...f the image $\mathrm{im}\, d$ are called ''boundaries''. The ''homology'' of $C$ is the quotient $\ker d / \mathrm{im}\,d$.
513 bytes (78 words) - 14:52, 8 April 2023
...tained as the extension of the cyclic group of order $2$ by a cyclic group of order $2n$. It has the presentation $\langle n,2,2 \rangle$ and [[group pr
It may be realised as a subgroup of the [[unit quaternion]]s.
601 bytes (92 words) - 20:50, 23 November 2023
...ithmetic functions that can be stated as answers to problems on the number of integral points (cf. [[Integral point|Integral point]]) in some manifolds,
...isor problems]] (P.G.L. Dirichlet) are classical (starting points) as well as their numerous generalizations.
1 KB (188 words) - 17:31, 30 April 2014
...approximation of functions. Nowadays the phrase "the constructive theory of functions" is seldom used.
...G. Alexits (ed.) S.B. Stechkin (ed.) , ''Proc. Conf. Constructive Theory of Functions'' , Akad. Kindó (1969) pp. 19–26</TD></TR></table>
2 KB (252 words) - 17:17, 7 February 2011
See [[Algebraic systems, quasi-variety of|Algebraic systems, quasi-variety of]].
...ally called Horn sentences. Correspondingly, a quasi-variety is also known as a universal Horn class; it is also called a quasi-primitive class.
607 bytes (77 words) - 17:15, 7 February 2011
''quadratic variance, standard deviation, of quantities $x_1,\dots,x_n$ from $a$''
The square root of the expression
2 KB (285 words) - 14:22, 30 December 2018
...ations includes, first of all, ordinary differential equations and systems of the form
...l as their corresponding difference equations, usually belong to the class of evolution equations.
3 KB (443 words) - 15:35, 14 February 2020
...ncountable metrizable space contains an uncountable subspace that, as well as its complement, is totally imperfect.
A subset of $\mathbf R$ such that it and its complement are totally imperfect is usuall
732 bytes (104 words) - 12:02, 5 July 2014
''in the theory of partial differential equations''
The same as a [[Characteristic|characteristic]].
101 bytes (13 words) - 16:57, 7 February 2011
''of a topological space $X$''
...as the same [[homotopy type]] as does $X$. See also [[Retract]]; [[Retract of a topological space]].
536 bytes (94 words) - 19:45, 5 February 2016
...egardless of its origin. A syntactic language is used to study this aspect of formal systems.
...a formal system, two languages are connected: one is the research language of the formal system itself (the object language) and the other is that in whi
2 KB (394 words) - 17:28, 7 February 2011
''of a stochastic process''
The same as the [[Correlogram|correlogram]].
73 bytes (10 words) - 17:04, 7 February 2011
...function (or that of some derivative of it) or a majorant of it may figure as $\phi(\tau)$.
...f. [[Approximation of functions, direct and inverse theorems|Approximation of functions, direct and inverse theorems]]).
2 KB (326 words) - 09:43, 26 April 2014
Out of 20 formulas, 20 were replaced by TEX code.-->
...ports. It can be extended as a sheaf morphism to an imbedding of the space of distributions $\mathcal{D} ^ { \prime } ( \Omega )$.
2 KB (342 words) - 16:45, 1 July 2020
...nd [[Non-Euclidean geometries|non-Euclidean geometries]]. The trigonometry of a sphere in Euclidean space is called [[Spherical trigonometry|spherical tr
639 bytes (81 words) - 17:07, 7 February 2011
...which any even natural number larger than 2 can be represented as the sum of two prime numbers.
...oth the Goldbach–Euler problem and the more general problem of solvability of the linear Diophantine equation
1 KB (201 words) - 20:18, 14 October 2014
...ins unchanged in all its applications. The number of possible applications of a given rule, however, is in principle unlimited.
...ithms, whether $P_0$ is deducible from $P_1,\ldots,P_l$ by one application of the rule.
3 KB (431 words) - 19:19, 17 October 2014
...his inequality appeared as late as 1884 (without any reference to the work of Bunyakovskii).
2. W. Rudin, "Principles of mathematical analysis" , McGraw-Hill (1953)
2 KB (248 words) - 09:09, 31 May 2016
...tertiary ideals are the same as [[primary ideal]]s (cf. [[Additive theory of ideals]]; [[Primary decomposition]]).
...there exists a tertiary radical, $\mathrm{ter}(Q)$, the largest ideal $T$ of $R$ such that, for any ideal $B$,
2 KB (297 words) - 19:23, 5 October 2017
...h any node and connect it to the node nearest to it. Given a connected set of nodes, take the unconnected node that is nearest to one in the connected se
...ideas. See [[#References|[a1]]] for more details and for the justification of such methods.
2 KB (387 words) - 15:16, 20 November 2014