Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2008, No.3

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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2008, No.3

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 3, 2008

MATHEMATICS

Zhuk E. E.
Improvement of the statistical properties of uniformly distributed random variable sequences based on the empirical distribution function. pp. 4--10

Summary: The problem of improvement of the statistical properties of uniformly distributed random variable sequences is considered. The special transformation based on the empirical distribution function, which provides passing the basic statistical tests, is proposed.

Kharin A. Yu.
Asymptotic expansions for probabilistic characteristics of the sequential test for composite parametric hypotheses. pp. 11--16

Summary: The problem of sequential testing of composite hypotheses is considered. Asymptotic expansions are obtained for error probabilities and expected sample sizes. The case of normal data is analyzed in detail as an example.

Dobrovolsky A. I., Doubrov B. M., Rabinovich M. M.
Classification of subalgebras in the exceptional Lie algebra of type G₂. pp. 17--22

Summary: The article provides the complete classification of all subalgebras in the simple Lie algebra of type G₂ up to conjugation. The classification algorithm is based on the notion of an almost algebraic hull of subalgebras in semisimple Lie algebras. It is reduced to the description of all subalgebras consisting of nilpotent elements, of separating subalgebras and non-separating subalgebras with a given almost algebraic hull.

Vorob'ev N. N.
Multiply local formations with Stone lattice of subformations. pp. 23--27

Summary: n-Multiply local (totally local) formations having a Stone lattice of n-multiply local (totally local) subformations are described.

Gal'mak A. M.
Polyadic associative operations on Cartesian powers. pp. 28--34

Summary: In this article for every k ³ 2, l ³ 2 and each permutation s of the set {1,2,..., k) /-ary operations [ ]_l,k and ( )_{l, s, k} are defined and studied.

Prokopchuk A. V., Tikhonov S. V., Yanchevskii V. I.
Generic elements in groups SK₁ for central simple algebras. pp. 35--42

Summary: In this article Suslin's conjecture on SK₁ is reduced to the case of special bicyclic algebras. New cases of this conjecture are proved.

Kovalevskaya E. I., Rykova O. V.
Approximation to zero by monic polynomials of the third degree in the fields C and Qp. pp. 43--47

Summary: The analogues of two V. G. Sprindzuk's theorems (1963) are proved for monic polynomials of the third degree in the fields C and Q_p.

Erofeenko V. T., Pulko J. V.
Modeling of boundary conditions on screens with double layer surface currents and charges. pp. 48--54

Summary: Boundary conditions for an isotropic intermediate layer influenced by an arbitrary combination of TE- and TN-polarized electromagnetic fields were obtained. Induced with initial field surface currents and charges, which are concentrated on the layer planes, were taken into account.

Zhogal S. P., Safonov I. V.
Overtone synchronization of self-oscillating systems under the external polyharmonic influence. pp. 55--58

Summary: A problem of overtone synchronization of self-oscillating systems under the external polyharmonic influence was investigated. Based on the approach, an effect of overtone synchronization of an external force by the example of Van der Pol oscillator was considered.

PHYSICS

Tomilchik L. M.
Modeling of spatially localized quantum systems on the basis of conformally flat geometry. pp. 59--63

Summary: A model description of spatially localized quantum systems is given on the basis of the confining properties of conformally flat static metric. Supposing a quadratic coordinate dependence of conformally flat metric the exactly solvable two-dimensional analogs of Klein-Fock-Gordon and Dirac equations with a coordinate-dependent mass are obtained. The connection of the proposed model with the one-dimensional Dirac oscillator model is established.

Bogush A. A., Tokarevskaya N. G., Red'kov V. M.
Vector parameters for 4-dimensional matrices of inverse transformations in the theory of the group GL(4.C). pp. 64--69

Summary:

Avakyan E. Z., Avakyan S. L.
Light scalar mesons decays in the Quark Confinement Model. pp. 70--75

Summary: Low energy interactions of scalar mesons are investigated in the Quark Confinement Model. A good description of these decays in a two-quark scheme was made by means of the addition term in the scalar-quark Lagrangian. It turns out that introduction of the additional term with a derivative into the Lagrangian allow us to obtain numerical values for strong and electromagnetic decay widths in good agreement with experimental data.

Leonov A. V., Feranchuk I. D.
Evolution of the Jaynes--Cummings model out of the framework of the rotating wave approximation. pp. 76--85

Summary: Accurate eigenvalues and eigenfonctions of the Jaynes--Cummings model in the case of high quantum field excitations are calculated numerically out of the framework of the rotating wave approximation. A uniformly suitable approximation is obtained and the similarity dependence on the energy quantum numbers and coupling constant of these solutions is found.

Karpenko V. A., Laptinsky V. N., Romanenko A. A.
Coupled-wave analysis of light reflection from the inhomogeneous surface layer. pp. 86--93

Summary: The coupled-wave equation system, which can be solved by the subsequent approximation method, is developed for the problem of light reflection from the inhomogeneous surface layer. The accuracy of the first approximation is evaluated and the numerical examples of its application for ellipsometric researches of surface layers are presented.

Gatskevich E. I., Ivlev G. D., Rarenko A. I., Savchuk A. I., Strebegev V. N., Zakharuk Z. I.
Modification of the surface layers of CdMnTe crystals by the nanosecond laser impact. pp. 94--96

Summary: The impact of 80-nanosecond laser radiation on Cd_1-xMn_xTe (x = 0..0.3) single crystals has been studied. Irradiation was carried out in the range of energy densities E from 0.1 up to 0.6 J/cm2. During laser heating and following cooling down, the sample reflectivity was studied by the optical probing of a laser irradiated area at wavelengths of 1.06 and 0.53 µm. The state of a laser-modified surface was investigated by scanning electron microscopy method. From the analysis of reflectivity dynamics, energy densities E_m, at which the surface of samples starts to melt, were determined. The value of E_m rises with x increasing. At E > E_m with energy density increasing, the transition from epitaxial crystallization of the surface layer to the formation of a ripple micro structure on the surface takes place. In the range of energy densities 0.21-0.25 J/cm2, oriented filamentary crystallization is observed on some parts of the surface. The impact of laser pulses with E > E_m leads to the formation of Te inclusions on the surface of the samples with the small values of x.

Tochitskii T. A., Dmitrieva A. E.
Twinning influence on the anisotropy of the crystallites growth rate in the electrolytic cobalt-based films. pp. 97--101

Summary: The twinning influence on the texture and the surface morphology of the Co- and CoW-electrodeposited films was investigated. It was established that the mixed film textures were formed and the crystallites sizes increased in the direction of the twinning plane as a result of defects packing formation and twinning.

Akimov A. I., Sauchuk G. K., Zhukovetc D. A.
Influence of production conditions on the crystal structure and physical properties of piezoceramic materials based on Pb(Ni_1/3Nb_2/3)O₃--PbZrO₃--PbTiO₃ system. pp. 102--106

Summary: It is established that the piezoceramic materials based on 0.41PNN-0.23PZ-0.36PT solid solutions can be produced using a liquid-phase sintering procedure at temperatures 960--1100 °C. It is found that introducing micro additives causes of parameters of a crystal lattice to change and a phase transition temperature to grow. A perspective use of 0.41PNN-0.23PZ-0.36PT ceramics for creation on its basis of functional elements of multilayered devices is shown.

INFORMATICS

Voitikova M. V., Voitovich A. P.
Wavelet-analysis of the heart rate variability for ventricular tachycardia and fibrillation. pp. 107--111

Summary: Automatic prediction of ventricular tachycardia and fibrillation using RR-intervals processing has been developed. The predictor uses the diagnostic criterion: spontaneous paroxysm of ventricular tachycardia is preceded with the 10 or more time increase of a standard deviation of the wavelet coefficients and/or with the 5--10 time increase of the amplitude of its scale derivative.

Sobolevsky P. I., Bakhanovich S. V.
Optimization of tiling algorithms into macrooperations. pp. 112--119

Summary: The problem of tiling optimization for mapping algorithms onto distributed memory parallel architectures is investigated. The estimations of computation and communication volume of tile is made. The estimations take into account technical characteristics of computational environment: processor performance, latency and bandwidth of communication channels.

SCIENTISTS OF BELARUS

Nikolai Aleksandrovich Borisevich (To the 85^th Birthday Anniversary). pp. 120--122
Click here to read this article in Russian (Win 1251)

Aleskandr Fedorovich Chernyavsky (To the 70^th Birthday Anniversary). pp. 123--124
Click here to read this article in Russian (Win 1251)

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