Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2005, No.2

/ Publications / Scientific Journals

Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2005, No.2

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 2, 2005

MATHEMATICS

Mikhadiuk A. V., Kharin Yu. S.
Statistical analysis of a change point in a binary symmetric Markov chain. pp. 5--10

Summary: The problems of statistical analysis of change points in binary symmetric Markov chains are considered. We construct the ML-estimator of the change point and a test based on the statistic of the maximal relative deviation of the cumulative loglikelihood. The asymptotic probability distribution of the test statistics is found. Results of computer modelling are presented.

Yanovich L. A., Ignatenko M. V.
One class of the Hermite -- Birkhoff interpolation formulae for operators in the space of differentiable functions. pp. 11--16

Summary: The article is devoted to the construction of Hermite -- Birkhoff type interpolation formulae for operators based on the interpolation polynomials for numeral functions with respect to the Chebyshev system of functions. The obtained formulae are exact for a special class of operator polynomials of corresponding degrees. The special cases are considered.

Alekhno E. A., Zabreiko P. P.
Weak continuity of the superposition operator in the space L_¥. pp. 17--23

Summary: In the article the fact that the weak convergence of sequence in the space L_¥ implies the convergence almost everywhere has been proved. Classes of sequentially continuous and classes of weak continuous superposition operators are described.

Spichekova N. V.
Integral surfaces of one Pfaff equation with two singular points. pp. 24--29

Summary: The character of the integral surfaces of one Pfaff equation with two singular points is investigated.

Ustinov A. E.
Inhomogeneous approximations on the manifolds in Q_p. pp. 30--34

Summary: This article is devoted Maler's problem for the p-adic case. The metric theorem on approximations of zero by integer polynomials with the fixed p-adic last coefficient is proved.

Cattani C., Rogosin S. V.
Harmonic wavelets and their certain properties. pp. 35--41

Summary: A class of so-called harmonic wavelets is considered. The connection coefficients are computed in explicit form. Harmonic wavelets are completely characterized by a set of differential equations. The differential equations for the coefficients of so-called the N-th level wavelet-approximation to the solution of the equation of the wave propagation in a composite material with microstructure are found.

Lepeyev A. N.
One-dimensional homogeneous stochastic differential equations and inclusions without drift. pp. 42--47

Summary: We deal with the one-dimensional homogeneous stochastic differential equations and inclusions without drift, investigate different variants of the right sides of the inclusions, some properties and interrelationship. We give the existence conditions for the solutions of the equations in the sense of the corresponding differential inclusions. The main result is the existence criterion for the weak solutions of the equation in the sense of the corresponding inclusion.

Fu Li
Asymptotic properties of the statistical estimators of the pulse transfer functions of two-dimensional linear systems. pp. 48--53

Summary: The statistical estimator of the pulse transfer function of a two-dimensional linear system is proposed. The performance of this estimator is studied. Conditions for the asymptotic normality of finite dimensional distributions of the normalized error of the estimation of the pulse transitive function are given.

Fedosenko A. G.
Limit sum distributions of m-dependent rationed random variables. pp. 54--59

Summary: Sufficient conditions of convergence for a sum distribution of m-dependent random variables with regular "tails" to a distribution from L-class are obtained. There is an example to illustrate that a normal component can appear only as a result of a correlation between summands.

Demidenko V.M., Pratt J.-M.
Quadratic assignment problem: reaching the solution on the given permutations. pp. 60--64

Summary: Restrictions for the input data of the quadratic assignment problem are described which guarantee that its optimum solution is achieved on a given pair of permutations. The described restrictions generalize before the obtained results of the analogous plan.

PHYSICS

Gorbatsievich A. K., Fatma Dekosey
Field equation and equation of motion for a point-like test body in the post-Newtonian approximation in the 5-dimensional projective unified field theory. pp. 65--68

Summary: The Newtonian and post-Newtonian approximations of the field equations of projective unified field theory and of the equation of motion for a test body are studied in detail. In analyzing some experimental data we have performed some numerical estimates of the ratio of the inertial mass to the so-called "scalar" mass of matter.

Gorbatsievich A. K., Fatma Dekosey
Classical Einstein effects in the 5-dimensional projective unified field theory. pp. 69--73

Summary: The present article is concerned with the equation of motion for a point-like test body in the 5-dimensional projective unified field theory and the possibility of a functional dependence of the inertial mass of an external scalaric field. In the framework of this theory, the explicit formula for the Einstein effects, as perihelion Motion of Mercury, light deflection, and photon frequency shift are obtained. In analyzing some experimental data some numerical estimates of the ratio of the inertial mass to the so-called "scalar" mass of matter are made.

Le Van Hoang, Le Tran The Duy, Le Thi Ngoc Anh
Operator method for describing two-dimensional hydrogenic donor states in the magnetic field. pp. 74--79

Summary: The use of the Levi-Civita transformation allows us to formulate the problem of two-dimensional hydrogenic donor states in a magnetic field as that of two-dimensional anharmonic oscillator. Therefore, the operator method can be directly used and the exact solutions of the Schrodinger equation for the above-mentioned problem are obtained. In our approach, wave functions are constructed in the Dirac representation of annihilation and creation operators that permits one to use purely algebraic method in further calculations of other characteristics.

Ganjali M., Ivakin E. V., Sukhadolau A. V.
In-plane thermal diffusivity estimation of nanocrystalline diamond films on substrate through light-induced diffraction. pp. 80--83

Summary: Effective thermal diffusivity of silicon wafer supported nanocrystalline diamond film has been measured by the method of transient grating. It has been experimentally shown that a diamond film can be thermally characterized in the case if the film thickness is larger than 1/3 of a grating spacing.

Akimov A. I., Sauchuk G.K., Akimova T. M.
Electrophysical properties of the ceramic materials in the Bi₂Ti₄O₁₁ -- TiO₂ system. pp. 84--88

Summary: The approaches (the cold pressing method and the doping method) to improve the dielectric parameters of the synthesized in the Bi₂Ti₄O₁₁-- TiO₂ system ceramic specimens are studied. The results of the dielectric investigations of the ceramic Nd⁺³, Al⁺³, Mn⁺², Sn⁺⁴ doped specimens of the Bi2Ti4On-TiO2 system are presented in the temperature range -60 to +300 °C. It is shown that the modified ceramics of the Bi₂Ti₄O₁₁-- TiO₂ system has a potential for the use in the functional components of the microwave devices.

Shipilo V.B., Dutov A. G., Shipilo N. V., Komar V. A., Azarko I.I.
Titanium influence on diamond crystallization in the Mn -- Ni -- C system. pp. 89--92

Summary: The dependences of a degree change and speed phase transformation of graphite in diamond, its fractional composition, the content in diamonds of titanium, manganese, nickel and paramagnetic defects, and also the strength of diamonds on the content of titanium in the initial reactionary charge of system Mn -- Ni -- C are established.

Sheleg A. U., Hurtavy V. H., Guretskii S. A.
Elastic properties of the b-BaB₂O₄ nonlinear crystal in the temperature range 90 -- 300 K. pp. 93--95

Summary: Measurements of longitudinal elastic wave velocities in b-BaB₂O₄ nonlinear crystals in various crystallographic directions are performed in the temperature range 90- 300 K. On the basis of the obtained data, the c₁₁ and c₃₃ components of elasticity modules are determined. It is shown, that the elasticity module values decrease with a temperature growth. Significant anisotropy of the elastic properties in this crystal is observed in this case c₁₁ > c₃₃.

Grigorishin I. L., Belonuchkina I.I.
Analytical calculation of a potential in the coplanar system of screened electrodes. pp. 96--99

Summary: Analytical expressions are derived for a potential in the coplanar electronoptical systems bounded by a screen, yielding the initial potential distribution and the paths of charged particles while solving electron optics problems with an intense space charge.

INFORMATICS

Chernyavskii A. F., Rolich O. Ch., Sadov V. S., Shestakov K. M.
Object color forming model. pp. 100--105

Summary: In the proposed model the addition curves are issued from the spectral curve of human eye sensitivity and the proportion curves are submitted to the basic color distribution of the vision spectrum.

Medvedev A. G.
Optimal investment strategies in financial asset portfolios. pp. 106--111

Summary: By the scheme offered by Merton the problem of the financial asset portfolio management in two versions is discussed: 1) except risky assets the investor in the financial market has acces to some riskless asset, 2) one trades in the market only risky assets. It is considered that the dynamics of the prices of risky assets follows the Ito processes and the portfolio diversification can change continuously in time. The optimal strategies are determined in explicit form in the sense of the maximal utility of portfolio diversification when taking account that during time the investor consumes a part of his wealth.

Chebakov S. V.
Double-criterion model for generating the optimal subset of the alternatives with the maximal total probability of the target attaining. pp. 112--119

Summary: The double-criterion model has been proposed for generation the optimal subset of the alternatives with maximal total probability of the target attaining at the given restrictions for the general time of their execution. The condition have been obtained for representation of the optimal subset or its part as the joint set of the elements of the separate Pareto layers.

ABSTRACTS OF DEPOSITED PAPERS

Monastyrny P. I., Stelmakh S. N.
Computational schemes of hybrid type for the finite-difference equations in the case of inhomogeneous media. p. 119

SCIENTISTS OF BELARUS

Nikolai Mikhailovich Olekhnovich (On the occasion of the 70^th birthday). pp. 120--121
Click here to read this article in Belarusian (Win 1251)

Viktor Ivanovich Korzyuk (On the occasion of the 60^th birthday). pp. 122--123
Click here to read this article in Russian (Win 1251)

/ Publications / Scientific Journals / Back to Top of Page

Designed and maintained by Dr. Nikolai N. Kostyukovich. Last updated: August 5, 2005
Created with assistance of Dr. Ignatii I. Korsak
Copyright © 2005 The National Academy of Sciences of Belarus
Copyright © 2005 The Belaruskaya Navuka Publishing House