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1
Content available remote 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
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2011
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Vol. 16, no 3
893-898
EN
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.
2
Content available remote On the set-theoretic strength of countable compactness of the Tychonoff product 2R
Tachtsis E.
Bulletin of the Polish Academy of Sciences. Mathematics
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2010
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Vol. 58, no 2
91-107
EN
We work in ZF set theory (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) and show the following: 1. The Axiom of Choice for well-ordered families of non-empty sets (ACWO) does not imply "the Tychonoff product 2R, where 2 is the discrete space {0,1}, is countably compact" in ZF. This answers in the negative the following question from Keremedis, Felouzis, and Tachtsis [Bull. Polish Acad. Sci. Math. 55 (2007)]: Does the Countable Axiom of Choice for families of non-empty sets of reals imply 2R is countably compact in ZF? 2. Assuming the Countable Axiom of Multiple Choice (CMC), the statements "every infinite subset of 2R has an accumulation point", "every countably infinite subset of 2R has an accumulation point", "2R is countably compact", and UF(ω) = "there is a free ultrafilter on ω" are pairwise equivalent. 3. The statements "for every infinite set X, every countably infinite subset of 2X has an accumulation point", "every countably infinite subset of 2R has an accumulation point", and UF(ω) are, in ZF, pairwise equivalent. Hence, in ZF, the statement "2R is countably compact "implies UF(ω). 4. The statement "every infinite subset of 2R has an accumulation point" implies "every countable family of 2-element subsets of the powerset Ρ(R) of R has a choice function". 5. The Countable Axiom of Choice restricted to non-empty finite sets, (CACfin), is, in ZF, strictly weaker than the statement "for every infinite set X, 2X is countably compact".
3
Content available On preponderantly continuous functions
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2009
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Vol. 14
75-86
EN
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.
4
Content available remote Construction of an Uncountable Difference between Φ(B) and Φƒ(B)
Campbell J., Svanson D.
Bulletin of the Polish Academy of Sciences. Mathematics
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2008
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Vol. 56, no 2
121-130
EN
We construct a set B and homeomorphism ƒ where ƒ and ƒ[sup]-1 have property N such that the symmetric difference between the sets of density points and of ƒ-density points of B is uncountable.
5
Content available remote On the almost periodic functions in the sense of Levitan
Michałowicz A., Stoiński S.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2007
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Vol. 47, [Z] 2
149-159
EN
In this note we present some theorems on the superposition of an (NVp)-almost periodic (a.p. for short) function, a μ-a.p. function and an (Nμ)-a.p. function. Moreover, we prove a theorem on the bounded primary function of an (NS^p)-a.p. function. Finally, we prove that the inverse of a V_p-a.p. function is (NV_p)-a.p.
6
Content available remote A note on measures on time scales
Rzeżuchowski T.
Demonstratio Mathematica
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2005
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Vol. 38, nr 1
79--84
EN
A connection between the measures used on time scales and usual Lebesgue measure is established and applied to simple justifications of some recently published results on Vitali covering theorem and (delta)-differentiability of monotone functions defined on time scales.
7
Content available remote An application of modular spaces to approximation problems, IX
Stoiński S.
Fasciculi Mathematici
|
2002
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Nr 33
89-97
EN
By means of terms of a sequence (pn), where pn, n = l,2,..., are pseudomodulars, and by means of an infinite matrix A = [amn ] of non-negative numbers we shall construct the modular spaces XpAos' and Xp^os. Then we shall approximate elements of these spaces by means of terms of a sequence (p.), where p, i = l,2,..., are pseudomodulars. In particular, we will investigate the special cases when pn and pt are singular integrals.
8
Content available remote An application of modular spaces to approximation problems, VII
Stoiński S.
Demonstratio Mathematica
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2000
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Vol. 33, nr 4
805-814
9
Content available remote On compactness of almost periodic functions in the Lebesgue measure
Stoiński S.
Fasciculi Mathematici
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1999
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Nr 30
171-175
10
Content available remote Approximation with respect to a measure in a modular space, VI
Stoiński S.
Fasciculi Mathematici
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1999
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Nr 29
125-131
EN
Elements of a modular subspace of [...] are approximated by certain singular integrals.
11
Content available remote Approximation by means of certain non-linear operators in some modular spaces
Stoiński S.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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1999
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[Z] 39
173-180
EN
Elements of certain modular spaces are approximated by certain singular integrals.
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