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1
Content available remote Generalized parabolic Marcinkiewicz integrals associated with polynomial compound curves with rough kernels
Ali Mohammed, Katatbeh Qutaibeh
Demonstratio Mathematica
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2020
|
Vol. 53, nr 1
44--57
EN
In this article, we study the generalized parabolic parametric Marcinkiewicz integral operators M(r)Ω,h,Φ,λ related to polynomial compound curves. Under some weak conditions on the kernels, we establish appropriate estimates of these operators. By the virtue of the obtained estimates along with an extrapolation argument, we give the boundedness of the aforementioned operators from Triebel-Lizorkin spaces to Lp spaces under weaker conditions on Ω and h. Our results represent significant improvements and natural extensions of what was known previously.
2
Content available Differentiation and integration by using matrix inversion
Matlak D., Matlak J., Słota D., Wituła R.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 2
63--71
EN
In the paper certain examples of applications of the matrix inverses for generating and calculating the integrals are presented.
3
Content available The projective representations types of finite groups over a ring of formal power series
Klein D.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2009
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Vol. 14
63-73
EN
Let F be a field of characteristic p >0,S=F[[X]],S∗ the unit group of S, and W a subgroup of S ∗. We characterize finite groups depending on a projective (S,W)-representation type. We also give necessary and sufficient conditions for a finite group and its Sylow p-subgroups to be of the same projective (S,W) -representation type.
4
Content available Derivative of a function at a point and integral by professor Igor Kluvánek
Gunčaga J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2009
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Vol. 14
37-50
EN
Professor Igor Kluvánek had developed a unique course of calculus (mathematical analysis) to teach students the differential and integral calculus. In the present paper, this concept is briefly outlined. The notion of derivative is introduced via continuity. The definition of integral given in this article applies an idea of Archimedes.
5
Content available remote New integral and finite difference inequalities in three variables
Pachpatte B.
Demonstratio Mathematica
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2009
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Vol. 42, nr 2
339-349
EN
The objective of the present paper is to derive new estimates on some fundamental integral and finite difference inequalities in three variables which can be used as tools in the study of certain integral and sum-difference equations. Some applications are also given to convey the importance of one of our result.
6
Content available remote Strong maximum principles for infinite systems of parabolic differential-functional inequalities with nonstandard initial inequalities with integrals
Brandys J.
Demonstratio Mathematica
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2008
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Vol. 41, nr 3
571-581
EN
In this paper we consider infinite systems of parabolic differential-functional inequalities with nonstandard initial inequalities with integrals. For that systems we give strong maximum principles in relatively arbitrary (n+1)-dimensional time-space sets more general than the cylindrical domain.
7
Content available remote The corollary of green's theorem for curvilinear integrals
Bittnerová D.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
17-22
8
Globalne obliczanie całek po obszarze w purc dla dwuwymiarowych zagadnień brzegowych modelowanych równaniem Naviera-Lamego i Poissona
Zieniuk E., Szerszeń K., Bołtuć A.
Modelowanie Inżynierskie
|
2007
|
T. 2, nr 33
181-186
PL
W pracy przedstawiono globalny sposób numerycznego obliczania całek powierzchniowych w dwuwymiarowych zagadnieniach brzegowych. Prezentowana technika opiera się na matematycznym zdefiniowaniu obszarów za pomocą parametrycznych płatów powierzchniowych oraz wykorzystaniu kwadratur całkowania numerycznego wyższych rzędów. Praktyczną realizację proponowanej procedury przedstawiono dla zagadnień brzegowych definiowanych równaniem Poissona.
EN
The paper presents a novel technique for global considerations and numerical integration of domains in 2D boundary problems. It base on computation of these integrals in global way, i.e. without division of the domain into cells. In proposed approach the domain is treated globally as single parametric surface and using numerical quadratures of high orders. Included numerical examples for boundary problems described by Poisson confirm high accuracy of proposed method compared with analytical results
9
Content available remote The existence theory for the differential equation xm(t)=f(t,x) in Banach spaces and Henstock-Kurzweil integral
Sikorska-Nowak A.
Demonstratio Mathematica
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2007
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Vol. 40, nr 1
115-124
EN
Using the properties of the Henstock–Kurzweil integral and corresponding theorems, we prove the existence theorem for the equation x(m)(t) = f(t, x) in a Banach space, where f is HL integrable and satis.es certain conditions. Our fundamental tool is the measure of noncompactness developed by Kuratowski and Hausdorff.
10
Content available remote New inequalities of Cebysev type for double integrals
Pachpatte B.
Demonstratio Mathematica
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2007
|
Vol. 40, nr 1
43-50
EN
In this paper, we establish new inequalities of Čebyšev type involving functions of two independent variables by using certain integral identities.
11
Content available remote Parametrizations of integrals
Biernat G.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2005
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Vol. 4, nr 1
8-12
EN
In the present paper I give parametric formulas of integrals of meromorphic forms in the case of C2.
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