Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2007, No.3

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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2007, 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, 2007

MATHEMATICS

Lasy P. G.
Construction of a solution of the linear Pfaff equation with a given set of characteristic vectors. pp. 4--9.

Summary: A solution of one inverse problem in the theory of characteristic vectors is given. It allows one to construct, using elementary functions, examples of functions of two variables with a given set of characteristic vectors, when this set is represented by a smooth curve on a plane, which is a graph of a decreasing strictly convex function.

Trubnikov I. Yu.
Existence conditions of linear extension in the category of vector bundles. pp. 10--16.

Summary:

Egorov A. D., Zherelo A. V.
Measure interpolation based approximations of functional integrals in spaces of functions of many variables. pp. 17--23.

Summary: Approximate formulas are obtained, which reduce the evaluation of integrals with respect to the Gaussian measure in space of functions given on less intervals. The measure interpolation is used for obtaining the formulas.

Makevich P. V.
Optimal observation of time delay systems by discretely quasi-impulse signals. pp. 24--30.

Summary: A method of online optimal observation by discretely quasi-impulse signals is described for one type of time delay systems. The results are illustrated by the example.

Hrusheuski U. U.
Nonautonomous differential equations with generalized coefficients in the algebra of mnemofunctions. pp. 31--36.

Summary: Nonautonomous differential equations with generalized coefficients are considered. It is shown that the associated solution for an equation of such a type in the algebra of new generalized functions is the solution in the sense of differential inclusions.

Bashun S. Yu.
Schmidt subgroups of odd order in finite groups. pp. 37--40.

Summary: In this article simple finite K-groups, whose minimal nonnilpotent subgroups (Schmidt's subgroups) of odd order dividing by 3 are 3-closed, are described.

Yadchenko A. A.
On automorphisms and normal Hall subgroups of linear groups. pp. 41--46.

Summary: Some properties of order of coprime automorphisms of irreducible linear groups are established. Also, some sufficient conditions for existence of a normal Holl p-subgroup in a p-solvable irreducible complex linear group are obtained.

Borodich E. N., Borodich R. V.
Intersection of Á-abnormal maximal q-subgroups. pp. 47--52.

Summary: The intersections of the given systems of maximal subgroups of finite groups are investigated.

Krylov Y. V., Perez Tchernov A. J.
Efficient algorithm for domino recognition. pp. 53--57.

Summary: A linear algorithm for domino and linear domino recognition and for construction of a list of maximal cliques of such graphs is proposed. Unlike the domino recognition, the algorithm constructed by T. Kloks, D. Kratsch and H. Muller doesn't require a preliminary analysis of a graph. The characterizations of a domino and a linear domino are given in term of special clique covering existence.

Gadjieva L. E., Troush N. N.
Connection between parameters in different presentations of the characteristic function of steady random variables. pp. 58--62.

Summary: In this article, we consider a stable distribution and describe several methods of parametrization. We also prove some theorems which provide formulas of association between parameters of various methods of parametrization.

Monastirniy P. I., Kravchuk A. I., Kremen Yu. A.
Reduction of boundary-value problems for systems of differential equations to the Cauchy problems using unitary transformations. pp. 63--67.

Summary: A new method for solution of systems of differential equations is developed. It is based on unitary transformations.

Bernik V. I., Kalosha N. I.
Benford law and approximation of logarithms of natural numbers by rational numbers. pp. 68--73.

Summary: There are given several generalizations of the fact that in the record of 2ⁿ , n = 1, 2,... the digit and groups of digits are distributed according to the Benford law. Quantitative assessments and results of numerical experiments are also presented.

PHYSICS

Pilipovich V. A., Esman A. K., Goncharenko I. A., Kuleshov V. K.
Matrix of narrow-band optical filters based on ring microresonators. pp. 74--78.

Summary: We propose the structure of an optical narrow-band filter based on composite waveguide ring resonators. Because of the structure such filters have a less size than those of conventional shape and are easily combined into a matrix. We investigate the dependence of a transmission spectrum of such filters on waveguide coupling coefficients, waveguide bend radius, resonator optical length and optical radiation loss in the resonator. The optimization of the parameters of a composite optical filter with a resonator in the shape of an elongated ring is carried out. Our calculations show that for a ring radius of more than 35 µm and the length ratio of the larger and smaller resonators n = 3 the gain in area is more than 100%. For n = 5 the area ratio is more than 3.5. That means that the number of optoelectronics components on the same substrate can be produced by a factor of 3--1.

Ignatov B. I., Nepokoichitsky A. G.
Thermochemical reactions in the surface layer of ferrites under the laser-plasma influence. pp. 79--84.

Summary: Possibility of performing thermochemical reactions of metal reduction in the surface layer of granet ferrites under a combined laser-plasma action of moderate characteristics in a hydrogen medium was analyzed. It was shown that the reduction time of the processes decreased to 90--120 sec. preserving the initial characteristics of granet ferrites. The influence of a ruptured ayer on the process of formation and the structure of metal and transition layers was estimated. The adhesion value of the reduced metal layer was by 10% less than the strength of granet ferrites at tensile.

Tochitsky T. A., Dmitrieva A. E.
Twinning influence on the formation of primary orientation in nickel nanocrystalline films. pp. 85--91.

Summary: The twinning influence on the structure and texture of electrolytically deposited films is investigated. A contribution of this influence to the anisotropy of the growth rate of crystallines is evaluated.

Korshunov F. P., Bogatyrev Yu., V., Gurin P. M., Lastovsky S. B., Shvedov S. V., Shpakovsky S. V.
Influence of electron irradiation on the characteristics of epitaxial silicon p-n-structures. pp. 92--95.

Summary: The influence of 4 MeV electron irradiation on a lifetime of minority charge carriers and a forward voltage of epitaxial silicon p-n-structures has considered. It is shown that at the electron fluence Ф = (1 ¸ 2) • 10¹⁵ cm^-2 the lifetime values have decreased by a factor of 15 ¸ 19 without essential changes in the forward voltage. The dominating radiation defects (A-centers, complexes C_iO_i, divacancies), influencing researched parameters, have been determined by the method of DLTS-spectroscopy.

Starovoitov P. M., Shumeiko N. M.
Two-boson production of lepton pairs in hadron collisions. pp. 96--103.

Summary: We examine an inclusive production of lepton pairs in proton-proton collisions at LHC energy via two-boson exchange mechanism without applying The Equivalent Photon Approximation. We present a scheme of the analytical formula for cross section calculation and numerical results for the angle dependence of the cross section for various mass and energy of the pair as well as energy distributions of lepton pairs of different mass.

Mukha V. S.
Parallel factorial analysis as a regression problem on estimation of material concentration in solutions. pp. 104--107.

Summary: On the basis of the mathematical model for the parallel factorial analysis a regression problem on estimation of the material concentration in samples is formulated and solved.

INFORMATICS

Voitikova M. V., Voitovich A. P.
Wavelet-analysis of the human heart rate variability for paroxysmal atrial fibrillation. pp. 108--112.

Summary: A new algorithm for completely automated wavelet transform (WT) analysis of RR-intervals featuring paroxysmal atrial fibrillation (PAF) has been developed. The power spectrum of wavelet-coefficients of the RR-intervals sequence was intended to predict the onset of PAF. The absence of wavelet-coefficients correlation is observed at scale a ³ 3, indicating the independence of RR-intervals on distant intervals and the chaotic character of atrium excitation for the patients with PAF, unlike the correlation of all RR-intervals for healthy patients. The predictor uses the diagnostic criterion: 5--10 time increase of the amplitude of wavelet-coefficients precedes the onset of paroxysm.

Bakhanovich S. V., Sobolevsky P. I.
Optimization of tiling for mapping of algothims onto distributed memory superconductors strategy. pp. 113--118.

Summary: The problem of tiling optimization for mapping of algorithms onto distributed memory parallel architectures is investigated. An approach of tiling optimization in LSGP mapping strategy is developed. The approach takes into account technical characteristics of computational environment: quantity of processors, processor performance, latency and bandwidth of communication channels. The method is intended for algorithms with uniform dependences.

SCIENTISTS OF BELARUS

Anatoly Pavlovich Dostanko (On the occasion of the 70^th birthday). pp. 119--121.
Click here to read this article in Russian (Win 1251)

Leonid Aleksandrovich Shemetkov (On the occasion of the 70^th birthday). pp. 122--124.
Click here to read this article in Russian (Win 1251)

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