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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2010, No.3

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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2010, 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, 2010

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CONTENTS


MATHEMATICS

Rovba Y. A. Smatrytski K. A.
Convergence in the mean of rational interpolating processes in the zeroes of Bernstein fractures. pp. 5--9

Summary: In the present article the rational approximation to the continuous functions on the whole real axis is considered. It is shown that in the case of fixed poles rational interpolating processes with nodes in the zeroes of Bernstein cosine or sine fractions converge in the space of the square integrated functions with the weight р(x)=(1 + x2)-1 on R.

Kaliada D. U.
Upper estimate of the number of integral polynomials of third degree with a given bound of discriminants. pp. 10--16

Summary: In the article the author establishes the upper estimate for the number of integral polynomials of third degree that have bounded height and bounded discriminant.

Mukha V. S.
Optimal statistical decisions for continuous multidimensional-matrix states and observations. pp. 17--24

Summary: The optimal statistical decision making problem on a multidimensional random matrix through the observation of other multidimensional random matrix is formulated and solved. The polynomial decision for the non-Gaussian case is offered.

Gromak V. I., Hrytsuk E. V.
To the theory of nonlinear differential systems with the Painleve property. pp. 25--30

Summary: A relation between the resonant method for nonlinear differential systems and reduction of these systems to equivalent Briot--Bouquet systems is given.

Palchik E. M.
Finite groups with the factorization G=G>p×С(х). pp. 31--34

Summary:

Kovalkova D. P., Skiba A. N.
Finite groups with given systems of S-quasi-normal subgroups. pp. 35--43

Summary: The structure of finite groups, in which each maximal chain of length two has a proper S-quasi-normal subgroup, is described.

Zhiznevsky P. A., Safonov V. G.
Critical partially composition formations. pp. 44--49

Summary:

Korzyuk V. I., Kozlovskaya I. S.
Cauchy problem for the hyperbolic third-order equation. pp. 50--57

Summary: The Cauchy problem with a non-smooth boundary for a third-order linear partial differential equation of hyperbolic type with the wave operator in the main part is studied. By the methods of energy inequalities and mollifiers with variable step the existence and the uniqueness of strong solution are proved.

Khodas S. P., Lomovtcev F. E.
Generalized Euler¾Poisson¾Darboux operator differential equations with variable domains of operator coefficients discontinuous on a countable set. pp. 58--65

Summary: The existence, uniqueness and continuous dependence theorem of strong solutions of the Cauchy problems for generalized Euler¾Poisson¾Darboux operator-differential equation with variable domains of operator coefficients, which are discontinuous on a finite or countable set of the points, is proved.

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PHYSICS

Sotsky A. B., Glasunov E. V., Chudakovsky P. J., Primak I. U.
Inverse problem of waveguide spectroscopy with a bounded prism coupler. pp. 66--74

Summary: An improved method for solving the waveguide spectroscopy inverse problem is proposed and tested via numerical simulation and actual experiments. The method takes into consideration finite dimensions of a prism coupler and longitudinal variations of a prism-waveguide gap thickness. As a result, more correct measurement of the complex mode propagation constant is achieved.

Kudryashov V. V., Baran A. V.
Modified semiclassical description of quarkonium states. pp. 75--80

Summary: The phase-integral method is improved with the help of the exponential substitution and the explicit summation of the leading constituent WKB series. As a result, the new uniformly valid approximation is obtained for the radial wave functions in the case of the Cornell potential describiing the quark--antiquark interaction.

Korshunov F. P., Marchenko I. G., Zhdanovich N. E., Gurin P. M.
Cyclic radiation-thermal processing impact on speed performance of p+-n--n+--structures in silicon. pp. 81--85

Summary: The results of experimental study of cyclic radiation-thermal impact on processes of accumulation and annealing of structural defects, charge carriers recombination in silicon diode I>p+-n--n+--structures and their electrical characteristics are presented. It is established that at multistage fluence accumulation alongside with subsequent thermaltreatment being made after each irradiation stage it is possible to obtain better trade--off of static and switching parameters of power diodes as compared with traditional radiation--thermal treatment. Such devices will demonstrate better efficiency being utilized in energy saving equipment.

Vabishchevich S. A., Vabishchevich N. V., Brinkevich D. I., Prosolovich V. S, Yankovski Yu. N.
Defect formation in the surface layer of silicon implanted with high-energy ions: recearch by indentation method. pp. 86--90

Summary: Defect formation processes in silicon implanted with high-energy B+, Ar+ and O+ ions with an energy density of ~1 MэB/amu was investigated by microhardness and Hall effect methods. Implantation leads to surface hardening of silicon monocrystals caused by electrically inactive interstitial defects which are formed as a result of diffusion of own interstitials from the implanted region to the surface. The effect of surface radiating hardening depends on a kind, energy and a doze of implanted ions. At B+ implantation the specified effect reached the maximum at a doze of implantation of ~5×1014 sm-2, but it did not reach the saturation even at the maximal doze of 1×1016 sm-2 for oxygen and argon ions. In increasing the ion energy density up to ~3 MeV/amu (implantation Kr+, 210 MeV) a boomerang dishardening effect caused by the formation of radiating defects mainly of vacant type is observed.

Loktevich A. S., Gladeichuk V. V., Goncharenko I. A.
Influence of stimulated Raman scattering on the amplifier spacing of optical fiber communication lines. pp. 91--95

Summary: The article deals with estimating of the distance of signal propagation in the optical fiber communication line until its substantial attenuation due to the loss in the fiber material and signal power transmitting to the Stokes component caused by the effect of stimulating Raman scattering is carried out. The optimal input signal power is calculated, which makes it po ssible to achieve the maximal signal propagation length (amplifier spacing). The calculations show that by setting the optimal power of the optical signal source it is possible to increase 1.9 time the amplifier spacing of the existing communication lines.

Shishonok N. A., Petrashko V. V., Soshnikov L. E., Radyush Yu. V., Kuznetsov D. A.
Synthesis and properties of high-frequency dielectrics in the BaO--Рr203--ТiO2 and ВаО--Рr203-- ТiO2--Та205 systems. pp. 96--101

Summary: The (Ва1-aРba)4(Рr1-y-zBiySmz)9 + 1/3Тi18O54 compound in the ternary ВаО--Рr203--ТiO2 system and the Ва2Рr4Ti6Ta4030, Ва3Рr3Ti5Ta5030, Ва4Рr2Ti4Ta6030, and Ва5Рr1Ti3Ta7030 compound in the quaternary ВаО--Рr203-- ТiO2--Та205 system are obtained by the solid-phase synthesis under high (up to 7 GPa) pressure. The influence of the synthesis conditions and the partial substitution of Pb ions for Ba and Bi (or Bi/Sm) ions for Pr on the composition of the phases synthesized and their dielectric properties is studied. The dielectric properties of the compounds synthesized are studied at the frequencies 102, 103, 104, and 106 Hz in the temperature range from 20 to 100 0C. The synthesis modes and the Pb, Bi, Sm, and Bi/Sm concentrations necessary for the synthesis of materials with improved dielectric properties and an almost zero temperature coefficient of the resonance frequency are determined. In the ternary system of solid solutions, the compounds with the permittivity FONT FACE="Symbol">x » 100--110 and the dielectric--loss angle tg d » 0,0015--0,003 are synthesized. In the quaternary system, the compounds with FONT FACE="Symbol">x » 100--150 and tg d » 0,0015--0,003 are obtained.

Galias A. I., Demidenko O. F., Makovetskii G. I.
Crystal structure and magnetic properties of the system of MnSe1-xSx solid solutions. pp. 102--104.

Summary: The continuous series of the system of MnSe1-xSx (x = 0.0--1.0) solid solutions with the NaCl--type cubic structure were synthesized. The unit crystallographic cell lattice parameter a linearly decreases from 0.5455 nm in manganese selenide to 0.5231 nm in manganese sulphide. The solid solutions, as well as the limiting MnSe and MnS compounds have the manganese ion magnetic moments antiferromagnetic ordering. The effective manganese ions magnetic moment values of solid solutions were close to the predicted value of 5.92 mB for Mn2+ ions. A characteristic for MnSe incomplete transition of cubic structure in hexagonal one was observed in solid solutions up to x = 0.07 concentration. The Neel temperature linearly decreases from ~ 140 K for MnSe to ~ 175 K for MnS

Ryzhkovskii V. M., Goncharov V. S., Mitsiuk V. I., Glazkov V. P., Somenkov V. A.
Crystal structure transformation in the Мn1,2Zn0,8Sb alloy. pp. 105--108

Summary: The existence of the crystal structure transformation d®x in the Мn1,2Zn0,8Sb alloy at T>800 K was shown by neutron diffraction method. The transformation is accompanied by a change in the composition of the main d--phase with the precipitates of the hexagonal x--phase NiAs--type. The transformation is described by the scheme: Mn(Zn)2Sb (d--phase) ® Mn(Zn)1+DSb (x--phase) + Mn(Zn)2+DSb (d1--phase).

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INFORMATICS

Likhoded N. A., Tolstikov A. A.
Formalization of communication operations of multidimensional loops. pp. 109--112

Summary: A method of obtaining formal communication operations for the algorithms presented by consecutive programs is proposed. These operations are a prototype of operations of data exchange at realization of algorithms on parallel computers with distributed memory.

Benediktovich V. I.
Non-crossing perfect matching in geometric complements. pp. 115--121

Summary: In this article some sufficient conditions of existence of a non-crossing perfect matching in the geometric clique K2n after removing n edges have been found.

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SHORT NOTES

Goncharenko A. M.
To the theory of propagation of optical solitons in absorbing media. pp. 122--123

Summary: The variation of the shape of an optical soliton with a depth of its penetration in an absorbing medium is considered.

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