Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2007
Volume
Vol. 27
Number
No. 2
Description
Journal Volume
Opuscula Mathematica
Vol. 27 (2007)
Projects
Pages
Articles
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.
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.
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.
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 $u^{\prime\prime}(x)=f(x)u(x)$, $x \in [0,T]$, $u(0)=c$, $u^{\prime}(T)=0$, where $c,T \in \mathbb{R}$ ($c \neq 0$, $T \gt 0$) and $f$ is a nonnegative function with $r$ ($r\geq 0$) 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 $\varepsilon$-complexity.
Polynomials on the space of ω-ultradifferentiable functions
(2007) Grasela, Katarzyna
The space of polynomials on the space $D_{\omega}$ of $\omega$-ultradifferentiable functions is represented as the direct sum of completions of symmetric tensor powers of $D^{\prime}_{\omega}$.