...ng operator (cf. [[Generating operator of a semi-group|Generating operator of a semi-group]]).
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...part of the homology group with as domain of coefficients the group $\ZZ$ of integers, if this homology group is finitely generated. Named after E. Bett
...top">[1]</TD> <TD valign="top"> H. Seifert, W. Threlfall, "A textbook of topology" , Acad. Press (1980) (Translated from German)</TD></TR><TR><TD
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...f [[tiling]]s, '''protoset''' is sometimes used as abbreviation for "''set of [[prototile]]s''".
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...ential-geometric structures on fibre spaces that later simply became known as connections. (See [[Connection|Connection]].)
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$#C+1 = 8 : ~/encyclopedia/old_files/data/D032/D.0302650 Diophantine problems of additive type
...[[Additive problems|additive problems]], i.e. as problems of decomposition of an integer $ n $(
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...ar polyhedra (Platonic solids); if the edge length is $a$, then the volume of the octahedron is
...n nature as a crystal of chrome alum. In terms of its circumradius as unit of measurement, its six vertices have Cartesian coordinates
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''of a curve $ y = f(x) $
A straight line the distance of which from the point $ (x, f(x)) $
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Any topological space for which $X$ serves as a retract (cf. [[Retract of a topological space]]).
...fact no name for this concept. The standard Western usage of dominating is as follows: A space $X$ is said to dominate a space $Y$ if and only if there a
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...e eight cases, each of which can be reduced to a linear recurrent sequence of degree six in a completely standard way. I wonder whether this is really w
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== mathematics free of intuition ==
...then he/she explains the same to a computer in 3 months! This is the cost of no-intuition. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris T
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...o the given test" . The term "testing" is basically used in combinations as "repeated testing" , "independent testing" , "testing in a Markov chain"
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...f the image $\mathrm{im}\, d$ are called ''boundaries''. The ''homology'' of $C$ is the quotient $\ker d / \mathrm{im}\,d$.
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...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.
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...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.
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..."Comments" section. Some literature is given in that section, but a number of more recent books should be used, too.
...but the normal approximation holds on the logarithmic level is well-known as ''moderate deviations'' (only mentioned twice in our encyclopedia: in "[[Wi
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...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>
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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.
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''quadratic variance, standard deviation, of quantities $x_1,\dots,x_n$ from $a$''
The square root of the expression
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...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.
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...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
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