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1
Content available Wykres cosinusa jest elipsą
100%
Smoluk A.
Econometrics. Ekonometria. Advances in Applied Data Analytics
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2014
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nr 2(44)
57-61
EN
Periodic function – it is a proposition of a new definition – has as its domain the multiplicative group T = {z ∈C : |z| = 1} of complex numbers with module one. Therefore the graph of the function f : T → R lies on the cylinder T × R, and so the graph of cosine function is the ellipse (math formula)
2
Content available 1D and 2D finite-difference operators for periodic functions on arbitrary mesh
100%
Sobczyk T. J.
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tom Vol. 71, nr 1
265--275
EN
This paper presents novel discrete differential operators for periodic functions of one- and two-variables, which relate the values of the derivatives to the values of the function itself for a set of arbitrarily chosen points over the function’s area. It is very characteristic, that the values of the derivatives at each point depend on the function values at all points in that area. Such operators allow one to easily create finite-difference equations for boundaryvalue problems. The operators are addressed especially to nonlinear differential equations.
3
Content available remote About definition of a periodic function
86%
Rygał G. , Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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tom Vol. 12
375-380
EN
In this paper we consider various definitions of a periodic function and establish connections between them, in particular, we prove equivalence of some of them. In papers and textbooks one can find different definitions of a periodic function. This raises the question which of them are equivalent.
4
Content available Subadditive periodic functions
86%
Matkowski J.
Opuscula Mathematica
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2011
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tom Vol. 31, no. 1
75-96
EN
Some conditions under which any subadditive function is periodic are presented. It is shown that the boundedness from below in a neighborhood of a point of a subadditive periodic (s.p.) function implies its nonnegativity, and the boundedness from above in a neighborhood of a point implies it nonnegativity and global boundedness from above. A necessary and sufficient condition for existence of a subadditive periodic extension of a function ƒ0 : [0, 1) ? R is given. The continuity, differentiability of a s.p. function is discussed, and an example of a continuous nowhere differentiable s.p. function is presented. The functions which are the sums of linear functions and s.p. functions are characterized. The refinements of some known results on the continuity of subadditive functions are presented.
5
Content available remote About definition of a periodic function
86%
Rygał G. , Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
tom Vol. 12
375-380
EN
In this paper we consider various definitions of a periodic function and establish connections between them, in particular, we prove equivalence of some of them. In papers and textbooks one can find different definitions of a periodic function. This raises the question which of them are equivalent.
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