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Wyświetlanie 1-15 z 27
Tytuł:
Solutions of a class of singular linear systems of difference equations. Part 1
Autorzy:
Kanan, Asmaa M.
Powiązania:
https://bibliotekanauki.pl/articles/1030103.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Drazin inverse
Rank
Singular difference equations
Opis:
We extend results of Campbell, Meyer, Jr. and Rose of applications of the Drazine inverse to linear systems of differential equations with singular constant coefficients to solutions of linear systems of difference equations A x_(n+1)+B x_n= f_n ,n≥0 when A and B are m×m complex matrices and may both singular, under conditions that rank(A)=1 and trace of A is not equal zero. f_n is an arbitrary function in C^m, and x_n∈C^m. We give a new closed form for all solutions of those systems when they are tractable, using the theory of the Drazin inverse, and a matrix K∈C^(m×m).
Źródło:
World Scientific News; 2020, 143; 53-66
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of linear systems of differential equations with singular constant coefficients by the Drazin inverse of matrices
Autorzy:
Kanan, Asmaa M.
Hassan, Khadija
Powiązania:
https://bibliotekanauki.pl/articles/1046563.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Drazin inverse
Index
Singular differential equations
Opis:
Let A ,B be n×n matrices of complex numbers. Let G a vector-valued function of the real variable t. A and B may both be singular, rank(A) = 1, and the trac of A is not equal zero. The linear system of differential equations Ax^' (t)+Bx(t)=G(t) is studied using the Drazin inverse A^D of A, and a new matrix K∈C^(n×n). In this paper, we obtain a new closed form for the general solution of the differential system when the system is tractable.
Źródło:
World Scientific News; 2019, 137; 229-236
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Investigation of the dynamics of singular protected systems
Autorzy:
Naumeyko, I.
Alja'afreh, M.
Powiązania:
https://bibliotekanauki.pl/articles/411040.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Oddział w Lublinie PAN
Tematy:
"Man-Machine-Environment" model
non-linear system
singular equations
asymptotic
linearization
Opis:
The analysis of asymptotic representations of the systems protected from harmful influences is carried out. Various types of general models of the "manmachineenvironment" with protection are considered. Each of them adequately describes some of the practically important qualities of the object, and they all together describe the object in terms of its safe operation. The dynamic properties of complex ergonomic systems, presented in the form of systems of differential equations with a small parameter at the derivative are investigated The methods of reducing the impact on the person of harmful factors are theoretically substantiated. The dynamic protection response speed is considered to be significantly greater than the harmful factor production rate. Numerical solution of the general problem and the analytical solution for autonomous case is obtained for harmful effects. By using asymptotic the system of equations has been solved in closed form not only for autonomous case, but also for parameters smoothly changing in time. The estimates of the cost of protection was obtained for the various cost-functionals and for different functions in the right-hand side of the equation describing the dynamics of protection. To assess the accuracy of model calculations and for graphic representation of the results mathematical package MAXIMA is used.
Źródło:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2016, 5, 4; 37-42
2084-5715
Pojawia się w:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On 1-regular ordinary differential operators
Autorzy:
Łysik, Grzegorz
Powiązania:
https://bibliotekanauki.pl/articles/1207973.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
singular differential equations
Mellin transformation
Laplace integrals
Opis:
Solutions to singular linear ordinary differential equations with analytic coefficients are found in the form of Laplace type integrals.
Źródło:
Annales Polonici Mathematici; 2000, 74, 1; 201-214
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Controllability of degenerate and singular parabolic problems: the double strong case with Neumann boundary conditionsControllability of degenerate and singular parabolic problems: the double strong case with Neumann boundary conditions
Autorzy:
Fragnelli, Genni
Mugnai, Dimitri
Powiązania:
https://bibliotekanauki.pl/articles/952835.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
strongly singular/degenerate equations
non smooth coefficients
null controllability
Opis:
We prove a null controllability result for a parabolic problem with Neumann boundary conditions. We consider non smooth coefficients in presence of a strongly singular potential and a strongly degenerate coefficient, both vanishing at an interior point. This paper concludes the study of the Neumann case.
Źródło:
Opuscula Mathematica; 2019, 39, 2; 207-225
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel
Autorzy:
Wójcik, Paweł
Sheshko, Michail A.
Pylak, Dorota
Karczmarek, Paweł
Powiązania:
https://bibliotekanauki.pl/articles/747083.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Singular integral equations
Cauchy-type kernel
multiplicative kernel
logarithmic singularities
Opis:
In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2012, 66, 2
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Interaction between a stratified elastic half-space and an irregular base allowing for the intercontact gas
Oddziaływanie sprężystej półprzestrzeni warstwowej na sztywną przeszkodę oddzielona szczeliną wypełnioną gazem
Autorzy:
Machyshyn, I.
Nagórko, W.
Powiązania:
https://bibliotekanauki.pl/articles/280251.pdf
Data publikacji:
2003
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
contact problem
laminated half-space
gas
complex potentials
singular integral equations
Opis:
The paper is devoted to the investigation of contact interaction of a laminated half-space and a rigid body with a smooth cylindrical depression under conditions of plane deformation allowing for an intercontact ideal gas. To describe the homogenized model of the laminated body with microlocal parameters and to describe the behavior of the gas - equations of ideal gas state are used. Applying the method of comlex potentials the problem is reduced to the singular integral equation for the height of intercontact gap and its solution is obtained in a closed form. To find the lenght of the gap, its volume and the gas pressure a system of three equations is derived. With the aid of this system the dependence of the external loading and amount of the gas in the gap on the contact pressure and geometrical parameters of the gap is analyzed.
W pracy analizuje się oddziaływanie sprężystej półprzestrzeni warstwowo-niejednorodnej na ciało sztywne z walcową szczeliną wypełnioną gazem. Półprzestrzeń sprężystą poddaje się homogenizacji mikrolokalnej, a do rozwiązania otrzymanych równań modelowych stosuje się metodę potencjałów zespolonych. Analizowany problem sprowadza się do poszukiwania rozwiązania równania całkowego. W pracy uzyskuje się rozwiązania w postaci zamkniętej oraz przeprowadza analizę numeryczną zależności rozwartości szczeliny oraz jej objętości od obciążenia zewnętrznego.
Źródło:
Journal of Theoretical and Applied Mechanics; 2003, 41, 2; 271-288
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On solutions of integral equations with analytic kernels and rotations
Autorzy:
Nguyen, Mau
Nguyen, Tuan
Powiązania:
https://bibliotekanauki.pl/articles/1311183.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
integral operators
singular integral equations
algebraic operators
Riemann boundary value problems
Opis:
We deal with a class of integral equations on the unit circle in the complex plane with a regular part and with rotations of the form (*)     x(t) + a(t)(Tx)(t) = b(t), where $T = M_{n₁,k₁} ... M_{n_m,k_m}$ and $M_{n_j,k_j}$ are of the form (3) below. We prove that under some assumptions on analytic continuation of the given functions, (*) is a singular integral equation for m odd and is a Fredholm equation for m even. Further, we prove that T is an algebraic operator with characteristic polynomial $P_T(t) = t³ - t$. By means of the Riemann boundary value problems, we give an algebraic method to obtain all solutions of equation (*) in closed form.
Źródło:
Annales Polonici Mathematici; 1996, 63, 3; 293-300
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The thermoelastic problem for a penny-shaped anticrack with heat conductivity in a transversely isotropic space
Autorzy:
Kaczyński, A.
Monastyrskyy, B.
Powiązania:
https://bibliotekanauki.pl/articles/280177.pdf
Data publikacji:
2016
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
transversely isotropic space
circular anticrack
heat flow
singular integral equations
thermal stress singularities
Opis:
An analytical solution of a 3D transversely isotropic thermoelastic problem of a uniform heat flow disturbed by a penny-shaped rigid sheet-like inclusion (anticrack) with some small conductivity is obtained by using the potential theory method. The behaviour of thermal stresses near the edge of the disc is analysed from the standpoint of the mechanics of fracture initiation.
Źródło:
Journal of Theoretical and Applied Mechanics; 2016, 54, 2; 593-600
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the deformation fracture criterion to cracking of disc specimens with a central narrow slot
Autorzy:
Kazberuk, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/2204693.pdf
Data publikacji:
2022
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
cracked Brazilian disc
Dugdale model
plastic strip
fracture deformation criterion
singular integral equations
Opis:
Using the method of singular integral equations, the elastic-plastic problem for cracked Brazilian disk was solved. Based on the Dugdale model and deformation fracture criterion, the relationships between critical load, notch tip opening displacement and length of the plastic strips were established. Also, the comparison between the present solution for the finite domain and the known solution obtained for the semi-infinite notch in the elastic plane was performed.
Źródło:
Acta Mechanica et Automatica; 2022, 16, 4; 393--398
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Construction of integral equations describing limit equilibrium of cylindrical shell with a longitudinal crack under time-varying load
Autorzy:
Makhorkin, M.
Nykolyshyn, M
Powiązania:
https://bibliotekanauki.pl/articles/411396.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Oddział w Lublinie PAN
Tematy:
cylindrical shell
crack
exponential time dependence
varying load
system of singular integral equations
Opis:
The problem on limit equilibrium of a closed infinite cylindrical shell with a longitudinal crack under the action of time-varying load by the exponential law has been considered. According to presented conditions the expressions for the field of the stress-free deformations along the crack are presented in the form [wzory] are the operators identical to those given in [7] for the case of static load [wzory] and , are the operators that take into account the dependence of load on time. Using the same transformations that in the case of static load [7, 11], the key functions [wzory] are determined, and the clarification of the shell's stress-state is reduced to solving the system of singular integral equations (SIE). Its general form is similar to the same system constructed for static load [7], and the kernels of SIE have the form [wzory], where is a singular part [wzory], is a regular part in which the component [wzory] takes into account the time dependence of load [wzory], are described by the expressions similar to the same given in [7].
Źródło:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2016, 5, 3; 141-146
2084-5715
Pojawia się w:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mechanics of moving contacts involving functionally graded multiferroics
Autorzy:
Toktas, S. E.
Dag, S.
Powiązania:
https://bibliotekanauki.pl/articles/38697105.pdf
Data publikacji:
2023
Wydawca:
Instytut Podstawowych Problemów Techniki PAN
Tematy:
multiferroics
functionally graded materials
magneto-electro-elastic coatings
moving contacts
singular integral equations
Opis:
This article introduces solution procedures for moving contacts involving functionally graded multiferroic coatings. A moving rigid punch of a flat or a triangular profile is assumed to be in contact with a multi-layer medium comprising magneto-electro-elastic coating layers, elastic interlayers, and an elastic substrate, that is modelled as a half-plane. The formulation is based on wave equations of plane elastodynamics and Maxwell’s equations. Applying Fourier and Galilean transformations, a singular integral equation of the second kind is derived for each of the flat and triangular punch problems. An expansion-collocation technique utilizing Jacobi polynomials is developed to numerically solve the integral equations. Proposed procedures are verified through comparisons to the results available in the literature. Parametric analyses carried out considering functionally graded magneto-electro-elastic coatings demonstrate the effects of the property variation profile, punch speed, and coating thickness on contact stresses, electric displacement, and magnetic induction. The methods presented could be of use in analysis and design studies of multiferroic layered systems subjected to moving contacts.
Źródło:
Archives of Mechanics; 2023, 75, 4; 431-468
0373-2029
Pojawia się w:
Archives of Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A relation between the concepts of transposition, similarity, and symmetry, as well as matrix equations
Autorzy:
Kaczorek, Tadeusz
Powiązania:
https://bibliotekanauki.pl/articles/747820.pdf
Data publikacji:
2005
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Matrix equations and identities, Eigenvalues, singular values, and eigenvectors
Opis:
The author studies relationships among the notions of transpose, similarity, and symmetrization of matrices. It is shown that a square matrix is similar to its transpose, and that there exists a matrix that, simultaneously, carries this similarity transformation and symmetrizes the matrix. Furthermore, some equalities involving adjoint matrices are established as well. The proofs of the results are formulated for complex matrices, but they are valid also for other algebraically closed fields.
Źródło:
Mathematica Applicanda; 2005, 33, 47/06
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Anticrack in a transversely isotropic space
Autorzy:
Kaczyński, A.
Powiązania:
https://bibliotekanauki.pl/articles/387650.pdf
Data publikacji:
2013
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
three-dimensional elasticity
transversely isotropic material
plane anticrack
singular integral equations
stress singularity
naprężenie
równania całkowe
materiał izotropowy
Opis:
An absolutely rigid inclusion (anticrack) embedded in an unbound transversely isotropic elastic solid with the axis of elastic symmetry normal to the inclusion plane is considered. A general method of solving the anticrack problem is presented. Effective results have been achieved by constructing the appropriate harmonic potentials. With the use of the Fourier transform technique, the governing system of two-dimensional equations of Newtonian potential type for the stress jump functions on the opposite surfaces of the inclusion is obtained. For illustration, a complete solution to the problem of a penny-shaped anticrack under perpendicular tension at infinity is given and discussed from the point of view of material failure.
Źródło:
Acta Mechanica et Automatica; 2013, 7, 3; 140-147
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II
Autorzy:
Shirai, A.
Powiązania:
https://bibliotekanauki.pl/articles/255197.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
singular partial differential equations
totally characteristic type
nilpotent vector field
formal solution
Gevrey order
Maillet type theorem
Opis:
In this paper, we study the following nonlinear first order partial differential equation: [formula] The purpose of this paper is to determine the estimate of Gevrey order under the condition that the equation is singular of a totally characteristic type. The Gevrey order is indicated by the rate of divergence of a formal power series. This paper is a continuation of the previous papers [Convergence of formal solutions of singular first order nonlinear partial differential equations of totally characteristic type, Funkcial. Ekvac. 45 (2002), 187-208] and [Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type, Surikaiseki Kenkyujo Kokyuroku, Kyoto University 1431 (2005), 94-106]. Especially the last-mentioned paper is regarded as part I of this paper.
Źródło:
Opuscula Mathematica; 2015, 35, 5; 689-712
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 27

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