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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2006, No.1

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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2006, No.1

Proceedings of the National Academy of Sciences of Belarus
(Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICAL-MATHEMATICAL SCIENCES

Published by Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus

Number 1, 2006

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CONTENTS


MATHEMATICS

Pekarskii A. A.
Uniform rational approximation of conformal mappings. pp. 5--8

Summary: The uniform rational approximation of conformal mappings are investigated.

Ustinov A. E.
Approximation of complex numbers by values of polinomials with integer coefficients. pp. 9--14

Summary: The Maler's problem in complex case is considered. The metric approximation theorem for complex numbers is proved.

Malyutin V. B.
Method of evaluation of functional integrals over space of functions with finite number of values. pp. 15--18

Summary: The formula for functional integrals over space of functions, taking values ±1 is constructed. This formula represents functional integral over space of functions defined on interval [0, T] by means of functional integrals over space of functions defined on intervals [0, a] and [a, T],

Prohorovich M. A.
Capacities and Lebesgue points for Hajlasz -- Sobolev fractional classes on metric measure spaces. pp. 19--23

Summary: Capacities and Lebesgue points for Hajlasz -- Sobolev fractional classes on metric measure spaces are investigated.

Sobolevsky S. L.
About one class of irrational ordinary differential equations of the arbitrary order. pp. 24--28

Summary: The special class of irrational ordinary differential equations of the arbitrary order is considered. Necessary and sufficient conditions of Painleve property for this class are obtained.

Kostyukova O. I.
Differentiability of Solutions to Parametric Optimal Control Systems with Delay. pp. 29--34

Summary: For parametric linear-quadratic optimal control systems with delay, properties of solutions are investigated. Regular and irregular points are considered. In a neighborhood of regular point, solution differentiability with respect to a parameter is proved. Formulas for the corresponding derivatives are presented.

Vedernikov S. V.
On invariants of global pairs Lee groups. pp. 35--37

Summary: The theorem of coordination of invariant parts generated by pair of endomorphisms and invariant parts and generated by finite set endomorphisms is proved.

Meleshko I. N.
Approximate solution of the some third boundary value problem of heat conductivity in circle. pp. 38--43

Summary: An approximate presentation by polylogarithms of the solution of the third boundary value problem of the theory of heat conductivity for Laplace's equation in circle is obtained.

Stelmashuk N. Т., Shilinets V. A.
On integral representation of functionaly-invariant vector-analitic functions. pp. 44--47

Summary: Solution of boundary value problem for one class of functionally-invariant vector-analitic functions is obtained.

Naidenko V. G.
Topological properties and separability of directional convex sets. pp. 48--52

Summary: A generalized convexity (OC-convexity) consisting of the intersections of conic semispaces of directional convexity is investigated. Topological properties of OC-convexity are established. Halfspaces of OC-convexity are described, and conditions on separability of OC-convex sets are shown.

Dmitruk N. M.
Optimization of two-stage control processes. pp. 53--58

Summary: The problem of optimization of a nonstationary linear two-stage control process by bounded controls is under consideration. A dual method for open-loop solution and an algorithm for the optimal controller which calculates current values of the control in real time are presented.

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PHYSICS

Barkovsky L.M., Feranchuk S.I.
Self-consistent description of X-ray reflection from the roughness surface. pp. 59--65

Summary: Method for simulation of X-ray reflection spectra from non-ideal surfaces is described. Roughness correlation is taken into account. The experimental spectrum is analyzed in detail and several characteristic angular ranges are separated. X-ray scattering in these ranges is conditioned by the qualitatively different surface properties. Considered approach gives new possibilities for the analysis of the surface quality by means of X-ray reflectometry.

Chernichenko Yu. D.
Relativistic inverse problem for a sum of nonlocal separable quasipotentials. pp. 66--72

Summary: A relativistic inverse problem is solved for the case when the total quasipotential simulating the interaction of two relativistic spinless particles of unequal masses is the superposition of a local quasipotential and a sum of nonlocal separable quasipotentials. The problem is investigated within the relativistic quasipotential approach to quantum field theory. The local component of total interaction is supposed to be known and it not admits bound' states. It is shown that the nonlocal separable components of total interaction may be reconstructed if its the local component, the additionals phase shift and the true bound state energy are known.

Bondarev A. L.
Orthonormal bases in Minkowski space and its application for description of particle polarization states. pp. 73--78

Summary: The ortonormal bases construction by physical vectors in Minkowsky space is considered. The using of these bases for description of particles polarization is also analyzed.

Goncharenko A. M.
To the theory of the spatial dark solitons. pp. 79--80

Summary: It is considered the propagation of the spatial optical dark solitons in the nonlinear homogeneous media and in the inhomogeneous waveguide.

Shapovalov P. S., Ermolaev E. A.
About nonlinear interaction coaxial Gaussian light beams in the non-uniform medium. pp. 81--85

Summary: The interaction of two axially symmetric Gaussian light beams with different frequency and powering by propagation in the medium with cubic nonlinearity and quadratic nonuniformity is under consideration. Modes of changiny the cross-section and the critical power of beams are determined.

Prischepa S.L., Kushnir V. N., Ilyina E. A.
Angular characteristics of the upper critical magnetic field and dimensional properties of superconducting state in layer structures. pp. 86--89

Summary: Measured angular dependence of the upper critical field Hc2 (q) in Nb/Pd multilayer structures, in which superconductivity is caused by the proximity effect, are presented. Dimensional properties of the superconducting phase with respect to the orientation of the external magnetic field are determined.

Shipilo V. B. †, Dutov A. G., Shipilo N. V., Komar V. A.
Effect of silicon on crystallization of diamonds in manganesenickel system. pp. 90--93

Summary: Dependence of change of a degree and phase transformation speed of graphite in diamond, formations fractional and admixtures structure of diamonds and their strength in system Mn -- Ni -- C -- Si are established depending on the contents in a reactionary charge of silicon (0,25-10 mas. %) and a time of a synthesis.

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INFORMATICS

Voitikova M. V, Voitovich A. P.
Determination of the arterial febrillation type of the cardiac diagram on the base of wavelet transform. pp. 94--99

Summary: The algorithm for completely automated wavelet transform (WT) analysis of ECG signals featuring arterial febrillation (AF) is developed. WT based algorithm was intended to differentiate ECG signals with non-terminating permanent AF and signals with paroxysmal AF (spontaneous self-terminated AF). Discrete WT of ECG has been used for identification of QKS-complexes on the basis of threshold criterion for corresponding wavelet coefficients for the purpose to remove the ventricular signal parts. The remainder ECG signal (the arterial activity) into different scales (frequency bands) is decomposed with continuous WT. The distribution of wavelet power spectrum is the discriminant diagnostic criterion of AF forms -- a permanent or paroxysmal AF. If the WT power spectrum has a local maximum at scale higher than some predefine threshold parameter, AF is likely terminated within up to two minute. For ECG with WT power spectrum local maximum at scale lower than threshold parameter and AF is likely permanent AF.

Barketau M. S., Kovalyov M. Y.
Approximation algorithm for a supply chain scheduling problem. pp. 100--106

Summary: The problem of scheduling the production and delivery of a supplier to feed the production of F manufacturers is studied. The orders fulfilled by the supplier are delivered to the manufacturers in batches of the same size. The supplier's production line has to be set up whenever it switches from processing an order of one manufacturer to an order of another manufacturer. The objective is to minimize the number of setups, subject to maintaining continuous production for all manufacturers. The algorithm for this problem, which constructs a solution at most F times worse the optimal solution and runs in O(NF) time where N is the given number of delivery batches is presented.

Katkov V. L.
Symbolic manipulations by development and execution of programs. pp. 107--112

Summary: The question of symbolic manipulations use is discussed by programs development: at stages of coding, execution and debugging of programs. As an example it is considered operation of differentiation in a symbolic form, the analysis of dimensions of physical values and symbolic evaluation of the program. It is marked, that offered manipulations can be realized by expansion of programming languages, and also as the special tools supporting development of programs.

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SHORT NOTES

Bernik V. I., Vasilyev D. V.
Convergence case of Diophantine approximations on complex manifolds. pp. 113--115

Summary: The order of zero approximation by the values of linear combinations of analytic functions is investigated.

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ABSTRACTS OF DEPOSITED PAPERS

Rusilko T. V.
Analysis of the methods of queuing nets and its applications. p. 116

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SCIENTISTS OF BELARUS

Vladimir Antonovich Pilipovich (On the occasion of the 75th birthday). pp. 117--119
Click
here to read this article in Russian (Win 1251)

Viktor Semyonovich Burakov (On the occasion of the 75th birthday). pp. 120--121
Click here to read this article in Belarusian (Win 1251)

Leonid Ilyich Gurskii (On the occasion of the 70th birthday). pp. pp. 122--123
Click here to read this article in Russian (Win 1251)

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