Numer czasopisma
Opuscula Mathematica
Ładuję...
ISSN: 1232-9274
e-ISSN:
Data wydania
2007
Rocznik
Vol. 27
Numer
No. 2
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. 27 (2007)
Artykuły numeru (rel.)
Artykuł
Dostęp ograniczony
A note on Vizing's generalized conjecture
(2007) Blidia, Mostafa; Chellali, Mustapha
In this note we give a generalized version of Vizing's conjecture concerning the distance domination number for the cartesian product of two graphs.
Artykuł
Dostęp ograniczony
On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity
(2007) Bogoliubov, Nikolai N.; Blackmore, Denis L.; Samoylenko, Valeriy Hr.; Prykarpatsky, Anatoliy K.
A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.
Artykuł
Dostęp ograniczony
Transmission problems for the Helmholtz equation for a rectilinear-circular lune
(2007) Denysenko, Volodymyr
The question related to the construction of the solution of plane transmission problem for the Helmholtz equation in a rectilinear-circular lune is considered. An approach is proposed based on the method of partial domains and the principle of reflection for the solutions of the Helmholtz equation through the segment.
Artykuł
Dostęp ograniczony
The use of integral information in the solution of a two-point boundary value problem
(2007) Drwięga, Tomasz
We study the worst-case ε-complexity of a two-point boundary value problem u″(x) = ƒ(x) u (x), x Є [0,T], u(0) = c, u′ (T) = 0, where c,T Є R (c ≠ 0, T > 0) and ƒ is a nonnegative function with r (r ≥ 0) continuous bounded derivatives. We prove an upper bound on the complexity for linear information showing that a speed-up by two orders of magnitude can be obtained compared to standard information. We define an algorithm based on integral information and analyze its error, which provides an upper bound on the ε-complexity.
Artykuł
Dostęp ograniczony
Polynomials on the space of ω-ultradifferentiable functions
(2007) Grasela, Katarzyna
The space of polynomials on the space Dω of -ultradifferentiable functions is represented as the direct sum of completions of symmetric tensor powers of D′ω.
Artykuł
Dostęp ograniczony
Integrable three-dimensional coupled nonlinear dynamical systems related with centrally extended operator Lie algebras
(2007) Hentosh, Oksana Ye.; Prykarpatsky, Anatoliy K.
A hierarchy of Lax-type flows on a dual space to the centrally extended Lie algebra of integral-differential operators with matrix-valued coefficients is considered. By means of a specially constructed Backlund transformation the Hamiltonian representations for these flows coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems are obtained. The Hamiltonian description of the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax-type linearizations is analysed.
Artykuł
Dostęp ograniczony
Differential equation of transverse vibrations of a beam with local stroke change of stiffness
(2007) Kasprzyk, Stanisław; Wiciak, Margareta
The aim of this paper is to derive a differential equation of transverse vibrations of a beam with a local, stroke change of stiffness, and to solve it. The presented method is based on the theory of distributions.
Artykuł
Dostęp ograniczony
On the equivalence of pre-Schröder equations
(2007) Kalinowski, Józef
In the paper the equivalence of the system of two pre-Schröder functional equations (equations (Sn), (Sm) for m > n ≥ 3, n, m Є N) and the whole system (S), is considered. The results solve the problem of Gy. Targonski [4] in a particular case.
Artykuł
Dostęp ograniczony
A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations
(2007) Malec, Marian; Sapa, Lucjan
This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in R1+n. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.
Artykuł
Dostęp ograniczony
Algebraic construction of a coboundary of a given cycle
(2007) Mazur, Marcin; Szybowski, Jacek
We present an algebraic construction of the coboundary of a given cycle as a simpler alternative to the geometric one introduced in [4, 5].