 14 February 2020
  • 106 bytes (15 words) - 17:08, 7 February 2011
  • A function defined for all real numbers $x$ and equal to the difference betwe
    275 bytes (39 words) - 13:07, 16 December 2012
  • A continuous [[Function|function]] $f\neq0$ on the [[Group|group]] $G$ such t ...entation]] of $G$ in a [[Hilbert space|Hilbert space]] $H$, and let $u$ be a unit (length) vector. Then
    1 KB (214 words) - 17:51, 28 November 2018
  • ...ous-time dynamical system)|flow (continuous-time dynamical system)]] or of a [[Cascade|cascade]]) with phase space $X$'' ...n certain open surfaces (see [[#References|[8]]]–[[#References|[10]]]). In a complete metric space the centre coincides with the closure of the set of p
    4 KB (617 words) - 16:07, 19 August 2014
  • ...d modular lattice the centre coincides with the set of all elements having a unique complement.
    608 bytes (112 words) - 13:40, 31 July 2014
  • ...be treated as a special case of the concept of an algorithmic operator in a constructive metric space. See also [[Constructive analysis|Constructive an
    415 bytes (59 words) - 17:26, 7 February 2011
  • A module over a [[small category]] $\Gamma$ is a contravariant [[functor]] from $\Gamma$ to the [[category]] of $R$-modules, ...imilarly, equivariant local cohomology can be described using modules over a category depending on the space in question.
    3 KB (473 words) - 18:52, 28 October 2016
  • $#A+1 = 70 n = 0 ...= 70 : ~/encyclopedia/old_files/data/G043/G.0403920 Generating operator of a semi\AAhgroup
    5 KB (786 words) - 19:41, 5 June 2020
  • ...ordered sets of finite length. A partially ordered set of length zero is a [[trivial order]]. Dilworth's theorem [[#References|[1]]] states that in a finite partially ordered set the length is equal to the minimal number of [
    924 bytes (134 words) - 07:27, 14 November 2023
  • $#A+1 = 118 n = 0 ...= 118 : ~/encyclopedia/old_files/data/F041/F.0401170 Fourier transform of a generalized function
    8 KB (1,192 words) - 19:39, 5 June 2020
  • $#A+1 = 35 n = 0 $#C+1 = 35 : ~/encyclopedia/old_files/data/C021/C.0201450 Channel with a finite number of states,
    4 KB (540 words) - 16:43, 4 June 2020
  • 36 bytes (4 words) - 18:26, 9 September 2013
  • $#A+1 = 141 n = 0 ...cyclopedia/old_files/data/P071/P.0701640 Partial differential equations on a manifold
    9 KB (1,406 words) - 21:26, 3 January 2021
  • $#A+1 = 56 n = 0 ...6 : ~/encyclopedia/old_files/data/O070/O.0700350 Orthogonal polynomials on a complex domain
    9 KB (1,315 words) - 20:15, 12 January 2024
  • $#A+1 = 115 n = 0 ...ia/old_files/data/C024/C.0204790 Conformal mapping, boundary properties of a
    8 KB (1,180 words) - 17:46, 4 June 2020

Page text matches

  • $#A+1 = 52 n = 0 ...this family contained in such subspaces. More precisely, let $ {\mathcal A} $
    9 KB (1,382 words) - 08:22, 6 June 2020
  • ''of a semi-group $S$'' ...A subset $N$ is a normal complex of a semi-group $S$ if and only if $N$ is a class of some congruence on $S$ (cf. [[Congruence (in algebra)|Congruence (
    683 bytes (121 words) - 20:27, 14 April 2014
  • ...s/t/t093/t093470/t09347013.png" /> is a semi-group of unitary operators on a Hilbert space. ...g" />. Cf. also [[Irreducible representation|Irreducible representation]]. A totally-irreducible set is also called completely irreducible.
    8 KB (1,059 words) - 17:18, 7 February 2011
  • $#A+1 = 17 n = 0 be a positive quadratic form over $ \mathbf R $
    3 KB (421 words) - 22:10, 5 June 2020
  • ...s in the plane for which the sum of the distances from two given points is a constant magnitude. ..."geometric locus" is somewhat obsolete, and nowadays usually simply means a point set defined by some property.
    827 bytes (131 words) - 13:44, 27 September 2014
  • ...ch vertex exactly once. Suppose that the vertex set $V = A \cup B$ where $A = \{a_1,\ldots,a_n\}$ and $B = \{b_1,\ldots,b_n\}$ . The Edmonds matrix is an $n \times n$ matrix $A$ with entries
    1 KB (173 words) - 07:29, 14 November 2023
  • $#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
  • ''of a [[trapezium]]'' A segment joining the mid-points of the two lateral sides of the trapezium. T
    270 bytes (46 words) - 21:32, 13 December 2016
  • $#A+1 = 49 n = 0 $#C+1 = 49 : ~/encyclopedia/old_files/data/A010/A.0100710 Additive theory of ideals
    7 KB (1,035 words) - 20:23, 4 April 2020
  • $#A+1 = 101 n = 0 ...nclusions on unobservable parameters even if their [[A priori distribution|a priori distribution]] is unknown. Let $ (Y, X) $
    8 KB (1,315 words) - 10:33, 29 May 2020
  • $#A+1 = 63 n = 0 A function $ f $
    8 KB (1,125 words) - 07:04, 29 March 2024
  • ...$ in the whole group lies in $A$. The isolator of a set $M$ of elements of a group is the smallest isolated subgroup containing $M$. ...ntersection of isolated subgroups in an $R$-group is an isolated subgroup. A normal subgroup $H$ of an $R$-group $G$ is isolated if and only if the quot
    1 KB (209 words) - 05:49, 20 June 2023
  • ...a $q$-dimensional linking of $\Phi$ in $\mathbf R^n$ close to some point $a\in\Phi$. An analogous theorem has been proved concerning obstructions "mod
    2 KB (290 words) - 11:41, 19 November 2018
  • ''$\sigma$ of a set $X = \{1,2,\ldots,n\}$ into itself'' ...l $s \in\Sigma_n$. A realization of such a random mapping is the result of a simple random selection from $\Sigma_n$.
    782 bytes (121 words) - 17:57, 22 November 2016
  • ...hed by C. Jordan [[#References|[1]]]. Together with the similar assertion: A simple arc does not decompose the plane, this is the oldest theorem in set- ...nds $x_0$ and $x$ and all points of which, except $x_0$, are contained in $A$ (Schoenflies' theorem).
    4 KB (655 words) - 12:25, 26 July 2014
  • where $C$ is a positive constant and $\mathrm{li}(x)$ is the [[logarithmic integral]] of $ The de la Vallée-Poussin alternation theorem: If a sequence of points $ \{ x _ {i} \} $,
    4 KB (553 words) - 14:03, 17 March 2020
  • ...ed subspace of some $D^\tau$, and every $T_2$-compactum is homeomorphic to a closed subspace of some $I^\tau$. <TR><TD valign="top">[2]</TD> <TD valign="top"> A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: p
    3 KB (412 words) - 17:06, 7 May 2016
  • ...ent of $K$ is the root of a non-zero polynomial with coefficients in $k$. A finite degree extension is necessarily algebraic, but the converse does not Algebraic extensions form a ''[[Distinguished class of extensions|distinguished class]]'' : that is, th
    1 KB (190 words) - 14:18, 12 November 2023
  • $#A+1 = 38 n = 0 A function describing the influence of particles or groups of particles on on
    6 KB (842 words) - 17:31, 5 June 2020
  • ''to a curve'' The tangent line to a curve is
    2 KB (397 words) - 00:50, 25 April 2012

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