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  1. 4 Demonstratio Mathematica
  2. 4 Fasciculi Mathematici
  3. 4 Journal of Mathematics and Applications
  4. 3 Przegląd Elektrotechniczny
  5. 2 Computer Assisted Mechanics and Engineering Sciences
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  1. 2 Brzoza A.
  2. 2 Hetmaniok E.
  3. 2 Słota D.
  4. 2 Wróbel A.
  5. 2 Zielonka A.
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  1. 3 2020
  2. 1 2019
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1
Content available On the existence of continuous positive monotonic solutions of a self-reference quadratic integral equation
El-Sayed Ahmed M.A., Ebead Hanaa R.
Journal of Mathematics and Applications
|
2020
|
Vol. 43
67--80
EN
In this work we study the existence of positive monotonic solutions of a self-reference quadratic integral equation in the class of continuous real valued functions. The continuous dependence of the uniquesolution will be proved. Some examples will be given.
2
Content available remote On perturbed quadratic integral equations and initial value problem with nonlocal conditions in Orlicz spaces
Metwali Mohamed M. A.
Demonstratio Mathematica
|
2020
|
Vol. 53, nr 1
86--94
EN
The existence of a.e. monotonic solutions for functional quadratic Hammerstein integral equations with the perturbation term is discussed in Orlicz spaces. We utilize the strategy of measure of noncompactness related to the Darbo fixed point principle. As an application, we discuss the presence of solution of the initial value problem with nonlocal conditions.
3
Content available remote Existence results for nonlinear coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type
Nabil Tamer
Demonstratio Mathematica
|
2020
|
Vol. 53, nr 1
236--248
EN
The combined systems of integral equations have become of great importance in various fields of sciences such as electromagnetic and nuclear physics. New classes of the merged type of Urysohn Volterra-Chandrasekhar quadratic integral equations are proposed in this paper. This proposed system involves fractional Urysohn Volterra kernels and also Chandrasekhar kernels. The solvability of a coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type is studied. To realize the existence of a solution of those mixed systems, we use the Perov’s fixed point combined with the Leray-Schauder fixed point approach in generalized Banach algebra spaces.
4
Content available Nonincreasing solutions for quadratic integral equations of Convolution type
El-Sayed W. G., Abd El-Mowla A. A. H.
Journal of Mathematics and Applications
|
2019
|
Vol. 42
95--107
EN
We study a nonlinear quadratic integral equation of Convolution type in the Banach space of real functions defined and continuous on a bounded and closed interval. By using a suitable measure of noncompactness, we show that the integral equation has monotonic solutions.
5
Content available Application of the Taylor differential transformation for solving the integro-differential equations
Grzymkowski R., Pleszczyński M.
Silesian Journal of Pure and Applied Mathematics
|
2018
|
Vol. 8, iss. 1
33--48
EN
A method of solving the integro-differential equations is presented. The discussed equations will be solved by the Taylor differential transformation. By using appropriate properties of this transformation the integro-differential equation will be transformed to a respective recurrence equation. Unfortunately, the high degree of generality and complexity of such defined problem does not allow to obtain the solution in general form. Each equation requires a special method of solution.
6
Content available On a cubic integral equation of Urysohn type with linear perturbation of second kind
Awad H. K., Darwish M. A., Metwali M. M. A.
Journal of Mathematics and Applications
|
2018
|
Vol. 41
29--38
EN
In this paper, we concern by a very general cubic integral equation and we prove that this equation has a solution in C[0; 1]. We apply the measure of noncompactness introduced by Banaś and Olszowy and Darbo's fixed point theorem to establish the proof of our main result.
7
Content available remote Solution of the plane wave diffraction problem by a strip with different boundary conditions on its faces
Emets V., Rogowski J.
Przegląd Elektrotechniczny
|
2016
|
R. 92, nr 7
72--74
EN
A two-dimensional problem of electromagnetic wave diffraction by a plane strip with different boundary conditions on its sides is in the focus of our study. The diffracted field is expressed by an integral in terms of the induced electric and magnetic current densities. Applying the representation theorem for the scattering field, the problem is reduced to the solutions of the integral equations. Numerical solutions and high-frequency asymptotics for the scattering field in the wave zone of the inclusion are presented.
PL
W artykule przedstawiono dwuwymiarowy problem dyfrakcji elektromagnetycznych fal na płaskim włączeniu z różnymi warunkami brzegowymi na jego powierzchniach. Pole dyfrakcji przedstawiono w postaci całki indukowanych elektrycznych i magnetycznych gęstości prądu. Stosując twierdzenie o reprezentacji dla rozproszonego pola problem sprowadza się do rozwiązań układu równań całkowych. Przedstawiono numeryczne oraz asymptotyczne rozwiązania dla zakresu wysokich częstotliwości dla rozproszonego pola w strefie falowej włączenia.
8
Content available remote Local Recovery of Sub-Crustal Stress Due to Mantle Convection from Satellite-to-Satellite Tracking Data
Šprlák M., Eshagh M.
Acta Geophysica
|
2016
|
Vol. 64, no. 4
904--929
EN
Two integral transformations between the stress function, differentiation of which gives the meridian and prime vertical components of the sub-crustal stress due to mantle convection, and the satellite-to-satellite tracking (SST) data are presented in this article. In the first one, the SST data are the disturbing potential differences between twin-satellites and in the second one the line-of-sight (LOS) gravity disturbances. It is shown that the corresponding integral kernels are well-behaving and therefore suitable for inversion and recovery of the stress function from the SST data. Recovery of the stress function and the stress components is also tested in numerical experiments using simulated SST data. Numerical studies over the Himalayas show that inverting the disturbing potential differences leads to a smoother stress function than from inverting LOS gravity disturbances. Application of the presented integral formulae allows for recovery of the stress from the satellite mission GRACE and its planned successor.
9
Content available Application of the homotopy perturbation method for the systems of Fredholm integral equations
Hetmaniok E., Słota D., Wróbel A., Zielonka A.
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
|
2015
|
z. 5
61--70
EN
In this paper the convergence of homotopy perturbation method for the systems of Fredholm integral equations of the second kind is proved. Estimation of errors of approximate solutions obtained by taking the partial sum of the series is also elaborated in the paper.
PL
W artykule wykazano zbieżność homotopijnej metody perturbacyjnej dla układów równań całkowych Fredholma drugiego rodzaju. Podano także oszacowanie błędu rozwiązania przybliżonego uzyskanego jako suma częściowa tworzonego w metodzie szeregu.
10
Content available Application of the homotopy perturbation method for the systems of Volterra integral equations
Hetmaniok E., Słota D., Wróbel A., Zielonka A.
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
|
2015
|
z. 5
71--77
EN
In this paper the convergence of homotopy perturbation method for the systems of Volterra integral equations of the second kind is proved. Estimation of errors of approximate solutions obtained by taking the partial sum of the series is also elaborated in the paper.
PL
W artykule wykazano zbieżność homotopijnej metody perturbacyjnej dla układów równań całkowych Volterry drugiego rodzaju. Podano także oszacowanie błędu rozwiązania przybliżonego uzyskanego jako suma częściowa tworzonego w metodzie szeregu.
11
Content available On the solutions of a class of nonlinear functional integral quations in space C [0,a]
Özdemir İ., Çakan Ü.
Journal of Mathematics and Applications
|
2015
|
Vol. 38
105--114
EN
The principal aim of this paper is to give sufficient conditions for solvability of a class of some nonlinear functional integral equations in the space of continuous functions defined on interval [0,a]. The main tool used in our study is associated with the technique of measures of noncompactness. We give also some examples satisfying the conditions of our main theorem but not satisfying the conditions in [8].
12
Content available Kontakt skrętny z uwzględnieniem częściowych poślizgów dla stempla stożkowego
Brzoza A., Muszyński M.
TTS Technika Transportu Szynowego
|
2012
|
R. 19, nr 9
659--666, CD
PL
W artykule omówiono kontakt skrętny dla stempla stożkowego i sprężystej półprzestrzeni. Przedstawiono ogólne rozwiązanie osiowosymetrycznego zagadnienia skręcania z uwzględnieniem częściowych poślizgów dla znanego rozkładu naprężeń normalnych i znanej wielkości strefy styku. Prezentowane podejście jest odmienne, niż w rozwiązaniu klasycznym, w którym stosuje się teorię Hertza. Problem częściowych poślizgów sprowadza się do równań całkowych rozwiązywanych numerycznie. Przedstawione wyniki są porównywalne z klasycznym rozwiązaniem dla styku skrętnego stempla stożkowego i sprężystej półprzestrzeni w zagadnieniu Lubkina.
EN
This paper discusses torsional contact between a conical punch and an elastic half-space. It provides a general solution to the problem of axially symmetric torsion, taking into account partial slip for a known distribution of normal stress and a known contact area. The approach differs from the classical solution, in which the Hertz theory is used. The partial slip problem was reduced to integral equations solved numerically. The results are similar to those of the classical solution for a conical punch and an elastic half-space in a Lubkin's problem.
13
Kontakt skrętny z uwzględnieniem częściowych poślizgów
Brzoza A.
Logistyka
|
2012
|
nr 3
PL
Badane jest ogólne rozwiązanie osiowosymetrycznego zagadnienia skręcania z uwzględnieniem częściowych poślizgów dla znanego rozkładu naprężeń normalnych i znanej wielkości strefy styku. Rozważane są dowolne geometrie styku ciał. Przedstawione podejście jest odmienne, niż w rozwiązaniu klasycznym, w którym stosuje się teorię Hertza. Problem częściowych poślizgów sprowadza się do równań całkowych rozwiązywanych numerycznie. Przedstawione wyniki są zgodne z klasycznym rozwiązaniem dla styku skrętnego dwóch kul, a w szczególności z zależnością pomiędzy kątem skręcania i wielkością strefy przyczepności w zagadnieniu Lubkina.
EN
The purpose of the study was to analyze the general solution to an axially symmetric torsion problem taking into account partial slips for a known normal stress distribution and a known contact area. Different geometries of contact were considered. The approach presented in this paper differs from the classical solution in which the Hertz theory is used. The partial slip problem was reduced to integral equations solved numerically. The results are compatible with those of the classical solution to a torsional contact problem for two spheres, especially if there is a relationship between the angle of torsion and the size of the stick zone in a Lubkin's problem.
14
Content available remote An operational Haar wavelet method for solving fractional Volterra integral equations
Saeedi H., Mollahasani N., Mohseni Moghadam M., Chuev G. N.
International Journal of Applied Mathematics and Computer Science
|
2011
|
Vol. 21, no 3
535-547
EN
A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.
15
Content available remote The radial solution of the heat equation in the cylindrical ring
Koroński J.
Fasciculi Mathematici
|
2010
|
Nr 43
69-83
EN
The subject of the paper is the construction of a solution to the parabolic problem for the cylindrical ring with initial condition of Cauchy type and boundary conditions of Dirichlet type. To construct the radial solution we do not use the Bessel functions but we apply the convenient Green function, heat potentials and Banach fixed point theorem.
16
Content available remote Integral equation arising in the theory of partial differential equations
Pachpatte B. G.
Fasciculi Mathematici
|
2010
|
Nr 43
115-126
EN
The aim of the present paper is to study some basic qualitative properties of solutions of a certain integral equation arising in the theory of partial differential equations. The well known Banach fixed point theorem and the new integral inequality with explicit estimate obtained in the present paper are used to establish the results.
17
Content available remote New integral and finite difference inequalities in three variables
Pachpatte B.
Demonstratio Mathematica
|
2009
|
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.
18
Content available Self-regular stress integral equations for the axisymmetric elasticity
Sulym H., Pasternak I.
Acta Mechanica et Automatica
|
2009
|
Vol. 3, no. 4
80-84
EN
The stress hypersingular integral equations of axisymmetric elasticity are considered. The singular and hypersingular integrals are regularized using the imposition of auxiliary polynomial solution, and self-regular integral equations are obtained for bounded and unbounded domains. The stress-BEM formulation is considered basing on the proposed equations. Considered numerical examples show high efficiency of the proposed approach. New problem for inclusion in finite cylinder is considered.
19
Content available remote Indukcyjność przewodu o przekroju prostokątnym i dowolnej długości
Piątek Z.
Przegląd Elektrotechniczny
|
2007
|
R. 83, nr 2
119-121
PL
W pracy sformułowano równanie całkowe dla przewodu odosobnionego skąd zdefiniowano jego rezystancję i indukcyjność własną. Zakładając stałą gęstość prądu w przewodzie wyznaczono indukcyjność własną dla przypadku przewodu o przekroju prostokątnym. Wykonano obliczenia tej indukcyjności dla różnych długości przewodu i porównano je z obliczeniami uzyskanymi ze wzorów zawartych w literaturze.
EN
In the paper we define an integral equation for an isolated conductor from which we define its self-inductance and resistance. Assuming a constant current density in the conductor we determine the self-inductance for the case of a rectangular cross-section conductor. Calculations are performed for this inductance for different conductor lengths and compared with calculations obtained from formulas included in the reference.
20
Content available remote A Kneser-type theorem for an integral equation in locally convex spaces
Dutkiewicz A.
Demonstratio Mathematica
|
2007
|
Vol. 40, nr 1
197-202
EN
We shall give suffcient conditions for the existence of solutions of the integral equation (1) in locally convex spaces. We also prove that the set of these solutions is a continuum.
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