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  1. 4 Demonstratio Mathematica
  2. 4 Opuscula Mathematica
  3. 3 Fasciculi Mathematici
  4. 3 International Journal of Applied Mechanics and Engineering
  5. 3 Journal of Theoretical and Applied Mechanics
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  1. 4 Das S.
  2. 3 Hetmaniok E.
  3. 3 Hącia L.
  4. 3 Pauk V.
  5. 3 Słota D.
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  1. 1 2023
  2. 1 2019
  3. 2 2016
  4. 3 2015
  5. 1 2014
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1
Content available On the robustness of the integrable trajectories of the control systems with limited control resources
Huseyin Nesir, Huseyin Anar, Guseinov Khalik G.
Archives of Control Sciences
|
2023
|
Vol. 33, No. 3
527--537
EN
The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed ball of the space Lq(Ω; ℝm), q > 1, with radius r and centered at the origin. The trajectory of the system is defined as p-integrable multivariable function from the space Lp(Ω; ℝn), (1/q) + (1/p) = 1, satisfying the system’s equation almost everywhere. It is shown that the system’s trajectories are robust with respect to the fast consumption of the remaining control resource. Applying this result it is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the total control resource.
2
Content available Water wave scattering by an infinite step in the presence of an ice-cover
Ray S., De S., Mandal B. N.
International Journal of Applied Mechanics and Engineering
|
2019
|
Vol. 24, no. 4
157--168
EN
The classical problem of water wave scattering by an infinite step in deep water with a free surface is extended here with an ice-cover modelled as a thin uniform elastic plate. The step exists between regions of finie and infinite depths and waves are incident either from the infinite or from the finite depth water region. Each problem is reduced to an integral equation involving the horizontal component of velocity across the cut above the step. The integral equation is solved numerically using the Galerkin approximation in terms of simple polynomial multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge of the step. The reflection and transmission coefficients are obtained approximately and their numerical estimates are seen to satisfy the energy identity. These are also depicted graphically against thenon-dimensional frequency parameter for various ice-cover parameters in a number of figures. In the absencje of ice-cover, the results for the free surface are recovered.
3
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.
4
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.
5
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.
6
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.
7
Content available On the summability of divergent power series solutions for certain first-order linear PDES
Hibino M.
Opuscula Mathematica
|
2015
|
Vol. 35, no. 5
595--624
EN
This article is concerned with the study of the Borel summability of divergent power series solutions for certain singular first-order linear partial differential equations of nilpotent type. Our main purpose is to obtain conditions which coefficients of equations should satisfy in order to ensure the Borel summability of divergent solutions. We will see that there is a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients of equations.
8
Content available An analytical technique for solving general linear integral equations of the second kind and its application in analysis of flash lamp control circuit
Hetmaniok E., Słota D., Trawiński T., Wituła R.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2014
|
Vol. 62, nr 3
413--421
EN
In this paper an application of the homotopy perturbation method for solving the general linear integral equations of the second kind is discussed. It is shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in the homotopy perturbation method is convergent. The error of approximate solution, received by taking only the partial sum of the series, is also estimated. Moreover, there is presented an example of applying the method for approximate solution of an equation which has a practical application for charge calculation in supply circuit of the flash lamps used in cameras.
9
Content available Developing a new approach in diagnostic methods of technical state of propeller of gas pumping unit
Zamikhovskyi L., Ivanyuk N.
AGH Drilling, Oil, Gas
|
2013
|
Vol. 30, no. 2
345--351
EN
To estimate the influence of changes in aerodynamic and shape characteristics of propellers of the gas pumping unit on process variables of gas pumping unit using the mathematical modeling methods. The method theoretically based Fredholm equation of the second kind for the tangential velocity component, its computational solution, and estimation of aerodynamical characteristics of airfoil of blades in special chosen frame of reference depending on the airfoil and attack angle. For the estimation of influence of shape configuration changes, which are determined by the configuration of blades of propeller on vibration characteristics of blades, cross-sectional area of blades and its second moment the numerical methods are used. Different methods of reproducing of shape configuration of airfoil of blades using experimental data of coordinates of relevant set points of airfoil are considered. Theoretical results could be used in the research and estimation of influences of configuration blade change and quantity of strained blades on the productivity of pumping units. The conducted research and its results can be the basis of creating of new non-destructive testing methods for gas pumping units and creating a new system of control. Shown results allow increasing operational reliability of facilities that were under research and systems, which can be helpful for Ukrainian gas and oil industry facilities.
10
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.
11
Content available Fixed points and stability in neutral nonlinear differential equations with variable delays
Ardjouni A., Djoudi A.
Opuscula Mathematica
|
2012
|
Vol. 32, no. 1
5-19
EN
By means of Krasnoselskii's fixed point theorem we obtain boundedness and stability results of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and sufficient condition is given. The results obtained here extend and improve the work of C.H. Jin and J.W. Luo [Nonlinear Anal. 68 (2008), 3307-3315], and also those of T.A. Burton [Fixed Point Theory 4 (2003), 15-32; Dynam. Systems Appl. 11 (2002), 499-519] and B. Zhang [Nonlinear Anal. 63 (2005), e233-e242]. In the end we provide an example to illustrate our claim.
12
Content available Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels
Castro L. P., Saitoh S., Tuan N. M.
Opuscula Mathematica
|
2012
|
Vol. 32, no. 4
633-646
EN
This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).
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 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.
15
Numerical propositions for integral equations in the light field with multiple reflections
Hącia L.
Poznan University of Technology Academic Journals. Electrical Engineering
|
2009
|
No 59
73-85
EN
First the paper presents a multiple reflection method for calculation of luminous flux in interiors. The method of boundary integrals is applied. It leads to system of linear equations describing discrete values of overall luminous flux at particular surface elements of considered interior. Next, numerical propositions to solve integral equations modelling the light field with multiple reflections. Numerical examples are illustrated using the discretization method. In the paper quadrature method and projection methods (Galerkin method and collocation method) are proposed. In the future, a comparison between presented methods will be made.
16
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.
17
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.
18
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.
19
Content available remote Binary Search Trees, Recurrent Properties and Wave Equations
Fernández-Camacho M-I., Sánchez-Couso J-R.
Fundamenta Informaticae
|
2007
|
Vol. 81, nr 4
409-439
EN
We give a generic framework to analyze the average-case running time for computing the so called recurrent properties for pairs of binary search trees. Recurrent properties are algorithms that operate on pairs of trees testing some characteristic on nodes by performing a preorder traversal on both trees. Analysis of recurrent properties using the probability model associated with randomly grown binary search trees leads to wave equations. We use a "normalized" integral equation as a pattern to model a specific wave equation and investigate the asymptotic behavior of its solution. This methodology is applied to some particular cases of recurrent properties like testing equality, detecting direct occurrences and clashes or pattern matching.
20
Content available remote Analiza rozkładu pola elektrycznego w optymalizacji trójfazowych torów wielkoprądowych pracujących w układzie płaskim
Bednarek K., Nawrowski R., Tomczewski A.
Przegląd Elektrotechniczny
|
2006
|
R. 82, nr 12
49-52
PL
W artykule przedstawiono zagadnienia zastosowania analizy pola elektrycznego w procesie optymalizacji konstrukcji torów wielkoprądowych. Zaprezentowano całkowy opis pola elektrycznego wykorzystujący równania całkowe Fredholma I-szego i II-go rodzaju. Do numerycznego rozwiązania wyżej wymienionych równań zaproponowano metodę momentów. Zamieszczono wyniki przykładowych obliczeń dla trójfazowego toru wielkoprądowego pracującego w układzie płaskim.
EN
The paper presents the problems related to application of electric field analysis in the optimization process of three-phase heavy-current busways. An integral description of the electric field is provided with the use of Fredholm integral equations of the 1st and 2nd kind. For purpose of numerical solving the above mentioned equations the method of moments is proposed. The results of computation examples of a three-phase heavy-current busway operating in plane arrangement are shown.
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