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1
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.
2
Content available On cluster sets of connected functions
Jędrzejewski J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2009
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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.
3
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
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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.
4
Content available Comparison of ψ -sparse topologies
Goździewicz-Smejda A., Łazarow E.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2009
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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.
5
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
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2007
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Vol. 12
143-154
6
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
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2007
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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”.
7
Content available remote Problem of the existence of ω*-primitives
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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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.
8
Content available remote On mistakes connected with differentiating
Sochacki R., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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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.
9
Content available remote About definition of a periodic function
Rygał G., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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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.
10
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.
11
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
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2007
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Vol. 12
175-184
12
Content available remote Analiza wpływu obróbki cieplnej na niejednorodność osnowy żeliwa sferoidalnego
Dymski S., Trepczyńska-Łent M.
Archiwum Odlewnictwa
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2005
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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.
13
Content available remote Abstract Interpretation against Races
Barbuti R., Cataudella S., Tesei L.
Fundamenta Informaticae
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2004
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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.
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