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1
Content available Certain convergence results for homogeneous singular young measures
Puchała Piotr
Journal of Applied Mathematics and Computational Mechanics
|
2023
|
Vol. 22, nr 4
44--52
EN
We consider purely singular homogeneous Young measures associated with elements of sequences of piecewise constant functions and with limits of such sequences. We first consider a case when the limit of a such sequence is piecewise constant. The next point involves the sequences of bounded oscillating functions, divergent in the strong topology in L ∞ , but weakly∗ convergent to a homogeneous Young measure. We also present an example of a fast oscillating sequence, illustrating the result. In the presented results, generalizing to some extent known examples, we try to avoid advanced methods of functional analysis that are usually used when solving problems of this type.
2
Content available Obliczanie granic funkcji rzeczywistych jednej zmiennej rzeczywistej
Macura Janina
MINUT Matematyka i Informatyka na Uczelniach Technicznych
|
2020
|
Nr 2
112-123
PL
Artykuł jest kontynuacją artykułu „Obliczanie granic ciągów o wyrazach rzeczywistych”. Przedstawiono typowe przykłady obliczania granic funkcji rzeczywistych jednej zmiennej rzeczywistej. W związku z tym prezentowane przykłady są bardzo typowe, zawierają dokładne wyjaśnienia, co i dlaczego robimy. Na początku znajduje się lista twierdzeń oraz podstawowych granic, z których będziemy korzystać. Po każdym przykładzie znajdują się dwa bardzo podobne zadania do samodzielnego rozwiązania, na końcu kilka dodatkowych zadań.
3
Content available Discontinuities of real-valued functions of one real variable
Łobos Ewa
MINUT Matematyka i Informatyka na Uczelniach Technicznych
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2019
|
Nr 1
1-9
EN
The paper shows how to identify discontinuities of real valued functions of one real variable and how to determine types of discontinuities. There are a few practical tasks with step by step solutions.
4
Content available Uniformly continuous composition operator in the space of functions of two variables of Bounded ɸ-variation in the sense of Schramm
Aziz W., Ereú T., Merentes N., Sanchez J. L., Wróbel M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2012
|
Vol. 17
7-16
EN
We prove in this paper that if the composition operator H, generated by a function h : I b a x C(Iba) Y , maps ɸBV (Iba ,C) into ɸ2 BV (Iba , Y ) and is uniformly continuous, then the left-left regularization h* of h is an affine function with respect to the third variable.
5
Content available Twisted group algebras of sur-type of finite groups over an integral domain of characteristic p
Klein D.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2012
|
Vol. 17
49-56
EN
Let S be an integral domain of positive characteristic p, which is not a field, S∗ the unit group of S, G a finite group, and SλG the twisted group algebra of the group G over S with a 2-cocycle λ ∈ Z2(G,S∗). Denote by Indm(SλG) the set of isomorphism classes of indecomposable SλGmodules of S-rank m. We exhibit algebras SλG of SUR-type, in the sense that there exists a function fλ : N → N such that fλ(n) ≥ n and Indfλ(n)(SλG) is an infinite set for every integer n > 1.
6
Content available On upper and lower strong quasi-uniform convergence of multivalued maps
Dominik I., Sochaczewska A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2012
|
Vol. 17
25-35
EN
The concept of strong convergence of functions and multifunctions was introduced by I. Kupka, V. Toma and A. Sochaczewska. In this paper we consider new definitions of convergence for the nets of multifunctions – upper and lower strong quasi-uniform convergence.
7
Content available On preponderantly continuous functions
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
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.
8
Content available On cluster sets of connected functions
Jędrzejewski J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
Vol. 14
51-61
EN
In the article we discuss some properties of a few classes of connected functions and cluster sets of functions from those classes.
9
Content available Generalization of probability density of random variables
Ziółkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
Vol. 14
163-172
EN
In this paper we present generalization of probability density of random variables. It is obvious that probability density is definite only for absolute continuous variables. However, in many practical applications we need to define the analogous concept also for variables of other types. It can be easily shown that we are able to generalize the concept of density using distributions, especially Dirac’s delta function.
10
Content available Comparison of ψ -sparse topologies
Goździewicz-Smejda A., Łazarow E.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
Vol. 14
21-36
EN
The paper includes a necessary condition and sufficient conditions under which two ψ -sparse topologies generated by two functions ψ1 and ψ 2 are equal. Additionally we proved that the intersection of all ψ -sparse topologies is equal to the Hashimoto topology.
11
Content available remote Some inequalities connected with a quadratic functional equation
Troczka-Pawelec K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2008
|
Vol. 13
73-79
EN
Let (X, +) be an Abelian group. One can show that a mapping f: X R satisfying the inequality f(x + y) + f(x-y)≤2f(x)+2f(y) (1) for all x, y ∈ X also satisfies the inequalities f(2x + y)≤4f(:c) + f (y) + f (x + y) - f (x - y) and f(2x+y) + f(2x -y)≤ 8f(x) + 2f(y) for all x, y ∈ X. A question of finding sufficient conditions under which the inequalities (1), (2) and (3) are equivalent will be considered. In this note, some properties of the solution of (1) will be proved. We also consider another definition of a subquadratic function given in [1].
12
Content available remote On some properties of connected functions
Jędrzejewski J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2008
|
Vol. 13
15-26
EN
We consider some properties of functions defined in a topological space X with values in another topological space Y. We shall consider some properties of functions defined in a topological space X with values in a topological space Y. Topological terminology is taken from the books General Topology by R. Engelking [1] and General Topolowy by J. L. Kelley [7].
13
Content available remote The use of finite expansion of functions for evaluation of limits
Bryll A., Bryll G., Rygał G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
143-154
14
Content available remote The realisation of selected attributes of „function” using the project method
Orłowska J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
311-318
EN
The notion of function plays a crucial role in teaching mathematics. Why is this important issue so problematic for students? It is worth noticing that precise specification of this notion took place relatively late, in 19th century. This is why it is so important to attempt students” active participation in defining and understanding the notion of „function”.
15
Content available remote Properties of Fourier coefficients of spline wavelets
Šimsová J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
101-106
EN
Periodic B-spline functions have got many useful properties. Especially it is the property of its Fourier coefficients. In this article it is introduced and proved a similar property of Fourier coefficients of spline wavelets.
16
Content available remote Problem of the existence of ω*-primitives
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
61-68
EN
lf (X, ᵨ) is a dense in itself metric space and f : X →ℝ, then we define ω*(f,x) = infr >0 supy,z∈B (x,r) \ {x} ׀ f(y) - f(z)׀. We say that a function F : X →ℝ is an ω*-primitive for f : X →ℝ if ω* (F, .) = f. We discuss problem of the existence of ω*-primitives for an arbitrary upper semicontinuous function f : X → [0, ∞ ) defined on a dense in itself metric space. At the end we show that if an upper semicontinuous function f : X → [0, ∞) is defined on a nonmetrizable topological space, then ω*-primitive may not exists.
17
Content available remote On mistakes connected with differentiating
Sochacki R., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
399-405
EN
Many students have problems with solving tasks concerning the existence of the derivative of a function at a point. In this paper we discuss some of them.
18
Content available remote About definition of a periodic function
Rygał G., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
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.
19
Content available remote About definition of a periodic function
Rygał G., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
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.
20
Content available remote About a distribution of points on a line segment
Cihlář J., Eisenmann P., Krátká M., Vopĕnka P.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
175-184
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