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- ...ly one fixes a quotient module $X/A$, that is, an extension of the module $A$ by the module $B$ is an [[exact sequence]] 0 \rightarrow A \rightarrow X \rightarrow B \rightarrow 0 \ .2 KB (354 words) - 21:55, 30 October 2016
- A side of a face of a [[Polyhedron|polyhedron]].142 bytes (22 words) - 16:55, 7 February 2011
- $#A+1 = 71 n = 0 $#C+1 = 71 : ~/encyclopedia/old_files/data/S086/S.0806590 Spectrum of a ring5 KB (778 words) - 13:13, 6 January 2024
- 41 bytes (7 words) - 14:43, 11 July 2018
- The [[equivalence relation]] on the domain of a function expressing the property that equivalent elements have the same im ...onversely, every equivalence relation $\sim\,$ on a set $X$ gives rise to a function of which it is the kernel. Consider the ''quotient set'' $X/\sim1 KB (189 words) - 17:00, 23 November 2023
- $#A+1 = 16 n = 0 $#C+1 = 16 : ~/encyclopedia/old_files/data/G043/G.0403930 Generator of a category,3 KB (545 words) - 19:41, 5 June 2020
- $#A+1 = 29 n = 0 $#C+1 = 29 : ~/encyclopedia/old_files/data/N067/N.0607740 Normalizer of a subset2 KB (277 words) - 08:03, 6 June 2020
- $#A+1 = 101 n = 0 $#C+1 = 101 : ~/encyclopedia/old_files/data/N067/N.0607360 Norm on a field6 KB (1,003 words) - 21:35, 13 January 2021
- The inclusion of any finite number of zeros between adjacent terms of a series. For the series a diluted series has the form604 bytes (107 words) - 20:41, 14 October 2014
- $#A+1 = 33 n = 0 $#C+1 = 33 : ~/encyclopedia/old_files/data/I050/I.0500150 Image of a morphism4 KB (576 words) - 22:11, 5 June 2020
- ...$A$. Usually, $A$ is taken to be either the multiplicative group $k^*$ of a field $k$ or the subgroup ...character of a group was originally introduced for finite groups $G$ with $A = T$ (in this case every character $G → ℂ^*$ takes values in $T$).3 KB (438 words) - 13:36, 23 July 2015
- ...metry, and topology. Thus, in topology, each topological space $X$ defines a chain complex in the category $\textsf{Ab}$ of Abelian groups: $(C_n(X),\pa The concept of the cohomology of a cochain complex is defined in a dual manner.2 KB (265 words) - 21:51, 22 October 2016
- $#A+1 = 61 n = 0 $#C+1 = 61 : ~/encyclopedia/old_files/data/D032/D.0302330 Differentiation of a mapping6 KB (918 words) - 19:35, 5 June 2020
- The ''pole of a function'' is ...of the point at infinity $a=\infty$, the function $f(z)$ can be written as a [[Laurent series]] of special form:3 KB (549 words) - 09:10, 18 January 2014
- ...of points $a$, $b$, $c$, $d$ are said to be congruent if and only if $Q ( a - b ) = Q ( c - d )$. ...L$ be the set of all lines of $( P , \equiv )$. Such a structure is called a Euclidean plane if:12 KB (1,960 words) - 17:44, 1 July 2020
- $#A+1 = 54 n = 0 $#C+1 = 54 : ~/encyclopedia/old_files/data/G044/G.0404970 Graph of a mapping3 KB (568 words) - 19:42, 5 June 2020
- ...$. In a wider sense, a section of any morphism in an arbitrary category is a right-inverse morphism. If $U \subset Y$ is a subset of $Y$, a section over $U$ of $p$ is a mapping $s : U \rightarrow X$ such that $p(s(u)) = u$ for all $u \in U$.769 bytes (149 words) - 18:13, 15 November 2014
- ''$M_0=(x_0,y_0)$ relative to a circle'' $$(x-a)^2+(y-b)^2=R^2$$2 KB (298 words) - 06:25, 12 October 2023
- .... The quotient group $G/Z$ of a group $G$ by its centre is not necessarily a group without centre. <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A.G. Kurosh, "The theory of groups" , '''1–2''' , Chelsea (1955–1956)805 bytes (131 words) - 18:26, 5 December 2014
- Also called ''total variation''. A numerical characteristic of functions of one or more real variables which where $N$ is an arbitrary natural number. The total variation of a function $f: I\to \mathbb R$ is given by16 KB (2,511 words) - 16:07, 12 October 2012
Page text matches
- $#A+1 = 20 n = 0 Consider a regular [[Martingale|martingale]] $ ( X _ {n} , {\mathcal F} _ {n} ) $,3 KB (442 words) - 06:29, 30 May 2020
- $#A+1 = 78 n = 0 A [[Group|group]] $ \{ G; \cdot, \cle \} $3 KB (548 words) - 08:06, 6 June 2020
- ...nts) of a non-empty set $\Omega$ (the space of elementary events) which is a [[Algebra of sets|$\sigma$-algebra]]621 bytes (96 words) - 13:02, 6 December 2012
- ...ce]] $E$ that is simultaneously a [[vector lattice]] and whose topology is a [[locally convex topology]], while the mappings of $E \times E$ into $E$ de ...of a locally convex lattice $E$ into its second dual. The construction of a theory of extension of positive functionals and linear mappings between loc2 KB (289 words) - 16:48, 14 October 2016
- $#A+1 = 34 n = 1 A series defined by the expression4 KB (578 words) - 11:31, 21 March 2022
- ...lelopipedon all faces of which are squares is called a cube. The volume of a parallelopipedon is equal to the product of the area of its base and its he ...opipedon is a special case of a [[Parallelohedron|parallelohedron]] and of a [[Parallelotope|parallelotope]]. Two special parallelopipeda, namely the go1 KB (188 words) - 16:21, 11 April 2014
- ...y in the complex plane $\mathbf C$ having the following property: there is a univalent [[Conformal mapping|conformal mapping]] $z=\phi(w)$ from the disc ...es of analytic functions]] in the disc also hold for functions analytic in a Smirnov domain, and many of these properties hold only in Smirnov domains.3 KB (451 words) - 21:38, 15 December 2020
- $#A+1 = 15 n = 0 $#C+1 = 15 : ~/encyclopedia/old_files/data/K055/K.0505310 Kernel of a summation method3 KB (389 words) - 22:14, 5 June 2020
- ...ons in the alphabet $A$ are defined inductively: 1) every letter of $A$ is a regular expression; and 2) if $R_1$ and $R_2$ are regular expressions, then ...by presenting the set of words derivable in a formal system of the type of a semi-Thue system (see [[Thue system]]), by means of grammars, etc.5 KB (830 words) - 14:27, 12 November 2023
- $#A+1 = 56 n = 0 ...rtial differential equation|hyperbolic partial differential equation]], or a second-order hyperbolic system, in two independent variables with given val5 KB (813 words) - 19:42, 5 June 2020
- $#A+1 = 41 n = 0 ..., reduction of|Quadratic forms, reduction of]]) to canonical form by using a triangular transformation of the unknowns; it was suggested by C.G.J. Jacob7 KB (1,025 words) - 22:14, 5 June 2020
- $#A+1 = 46 n = 0 A branch of mathematical physics dealing with the problems involved in the ma14 KB (2,042 words) - 19:35, 5 June 2020
- $#A+1 = 31 n = 0 and of a rank lower than $ t $,4 KB (563 words) - 17:28, 26 December 2020
- $#A+1 = 15 n = 0 A continuous [[Probability distribution|probability distribution]] with densi3 KB (364 words) - 15:52, 7 June 2020
- ...s $n$, and $x^{m+n} = x^m \star x^n$. The set of powers of $x$ thus forms a [[semi-group]]. * Bruck, Richard Hubert ''A survey of binary systems'', Ergebnisse der Mathematik und ihrer Grenzgebiet524 bytes (78 words) - 10:28, 1 January 2016
- $#A+1 = 24 n = 0 ...: ~/encyclopedia/old_files/data/W097/W.0907400 Weierstrass conditions (for a variational extremum)3 KB (508 words) - 08:28, 6 June 2020
- $#A+1 = 20 n = 0 A square matrix $ A = \| a _ {ik} \| $2 KB (359 words) - 22:10, 5 June 2020
- $#A+1 = 46 n = 1 ...hod|balayage method]]. O. Perron [[#References|[1]]] was the first to give a full exposition of the method of upper and lower functions for this last ca6 KB (849 words) - 19:25, 11 January 2024
- $#A+1 = 61 n = 0 of a projective space $ P ^ {n} $.5 KB (782 words) - 16:44, 4 June 2020
- If an integer $a$ is not divisible by a prime number $p>2$, then the congruence a^{(p-1)/2} \equiv \left({\frac{a}{p}}\right) \pmod p1 KB (217 words) - 07:30, 19 December 2014