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Diophantine approximations and almost periodic functions

Nawrocki A.

Demonstratio Mathematica

2017

Vol. 50, nr 1

100--104

In this paper we investigate the asymptotic behaviour of the classical continuous and unbounded almost periodic function in the Lebesgue measure. Using diophantine approximations we show that this function can be estimated by functions of polynomial type and we give the best polynomial estimation.

Ellipses numbers and geometric measure representations

Richter W.-D.

Journal of Applied Analysis

2011

Vol. 17, nr 2

165-179

Ellipses will be considered as subsets of suitably defined Minkowski planes in such a way that, additionally to the well-known area content property A(r) = Π (a,b) r 2, the number Π (a,b) = abΠ reflects a generalized circumference property U (a,b)(r) = 2Π (a,b) r of the ellipses E (a,b)(r) with main axes of lengths 2ra and 2rb, respectively. In this sense, the number Π (a,b) is an ellipse number w.r.t. the Minkowski functional r of the reference set E (a,b)(1). This approach is closely connected with a generalization of the method of indivisibles and avoids elliptical integrals. Further, several properties of both a generalized arc-length measure and the ellipses numbers will be discussed, e.g. disintegration of the Lebesgue measure and an elliptically contoured Gaussian measure indivisiblen representation, wherein the ellipses numbers occur in a natural way as norming constants.

Creep transition stresses in a spherical shell under internal pressure by using the lebesgue measure concept

Pankaj T.

International Journal of Applied Mechanics and Engineering

2011

Vol. 16, no 3

893-898

The problem of elastic-plastic transition stresses in a spherical shell under internal pressure by using the lebesgue measure temperature are solved by using the concept of generalized strain measure. The result are same as given by Hulsurkar.

On preponderantly continuous functions

Kowalczyk S.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2009

Vol. 14

75-86

In the present paper, a few different notions of preponderant continuity of a real function are discussed. We study the relationship between them and give some properties of preponderant continuity.