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1
On symmetrically porouscontinuous functions
Kowalczyk S., Turowska M.
Journal of Applied Analysis
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2016
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Vol. 22, nr 2
141--151
EN
In the present paper, we introduce the notion of symmetrically porouscontinuous functions. We investigate some properties of symmetric porouscontinuity and its connections with the notion of porouscontinuity, studied by Borsík and Holos in [2]. We prove that there are 2c symmetrically porouscontinuous functions, which extends results of [1] concerning ρ-upper continuous functions.
2
Content available remote On the k-pseudo symmetric and ordinary differentiation
Łazarow E., Turowska M.
Demonstratio Mathematica
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2016
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Vol. 49, nr 2
155--160
EN
In 1972, S. Valenti introduced the definition of k-pseudo symmetric derivative and has shown that the set of all points of a continuous function, at which there exists a finite k-pseudo symmetric derivative but the finite ordinary derivative does not exist, is of Lebesgue measure zero. In 1993, L. Zajíček has shown that for a continuous function f, the set of all points, at which f is symmetrically differentiable but no differentiable, is σ-(1 – ε) symmetrically porous for every ε > 0. The question arises: can we transferred the Zajíček’s result to the case of the k-pseudo symmetric derivative? In this paper, we shall show that for each 0 < ε < 1 the set of all points of a continuous function, at which there exists a finite k-pseudo symmetric derivative but the finite ordinary derivative does not exist, is σ-(1 – ε)-porous.
3
Content available About differentiability and V BG * class
Turowska M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
245--249
EN
Let X be a finite dimensional real Banach space. We show that if the contingent of the curve Γ : (a, b) → X fulfils some conditions then each parametrization of that curve is V BG * . Stanisław Saks proved that each V BG * function is differentiable at a set of full Lebesgue measure. The result of this paper is a partial converse of that theorem.
4
Content available A note on weakly ϱ-upper continuous functions
Nowakowska K., Turowska M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
195--206
EN
In the article we present definition and some properties of weakly ϱ-upper continuous functions. We find maximal additive and maximal multiplicative families for the class of weakly ϱ-upper continuous functions.
5
Content available On the contingent of the graph of the sum of two mappings
Turowska M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2013
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Vol. 18
55--66
EN
It is shown that the graph of the sum of two Lipschitz mappings of the real line into a normed space of infinite dimension, whose graphs have tangents, need not have a tangent. Moreover, it turns out that the contingent of the graph of their linear combination may depend on the coefficients of that combination in quite "nonlinear" way.
6
Application of uncertain variables to performance analysis of ATM ABR congestion control system
Turowska M.
Systems Science
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2006
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Vol. 32, no 2
37-44
EN
The present study discusses the problem of performance analysis of congestion control system in a computer network. The assessment of performance is performed by determining a certainty index of satisfying the expert's "soft" requirement. The requirement is formulated using the theory of uncertain variables.
7
Effect of the Electrode Material on the Electrochemical Reduction of Some 2,5-Dihydro-1,3,4-thiadiazoles
Turowska M., Mlostoń G., Romański J., Raczak J.
Polish Journal of Chemistry
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2003
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Vol. 77 / nr 2
237-250
EN
During cyclic voltammetric studies of the 2,5-dihydro-1,3,4-thiadiazoles (_3-1,3,4- thiadiazolines) (1a-e) onHMDEin 0.1_10-3 mol/dm3 LiClO4 acetonitrile and aqueousacetonitrile or aqueous-ethanol Britton-Robinson's buffer solutions in second polarization cycle, besides peaks equivalent to polarographic waves, an additional new system of peaks was observed. The corresponding analogous system of additional peaks has not been observed during the reduction of these substances on electrodes of other materials, as i.e., platinum, gold or glassy carbon. This study showed that it results from the oxidation and reduction of organo-mercury compounds, formed in reaction of the electrode material (Hg) with an adsorbed product of 2,5-dihydro-1,3,4-thiadiazoles reduction.
8
Study of Electrochemical Behaviour of Some 2,5-Dihydro-1,3,4-thiadiazoles
Turowska M., G. Mlostoń G., M. Celeda M., J. Raczak J.
Polish Journal of Chemistry
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2002
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Vol. 76 / nr 6
839-855
EN
Polarographic, linear-sweep cyclic voltammetric and coulometric at controlled potential studies of some 2,5-dihydro-1,3,4-thiadiazoles ( 3-1,3,4-thiadiazolines) on mercury electrodes have been performed in acetonitrile over pH range 1.2-13 in water-ethanol and water-acetonitrile mixtures with Britton-Robinson's buffer. Under conditions of present study, thiadiazoles are reduced to respective thiadiazolidines, and the N=N bond is reduced faster than the C=O group. All electrochemical reactions at pH < 7 are pH dependent and at pH > 7 influenced by surface characteristics. Electrode reaction mechanisms are presented and discussed.
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