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1
Content available remote Obliczanie granic funkcji rzeczywistych jednej zmiennej rzeczywistej
Macura Janina
MINUT Matematyka i Informatyka na Uczelniach Technicznych
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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.
2
Content available remote Discontinuities of real-valued functions of one real variable
Łobos Ewa
MINUT Matematyka i Informatyka na Uczelniach Technicznych
|
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.
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 On cluster sets of connected functions
Jędrzejewski J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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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.
5
Content available Generalization of probability density of random variables
Ziółkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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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.
6
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.
7
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].
8
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].
9
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
10
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”.
11
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.
12
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.
13
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.
14
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.
15
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
16
Content available remote Analiza wpływu obróbki cieplnej na niejednorodność osnowy żeliwa sferoidalnego
Dymski S., Trepczyńska-Łent M.
Archiwum Odlewnictwa
|
2005
|
R. 5, nr 17
341--352
PL
Mikrosegregacja pierwiastków w żeliwie sferoidalnym ma wpływ na przemiany struktury i własności mechaniczne. Trzy rodzaje niestopowego żeliwa sferoidalnego poddano różnym operacjom cieplnym, po czym wyznaczono zawartość krzemu i manganu w ziarnach eutektycznych osnowy metalowej żeliwa. Z wykorzystaniem sztucznych sieci neuronowych wyznaczono równanie matematyczne i wartości współczynników. Stwierdzono wpływ operacji cieplnych na niejednorodność Si i Mn.
EN
The microsegregation of alloying elements in ductile cast iron has an of influence on structural change and mechanical properties. Three melts of ductile iron were subjected different operations of heat treatment, and next content of Si and Mn in eutectic cells of matrix metals cast iron were determined. With use of neuron artificial network mathematic function and values of coefficients function were calculated. The influence of the operations of heat treatment on inhomogeneity of Si and Mn it were affirmed found that.
17
Content available remote Abstract Interpretation against Races
Barbuti R., Cataudella S., Tesei L.
Fundamenta Informaticae
|
2004
|
Vol. 60, nr 1-4
67--79
EN
In this paper we investigate the use of abstract interpretation techniques for statically preventing race conditions. To this purpose we enrich the concurrent object calculus concV by annotating terms with the set of ``locks'' owned at any time. We use an abstract form of the object calculus to check the absence of race conditions. We show that abstract interpretation is more flexible than type analyses, and it allows to certify as ``race free'' a larger class of programs.
18
Content available remote The Principles of Creating the Critical Path of the Formation
Borowik A., Piech H.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1998
|
Vol. 4
74-84
EN
Assumptions and the algorithm for creating the critical path the formation of variables have been presented for programming procedures. The algorithm is based on the parallelization map and information related to the actions that are performed when calculating the values of variables in the particular phases of parallelization. Also, information was used in the algorithm for the analysis, which related to the time of the execution of the particular actions, and each time the time of the operation of each node was determined. i.e. the time of the calculation of a variable in the particular phase of its modification. The critical paths created are used for the optimization of distribution in multi-processor systems with a limited number of conversion nodes.
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