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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2006, No.2

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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2006, 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, 2006

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CONTENTS


MATHEMATICS

Kilbas A. A., Koroleva A. A.
The extension of Mittag-Leffler function. pp. 5--9

Summary: Special functions, represented by the Mellin--Barnes integrals and generalizing the classical Mittag-Leffler type functions, are introduced. Conditions for the existence of the considered functions are proved, and their series representations are established. Their asymptotic relations at zero and infinity are deduced, and special cases are given.

Semerikova N. V.
On higher exponent of linear systems with perturbations which are integrable or vanishiDg in the mean with power and nonmonotonic weight. pp. 10--13

Summary: Perturbed linear systems with perturbation which are power integrable on the semiaxis with positive weight and with perturbation which are vanishing in the power mean with positive weight are considered. A sufficient condition for the upper bound of Lyapunov exponent of such systems to be evaluable by means of the algorithm by N. A. Izobov is established.

Krasovskii S. G.
On noninvariance of asymptotic properties of three-dimensional singular linear differential systems under small perturbations. pp. 14--19

Summary: The explicit method of the construction of the three-dimensional linear differential systems with piecewise continues coefficients and small parameter at the derivative is obtained. It is shown that all nontrivial solutions of such systems under constructed small perturbations do not possess their asymptotic properties on the previously given segment.

Kharin Y. S., Yarmola A.N.
Statistical estimation of parameters for the MTD model of discrete-valued time series. pp. 20--26

Summary: New probabilistic properties of MTDg and MTDg models axe introduced. New method of estimation of MTD model is proposed. It based on properties of stationary distribution of probability. It is shown that new estimations are consistent and asymptotically unbiased.

Voroshilov A. A.
Cauchy problem for the non-homogeneous diffusion equation of fractional order. pp. 27--32

Summary: The Cauchy problem for the non-homogeneous linear differential equation with the Caputo partial fractional derivative of positive order with respect to the time and the Laplace operator with respect to the space is investigated. The equation under consideration generalizes the heat equation and the wave equation. Using direct and inverse Laplace and Fourier transforms, a solution in closed form of the above problem is established in terms of the H-function. It is shown that this solution is represented in terms of the special Wright function in a one-dimensional case.

Khartovski V. E.
To the problem about complete controllability of linear systems with many delay. pp. 33--38

Summary: The problem of calming linear stationary difference-differential system with commensurable delays is investigated. The boundary problem for calculating calmining control are obtained.

Zyuzina E. L.
Conservative difference schemes of the raised order of accuracy on non-uniform grids for two-dimensional wave equation. pp. 39--45

Summary: New conservative difference scheme of the second order of approximation with respect to space and time is constructed and investigated for a two-dimensional wave equation on non-uniform spatial-time grid. For the scheme introduced the a priori estimates of stability and convergence are obtained without requirement of Lipschitz-continuity of operators.

Zagursky V. N., Vorob'ev N. T.
Maximal local functions of Pitting classes. pp. 46--50

Safonova I. N.
On critical partially saturated formations of finite groups. pp. 51--55

Hodalevich A. D.
Schunk classes of the universal algebras of Malcev varieties. pp. 56--59

Summary: The existence of F-semiprojectors and F-projectors in finite universal algebras of Malcev variety is proved for non-empty Schunk class.

Naidenko V. G.
Product of transrecursive operators. pp. 60--63

Summary: It is proved that for any nondiscrete Hausdorff topology on a word space there exists a pair of transrecursive operators such that their product is not d-decomposable. At the same time for the constructive transrecursive operators there exists a topology such that every product is d-decomposable. For any topology t, if the t-base of transrecursive operators is finite then every product is also d-decomposable.

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PHYSICS

Privalchuk A. N., Tolkachev E. A.
The equations (2 + l)-electrodynamics in quaternions and finite SO(2.1) transformations of fields. pp. 64--67

Summary: Quaternion formalism for (2 + l)-electrodynamics based on Maxwell--Lorentz equations is constructed. Finite transformations of electric field strength are obtained.

Feranchuk I. D., Feranchuk S. I.
Grazing incidence parametric X-radiation in super-lattice. pp. 68--73

Summary: Grazing incidence parametric X-radiation from relativistic electrons in periodical multilayer structure (super-lattice) is considered and its intensity is calculated. The radiation can be generated by electron moving in parallel to surface of the structure without scattering in the media. It is shown that this radiation mechanism can be used in storage rings to obtain intensive monochromatic X-rays.

Dvurechenskii A. V., Yakimov A. I., Volodin V. A., Gatskevich E. I., Efremov M. D., Ivlev G. D., Nikiforov A. I.
Modification of quantum dots in Ge--Si nanostructures by pulsed laser processing. pp. 74--77

Summary: Development of approaches for modification of quantum dots (QDs) in Ge/Si nanostructures by pulsed laser irradiation is considered. Energy density of ruby laser was ~ 1 J/cm2 and corresponded to the melting threshold of Si surface at pulse duration of 80 ns. One-pulsed and ten-pulsed processing was used. QD GexSi1-x structure was analyzed on the basis of Raman spectroscopy. Frequency-dependent admittance measurements were carried out to investigate hole energy spectrum in the as-grown and laser-modified QDs. The obtained results show that the laser treatment allows to decrease area density of QDs, modify its composition, and increase its average size. It has been obtained that the laser processing gives an opportunity to improve the homogeneity of QD parameters.

Goncharenko I. A., Esman A. K., Kuleshov V. K.
Optical temperature-sensing device on the base of waveguide microresonators. pp. 78--82

Summary: The possibility to use the ring waveguide resonators as a sensor of the temperature-sensing device is considered. The results of calculation allowing optimizing the range and accuracy of the temperature measurement are presented. The accuracy of the temperature measurement depends on the optical length of the resonator and coupling coefficient of the input and ring waveguides. In order to measure the temperature in wide range with high resolution it is possible to use several microresonators with different size or apply the signals on different wavelength in one resonator of small size. The advantages of the proposed temperature-sensing device are immunity to electromagnetic radiation, high sensitivity and wide dynamic range of measurement, reliability, repeatability, small size and weight etc.

Kulak G. V., Lutsenko E. V., Nikolaenko T. V., Ropot P. I.
Reflection of light from the intensifying layer, modulated by ultrasound. pp. 83--87

Summary: The features of Bragg reflection of light from plane-parallel intensifying layer, disturbed by stationary ultrasound wave have been examined. The effect of acoustostimulated light generation on the basis of three-layer structure GaAs--AlGaAs--GaAs has been investigated. The dependencies of reflectivity and transmission factors of a layer on a deformation amplitude of an ultrasound wave, thickness and gain factor of a layer have been established. It has been offered to use the investigated effect for acoustostimulated generation of lasers on the basis of multilayer acoustooptic crystals.

Danik S. V.
Temperature breakpoint in cadmium at small-angle electron-photon scattering. pp. 88--91

Summary: Results of the investigation of transverse magnetoresistance temperature dependence in a single-crystal Cd specimen of [1010] orientation in the 8T magnetic field has lead to the discovery of the temperature breakdown effect in the[1120] direction. It has been established, that phonons with wave vector, which length is equal or larger than the minimal distance between the contingent Fermi surface sheets, are needed for the implementation of this effect. Realization of this condition is possible only in the area of the maximal contingence of a "packet" and the "monster" corrugated cylinder of the second Brillouin zone on the hexagonal AHL plane.

Shipilo V. B. †, Dutov A. G., Shipilo N. V., Komar V. A.
Effect of zinc and bismuth on crystallization of diamonds in system Mn--Ni--C. pp. 92--95

Summary: Dependence of change of a degree and speed of a phase change of graphite in diamond, formations fractional and admixtures structure of diamonds and their strength in systems Mn--Ni--C--Zn and Mn--Ni--C--Bi are established depending on the contents in a reactionary charge of zinc and bismuth and a time of a synthesis.

Akimov A. I., Lebedev S.A., Tkachenka T. M.
Phase formation and superconductive features of Tl2Ba2CaCu2O8-x/2Fx. pp. 96--98

Summary: A fluorination of high-temperature Tl2Ba2CaCu2O8-x/2Fx (0 £ x £ 0.3) superconductor has been performed. BaO2 was partly replaced by BaF2 in an initial mixture. It was found that the superconductor under synthesis conditions described is a mono phase 2212 one when the fluorine content is not greater than 0.10. As a result of fluorination, the superconductor transition temperature increases from 106 K (for x = 0) to 110 K (x = 0.1).

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INFORMATICS

Kolyada A. A., Kravtsov V. K., Starovoitov A. M., Shabinskaya H. V., Shulyak V. I.
Methods and algorithms of code transformations for minimally redundant numeric systems of the positional-modular type. pp. 99--105

Summary: For the class of positional-modular numeric systems (PMNS) the methods and algorithms of code transformations are offered. Alongside with universal procedures the procedure of coding for PMNS of a private aspect -- for so-called recursive minimally redundant interval-modular numeric systems is synthesized also.

Bakhanovitch S. V., Sobolevsky P. I.
Mapping of algorithms onto distributed memory parallel architectures: optimizating of tiling for one- and twodimensional topologies. pp. 106--112

Summary: The problem of tiling optimization for mapping of algorithms onto distributed memory parallel architecture is investigated. A method of tiling optimization for algorithms with uniform dependence is developed. The method takes into account technical characteristics of computational environment: quantity of processors, processor performance, latency and bandwidth of communication channels.

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SHORT NOTES

Vasilyev D. V.
On Lucas--Lehmer test for Mersenne primes. pp. 113--115

Summary: The short proof of the the Lucas--Lehmer primality test for Mersenne numbers is given.

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SCIENTISTS OF BELARUS

Fyodor Dmitrievich Gakhov (On the occasion of the 100th birthday). pp. 116--118
Click
here to read this article in Russian (Win 1251)

Lev Mitrofanovich Tomil'chik (On the occasion of the 75th birthday). pp. 119--121
Click here to read this article in Russian (Win 1251)

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

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