$#A+1 = 61 n = 0
$#C+1 = 61 : ~/encyclopedia/old_files/data/D032/D.0302330 Differentiation of a mapping
6 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
$#A+1 = 54 n = 0
$#C+1 = 54 : ~/encyclopedia/old_files/data/G044/G.0404970 Graph of a mapping
3 KB (568 words) - 19:42, 5 June 2020
...$. 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 $u \in U$.
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''$M_0=(x_0,y_0)$ relative to a circle''
$$(x-a)^2+(y-b)^2=R^2$$
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.... 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 by
16 KB (2,511 words) - 16:07, 12 October 2012
A non-negative real-valued function $d$ defined on the set of all pairs of el
...(relative to $d$) if and only if $d(x,A) > 0$ for each $x \in X \setminus A$. Here
2 KB (339 words) - 20:16, 11 December 2016
''$G$ by a subgroup $H$ (from the left)''
A set of elements of $G$ of the form
1 KB (215 words) - 20:26, 4 December 2014
...ages/c/c025/c025860/c02586012.png" /> is
a continuous representation, then
a contraction of <img align="absmiddle" border="0" src="https://www.encyclope
...w.encyclopediaofmath.org/legacyimages/c/c025/c025860/c02586053.png" /> and
a representation <img align="absmiddle" border="0" src="https://www.encyclope
8 KB (1,091 words) - 17:21, 7 February 2011
$#A+1 = 76 n = 0
$#C+1 = 76 : ~/encyclopedia/old_files/data/I052/I.0502440 Inversion of a matrix
11 KB (1,584 words) - 22:13, 5 June 2020
#REDIRECT [[Homology of a complex]]
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The centre of a ring $R$ is
$$Z=\{z: az = za \textrm{ for all }a \in R\}.$$
434 bytes (78 words) - 21:43, 5 March 2012
''in a group $G$''
...$G$ is usually denoted by $\left|G:H\right|$. The product of the order of a subgroup $H$ by its index $\left|G:H\right|$ is equal to the order of $G$ (
1 KB (186 words) - 11:18, 20 April 2012
$#A+1 = 29 n = 1
$#C+1 = 29 : ~/encyclopedia/old_files/data/R077/R.0707470 Rank of a module
3 KB (439 words) - 08:09, 6 June 2020
...icient|asymmetry coefficient]] is positive (negative). If the asymmetry of a distribution is positive (negative), then the "longer" part of the densit
In Western literature one commonly calls this notion the skewness of a distribution, and accordingly one speaks of the skewness coefficient.
589 bytes (87 words) - 17:11, 7 February 2011
$#A+1 = 38 n = 0
$#C+1 = 38 : ~/encyclopedia/old_files/data/G043/G.0403990 Genus of a curve
3 KB (483 words) - 06:28, 31 March 2023
$#A+1 = 39 n = 1
$#C+1 = 39 : ~/encyclopedia/old_files/data/D030/D.0300900 Degree of a mapping,
4 KB (562 words) - 17:50, 13 January 2024
''$N$ to a base $a$''
...very positive number $N$ and given base $a>0$, $a\neq1$, there corresponds a unique real logarithm (logarithms of negative numbers are complex numbers).
3 KB (453 words) - 15:11, 19 August 2014
$#A+1 = 14 n = 0
$#C+1 = 14 : ~/encyclopedia/old_files/data/B017/B.0107320 Boundary (of a manifold)
1 KB (204 words) - 06:28, 30 May 2020
\left[ \int_{a}^{b}f(x)g(x)\,dx\right]^2 \le \int_{a}^{b}f^2(x)\,dx \int_{a}^{b}g^2(x)\,dx.
...; however, Bunyakovskii published his study as early as 1859, whereas in H.A. Schwarz' work this inequality appeared as late as 1884 (without any refere
2 KB (248 words) - 09:09, 31 May 2016
''of an $m \times n$-matrix $A = \left\Vert a_{ij} \right\Vert$''
\mathrm{per}(A) = \sum_\sigma a_{1\sigma(1)}\cdots a_{m\sigma(m)}
8 KB (1,228 words) - 19:13, 17 March 2023
$#A+1 = 8 n = 1
A Carleman operator on the space $ L _ {2} ( X, \mu ) $
2 KB (299 words) - 09:13, 26 March 2023
...bb{R}^n$ with an [[inner product]] $(x,y)$, $x,y\in\mathbb{R}^n$, which in a suitably chosen ([[Cartesian orthogonal coordinate system|Cartesian]]) coor
872 bytes (132 words) - 14:38, 1 November 2023
$#A+1 = 7 n = 0
A [[Propositional calculus|propositional calculus]] using only the primitive
2 KB (329 words) - 22:11, 5 June 2020
...summation method]] for summing series of numbers and functions, defined by a sequence of functions
where $ \Gamma(x) $ is the gamma-function. A series
2 KB (377 words) - 02:56, 2 June 2013
''of three points $M_1,M,M_2$ on a straight line''
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$A \subset {\mathbb R}$ not containing $m$ in its closure,
$P(\bar X_n \in A) \to 0$ as $n \to \infty$, but does not tell us how fast
13 KB (2,280 words) - 10:48, 28 October 2023
$#A+1 = 90 n = 0
...rhood of the identity, see [[#References|[1]]]). The precise definition of a local topological group is as follows.
6 KB (894 words) - 22:17, 5 June 2020
$#A+1 = 37 n = 0
be a finite group. The intertwining number between two representations $ \pi _
3 KB (382 words) - 04:11, 6 June 2020
...geneous structures), etc. The name finite mathematics is sometimes used as a synonym for discrete mathematics and discrete analysis. In what follows the
...of investigation will depend on the objective of the study and on whether a discrete or continuous model of the phenomenon under study is to be conside
9 KB (1,264 words) - 16:56, 15 April 2012
$#A+1 = 37 n = 0
A [[Bilinear form|bilinear form]] $ B ( f , g) $
4 KB (649 words) - 08:03, 6 June 2020
$#A+1 = 56 n = 1
$#C+1 = 56 : ~/encyclopedia/old_files/data/A011/A.0101860 Algorithmic problem
21 KB (3,264 words) - 06:46, 26 March 2023
$#A+1 = 20 n = 0
and let $ A _ {1} \dots A _ {n} $
3 KB (421 words) - 08:29, 6 June 2020
$#A+1 = 54 n = 0
...n [[#References|[1]]] as a generalization of the method of straight lines, a generalization of it with the introduction of smoothened functions was give
11 KB (1,704 words) - 22:12, 5 June 2020
''of a set $M$ in a metric space $R$''
...^k$ in a Riemannian space $V^n$, then the equi-distant of $M$ is given (in a more restricted sense) by the set of end-points of the segments of equal le
1 KB (212 words) - 21:08, 14 April 2014
$#A+1 = 72 n = 0
$#C+1 = 72 : ~/encyclopedia/old_files/data/V096/V.0906430 Vector field on a manifold
6 KB (884 words) - 08:28, 6 June 2020
$#A+1 = 47 n = 0
...quite good smoothness properties; it was introduced in potential theory by A.M. Lyapunov at the turn into the 20th century.
4 KB (507 words) - 04:11, 6 June 2020
$#A+1 = 15 n = 0
A continuous [[Probability distribution|probability distribution]] with densi
3 KB (364 words) - 15:52, 7 June 2020
...chwarzian derivative of the function $z(t)$ and is denoted by $\{z,t\}$. H.A. Schwarz applied this equation in his studies [[#References|[1]]].
If $x_1(t),x_2(t)$ is a [[Fundamental system of solutions|fundamental system of solutions]] of the
2 KB (337 words) - 17:29, 14 February 2020