Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 2010, No.1
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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 2010, No.1

Proceedings of the National Academy of Sciences of Belarus (Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICALMATHEMATICAL SCIENCESPublished by Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Egorov A. D.
Composite formula for mathematical expectation of functionals of solution of Ito's equation. pp. 48
Summary: An approximate formula for evaluation of mathematical expectation of nonlinear functionals of solution of stochastic differential equations is considered. The formula is based on using Euler's iterative scheme of approximate solution of stochastic differential equations. It is exact for functionals of special form.
Demenchuk А. К.
Necessary condition for existence of irregular oscillations of linear systems with trivial average coefficient matrix. pp. 913
Summary: We consider the linear control periodic system with the trivial average coefficient matrix and with reverse communication. The excitation problem of irregular oscillations is considered. A necessary condition for solution of this problem is given.
Minchenko L. L, Stakhovsky S. M.
New regularity conditions in mathematical programming problems. pp. 1418
Summary: The relation between the constant positive linear dependence regularity condition and the error bound property is studied for parametric mathematical programming problems.
Vas'kovskii M. M.
Theorem on the dependence of Pmartingale solutions of stochastic parabolic evolution equations on the initial conditions and the righthand sides. pp. 1926
Summary:
Davyalova E. V.
Markushevich's problem with three discontinuity points. pp. 2733
Summary:
Grin'ko A. P.
Asymptotic expansions of local fractional integrals. pp. 3440
Summary: Examples of local fractional integrals of the exponential function are calculated. The asymptotic expansions of local fractional integrals are obtained if the interval integration length tends to zero and infinity at a finite point of the real line.
Mardvilko T. S.
Inequality for the quasinorm rational function with respect to linear and planar measures and its applications. pp. 4148.
Summary:
Rykova V. V.
Number of integer polynomials with a given order of discriminants. pp. 4952
Summary: The lower estimation for the number of integer polynomials having a given bound for discriminates is obtained.
Tihonenko T. V.
Factorization of finite groups with supersoluble and Hall subgroups. pp. 5357
Summary:
Ageev S. M., Silayeva Z. N.
Generalization of Borsuk's problem. pp. 5862
Summary: Borsuk's wellknown problem on preserving the absolute extensor by the functor of finite exponent is resolved in the category of metric filtered spaces.
Kuzmenkov D. S.
Optimal observation of parabolik system. pp. 6370
Summary: An optimal observation problem of a thermal process in the rod in conditions of uncertainty is considered. The differential equation of parabolic type describing the process is approximated by largescale differential equations. This problem is solved by a method of quasidecomposition, the algorithm of operation of the optimal estimator forming in real time estimations of a current state of a thermal process is described.
PHYSICS
Babich A. A., Karpenko N. V., Pankov A. A., Tsytrinov A. V.
Identifying new heavy Z'bosons in е^{+}е^{} annihilation processes with longitudinal polarized beams. pp. 7179
Summary: The method to distinguish the signals induced by new gauge neutral Z' bosons within different classes of theories with an extended gauge sector in the annihilation processes of fermion pair production is developed. This method is based on the polarized differential observables which yield higher sensitivity to Z' parameters with respect to the integrated ones. Polarized experiments performed at the International Linear Collider with an energy of 0,5 TeV will allow one to identify unambiguously the E_{6} models (besides ciriodel) predicted Z' bosons with masses M_{Z'} < 24 TeV, and substantially improve the expected bound obtained from unpolarized experiments.
Tarasenko A. N., Gorbatsievich А. К.
Green's function approach to the calculation of the gravitational radiation of aparticle radially moving in the Schwarzschild spacetime. pp. 8085
Summary: In the present work the Green's function method is used to calculate the gravitational radiation of an arbitrary source moving in the vicinity of a Schwarzschild black hole. An explicit expression for some components of the Green's function is obtained. The general method is applied to calculate the gravitational radiation of a free particle radially falling into the black hole. An explicit expression for the gravitational wave amplitude is obtained. The emission of the radially falling particle is modeled numerically. The results are shown to be in agreement with the results of the earlier works.
Grabchikov S. S., Potuzhnaya O. L., Sheleh M. U.
Influence of pulse and reverse electrolysis modes on the phase and chemical composition of CoP and CoNiP alloys. pp. 8693
Summary: In this article the influence of pulse and reverse electrolysis modes on the phase and chemical composition and microstructure of CoP and CoNiP alloy films was studied. During film deposition of CoP and CoNiP alloys in the pulse and reverse modes, concentration areas of the amorphous phase of synthesized covers to 32 at.% P extend, the limit of a transition from the crystal into the amorphous state decreases at 23 at.% P. When varying the values of the densities of direct and reverse currents, the duration of direct and reverse current pulses and pauses allows changing the chemical composition of CoP and CoNiP alloy films in a wide range: phosphorus from 15 to 32 at.%, base metal of 20 to 50 at.%. With increasing frequency pulse currents from 1 to 1000 Hz in amorphous films there occurs grinding of the grid microstructure, the longitudinal size of structural inhomogeneities decreases from 80200 and 40100 A. Use of the modes of pulse and reverse electrolysis enables to synthesize amorphous alloys with a uniform grid microstructure characterized by a factor of 1.52 smaller structural inhomogeneities, as compared to the samples deposited at constant current.
Anisimova A. E., Kulak G. V.
Acoustooptical interaction in the planeparallel slab. pp. 9498
Summary: The participants of Bragg diffraction of light by ultrasound in the uncoordinated planeparallel slab from fused quartz or s and p incident wave polarization have been investigated. It is shown that maximal transmission and reflected diffracted aves is reached by changing the ultrasonic intensity, slab thick and light incident angle. It is established that a narrow strip of switch over the acoustooptical filter under diffraction in the slab is conditioned by the Fresnel reflection of light on its boundaries.
Esman A. K., Kuleshov V. K., Zykov G. L.
Buffering of the optical signals in the nanosecond range. pp. 99102
Summary: A buffering method of the digital optical data based on using a sequentially disposed optically coupled waveguide silicon avity structures with micron sizes is proposed. Using the mathematical modeling, it is shown that the optical buffer provides digital signals delay of 0.5 nsec, when it occupied the area of approximately 0.02 mm^{2}. In this case, the maximum frequency f the optical digital signals repetition can reach 17 GHz.
INFORMATICS
Benediktovitch V. I.
Noncrossing spanning tree in the geometric complement of the spanning tree. pp. 103109
Summary: In this article the existence criterion of a noncrossing spanning tree in the geometric complement of a spanning tree has been obtained.
Voitikova M. V., Voitovich A. P.
Atrial arrhythmia identification by means of the wavelet analysis of an electrocardiogram. pp. 110118
Summary: Automated discrimination between atrial fibrillation (AF), atrial flutter (AFL) and sinus (normal) rhythm by means f stationary wavelet transform (WT) of the 2leads ECG was developed. The distribution of the 8level WT energy of he ECG is used as diagnostic discriminator to determine several atrial activity patterns. Standard deviations (SD) f the wavelet coefficients from coarse scales (scale 68) were calculated. For AF, unlike AFL, a uniform distribution of WT energy in all levels of decomposition is observed. SD at coarse scales was higher for AF than for AFL. SD at scale 8 discriminated between AF from AFL with 93% sensitivity and specificity.
SHORT NOTES
Goncharenko A. M.
Propagation of optical solitons in absorbing selfoc. pp. 119121.
Summary: It is considered some properties of the optical solitons in the absorbed waveguide
SCIENTISTS OF BELARUS
Nikolai Alekseevich Izobov (To the 70th Anniversary of the Birthday). pp. 122123
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