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1
Content available Schramm spaces and composition operators
Wróbel Małgorzata
Journal of Applied Mathematics and Computational Mechanics
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2023
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Vol. 22, nr 2
87--98
EN
We give some properties of Schramm functions; among others, we prove that the family of all continuous piecewise linear functions defined on a real interval I is contained in the space ΦBV (I) of functions of bounded variation in the sense of Schramm. Moreover, we show that the generating function of the corresponding Nemytskij composition operator acting between Banach spaces CΦBV (I) of continuous functions of bounded Schramm variation has to be continuous and additionally we show that a space CΦBV (I) has the Matkowski property.
2
Content available Operators with memory in Schramm spaces
Wróbel Małgorzata
Journal of Applied Mathematics and Computational Mechanics
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2023
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Vol. 22, nr 3
69--80
EN
We show that every operator with memory acting between Banach spaces CΦBV(I) of continuous functions of bounded variation in the sense of Schramm defined on a compact interval I of a real axis, is a Nemytskij composition operator with the continuous generating function. Moreover, some consequences for uniformly bounded operators with memory will be given. As a by-product, we obtain that a Banach space CΦBV(I) has the uniform Matkowski property.
3
Content available remote On almost e-I-continuous functions
AL-Omeri Wadei, Noiri Takashi
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
168--177
EN
This work is concerned with a new class of functions called almost e-I-continuous functions containing the class of almost e-continuous functions. This notion is stronger than almost δβI-continuous functions and is weaker than both almost e-continuous functions and e-I-continuous functions. Relationships between this new class and other classes of functions are investigated and some characterizations of this new class of functions are studied.
4
Content available Some properties of openly ϱ-continuous functions
Nowakowska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2016
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Vol. 21
73--84
EN
In the paper we present definition and some properties of openly ϱ-upper continuous functions. Connections with ϱ-upper continuous and porouscontinuous functions are studied.
5
Content available On e-I-open sets, e-I-continuous functions and decomposition of continuity
Al-Omeri W., Noorani M.S.M., Al-Omari A.
Journal of Mathematics and Applications
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2015
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Vol. 38
15--31
EN
In this paper, we introduce the notations of e-I-open sets and strong B*I -set to obtain a decomposition of continuing via idealization. Additionally, we investigate properties of e-I-open sets and strong B*I -set. Also we studied some more properties of e-I-open sets and obtained several characterizations of e-I-continuous functions and investigate their relationship with other types of functions.
6
Content available remote Rδ-supercontinuous functions
Kohli J. K., Tyagi B. K., Singh D., Aggarwal J.
Demonstratio Mathematica
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2014
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Vol. 47, nr 2
433--448
EN
A new class of functions called ‘Rδ-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of Rδ-supercontinuous functions (Math. Bohem., to appear) properly contains the class of Rz-supercontinuous functions which in its turn properly contains the class of Rcl-supercontinuous functions (Demonstratio Math. 46(1) (2013), 229–244) and so includes all cl-supercontinuous (=clopen continuous) functions (Applied Gen. Topol. 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772) and is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703–723).
7
Maximal classes for rho-upper continuous functions
Kowalczyk S., Nowakowska K.
Journal of Applied Analysis
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2013
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Vol. 19, nr 1
69--89
EN
In this paper we present some properties of ρ-upper continuous functions. We give a condition equivalent to ρ-upper continuity and find maximal additive and maximal multiplicative classes for the family of ρ-upper continuous functions. These classes depend on whether ρ<1 or ρ=1. To describe maximal additive and maximal multiplicative classes for 1-upper continuous function, we need the notions of sparsity and T*topology.
8
Content available On local Whitney convergence
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2012
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Vol. 17
57-68
EN
In this paper we will give definitions of local Whitney convergence in F(X,Y ) and in C(X,Y ), where X is a topological space, (Y,d) is a metric space and F(X,Y ) is the space of all functions from X to Y and C(X,Y ) is the space of all continuous functions from X to Y . We will study some properties of this notion and connections with other kinds of convergence.
9
Content available remote Exponent in one of the variables
Mityushev V.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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Vol. 12
77-79
EN
A periodicity functional equation of one complex variable which characterizes the exponential function is discussed. This functional equation can be generalized to equation for functions depending on two complex variables. It is conjectured that the second functional equation also characterizes the exponent. Applications to representations of complex continuous elementary functions are discussed.
10
Content available remote On gβ-regular and gβ-normal spaces
Tahiliani S.
Demonstratio Mathematica
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2007
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Vol. 40, nr 3
739-743
EN
The aim of this paper is to introduce and study two new classes of spaces, called gβ-regular and gβ-normal spaces. The concept of gβ-regularity and gβ-normality are separation properties obtained by utilizing gβ-closed sets. Recall that a subset A of a space (X, r ) is called gβ-closed if β Cl(A) is a subset of U where A is a subset of U and U is open in X.
11
Content available remote Knot Point Method in Extrapolation of Boundary Measurement Results
Pisarek J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2006
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Vol. 11
67--78
EN
The new measurement technique that relies on distinguishing the ranges in object's space in which the searched quantities are approximated by multiparameter continuous functions has been introduced. The parameters of these functions are calculated by minimizing the functional describing the distance between different functions determined at the same points and distance between numerical solution and experimental results and assumed’a priori’ theoretical guidelines. Functions’ spaces might be determined in any way and might be changed during the computation. This method is especially usefull in extrapolation of the boundary measurement results on the object interior and in joining the local and whole object (global) solutions.
12
Content available remote Czebyszew, Weierstrass, Jackson, Bernstein i ich kontynuatorzy
Pleśniak W.
Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne
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2004
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[Z] 40
97-106
13
Modelowanie maszyn szyjących
Zajączkowski J.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
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2001
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z. 17
231-236
PL
W pracy opisano algorytm tworzenia modeli matematycznych maszyn szyjących. Uwzględniono silnik indukcyjny, przekładnię pasową oraz mechanizmy dźwigniowe i krzywkowe. Równania dynamiczne ruchu wyprowadzono korzystając z zasady prac wirtualnych i zasady d’ Alamberta. Związki kinematyczne znaleziono wykorzystując metodę Brenta. Ich postać dyskretną zastąpiono funkcjami ciągłymi korzystają z wielomianów. Przybliżenia atraktorów znaleziono całkując układ równań numerycznie przez odpowiednio długi czas.
EN
An algorithm of creating mathematical model of a sewing machine is described in this paper. The electric motor, the belt drive, the linkage and cam mechanisms are taken into account. The equations of the motion are derived by the use of the principle of virtual work together with d ’ Alambert principle. The kinematics relationships were found by the utilization of Brent method. Their discrete form was replaced by a continuous one using polynomials. The approximations of attractors were found by integrating the set of differential eąuations for sufficiently long time.
14
Content available remote On almost weakly continuous functions
Jafari S., Noiri T.
Demonstratio Mathematica
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1998
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Vol. 31, nr 2
437-443
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