Numer czasopisma
Opuscula Mathematica
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ISSN: 1232-9274
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Data wydania
2005
Rocznik
Vol. 25
Numer
No. 1
Prawa dostępu
Dostęp: otwarty dostęp
Uwagi:
Prawa: CC BY 4.0 
Uznanie autorstwa 4.0 Międzynarodowe (CC BY 4.0)
Strony
Opis
Rocznik czasopisma (rel.)
Rocznik czasopisma
Opuscula Mathematica
Vol. 25 (2005)
Artykuły numeru (rel.)
Artykuł
Otwarty dostęp
Solution of the Stieltjes truncated matrix moment problem
(2005) Adamân, Vadim Movsevovič; Tkačenko, Igor M
The truncated Stieltjes matrix moment problem consisting in the description of all matrix distributions sigma(t) on [0, ∞) with given first 2n + 1 power moments (Cj)nj=0 is solved using known results on the corresponding Hamburger problem for which sigma(t) are defined on (-∞, ∞). The criterion of solvability of the Stieltjes problem is given and all its solutions in the non-degenerate case are described by selection of the appropriate solutions among those of the Hamburger problem for the same set of moments. The results on extensions of non-negative operators are used and a purely algebraic algorithm for the solution of both Hamburger and Stieltjes problems is proposed.
Artykuł
Dostęp ograniczony
A sufficient condition for Schur stability of the convex combination of the polynomials
(2005) Białas, Stanisław
In this paper is given a simple suffcient condition for Schur stability of the convex combination of the real polynomials.
Artykuł
Dostęp ograniczony
Monotone iterative methods for infinite systems of reaction-diffusion-convection equations with functional dependence
(2005) Brzychczy, Stanisław
We consider the Fourier first initial-boundary value problem for an infinite system of semilinear parabolic differential-functional equations of reaction-diffusion-convection type of the form where [formula] in a bounded cylindrical domain. The right-hand sides of the system are Volterra type functionals of the unknown function z. In the paper, we give methods of the construction of the monotone iterative sequences converging to the unique classical solution of the problem considered in partially ordered Banach spaces with various convergence rates of iterations. We also give remarks on monotone iterative methods in connection with numerical methods, remarks on methods for the construction of lower and upper solutions and remarks concerning the possibility of extending these methods to more general parabolic equations. All monotone iterative methods are based on differential inequalities and, in this paper, we use the theorem on weak partial differential-functional inequalities for infinite systems of parabolic equations, the comparison theorem and the maximum principle. A part of the paper is based on the results of our previous papers. These results generalize the results obtained by several authors in numerous papers for finite systems of semilinear parabolic differential equations to encompass the case of infinite systems of semilinear parabolic differential-functional equations. The monotone iterative schemes can be used for the computation of numerical solutions.
Artykuł
Dostęp ograniczony
The Abel summation of the Kontorovich-Lebedev integral representation
(2005) Cojuhari, Petru A; Gomilko, Aleksandr M
A new result on the summation of the Kontorovich–Lebedev integral representation in the sense of Abel mean is given.
Artykuł
Dostęp ograniczony
Numerical approximations of difference functional equations and applications
(2005) Kamont, Zdzisław
We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.
Artykuł
Dostęp ograniczony
Recovering a part of potential by partial information on spectra of boundary problems
(2005) Pivovarčik, Vâčeslav
Under additional conditions uniqueness of the solution is proved for the following problem. Given 1) the spectrum of the Dirichlet problem for the Sturm-Liouville equation on [0, a] with real potential q(x) mem L2(0, a), 2) a certain part of the spectrum of the Dirichlet problem for the same equation on [a/3, a] and 3) the potential on [0, a/3]. The aim is to find the potential on [a/3 ,a].
Artykuł
Dostęp ograniczony
A note on inductive limit model of Bargmann space of infinite order
(2005) Stochel, Jerzy
It is shown that the generalized creation and annihilation operators on Bargmann space of infinite order in a direction a = (a₁, a₂, ...) ∊ l² are inductive limits of the creation and annihilation operator acting on Bargmann space on n-th order
Artykuł
Dostęp ograniczony
On some application of biorthogonal spline systems to integral equations
(2005) Wronicz, Zygmunt
We consider an operator PN : LP(I) - Sn(deltaN), such that PN f = f for f mem Sn(deltaN), where Sn(deltaN) is the space of splines of degree n with repect to a given partition deltaN of the interval I. This operator is defined by means of a system of step functions biorthogonal to B-splines. Then we use this operator to approximation to the solution of the Fredholm integral equation of the second kind. Convergence rates for the aproximation of the solution of this equation are given.