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 PHYSICALMATHEMATICAL SCIENCESPublished by Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Rovba Y. A. Smatrytski K. A.
Convergence in the mean of rational interpolating processes in the zeroes of Bernstein fractures. pp. 59
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 + x^{2})^{1} on R.
Kaliada D. U.
Upper estimate of the number of integral polynomials of third degree with a given bound of discriminants. pp. 1016
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 multidimensionalmatrix states and observations. pp. 1724
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 nonGaussian case is offered.
Gromak V. I., Hrytsuk E. V.
To the theory of nonlinear differential systems with the Painleve property. pp. 2530
Summary: A relation between the resonant method for nonlinear differential systems and reduction of these systems to equivalent BriotBouquet systems is given.
Palchik E. M.
Finite groups with the factorization G=G_{>p}×С(х). pp. 3134
Summary:
Kovalkova D. P., Skiba A. N.
Finite groups with given systems of Squasinormal subgroups. pp. 3543
Summary: The structure of finite groups, in which each maximal chain of length two has a proper Squasinormal subgroup, is described.
Zhiznevsky P. A., Safonov V. G.
Critical partially composition formations. pp. 4449
Summary:
Korzyuk V. I., Kozlovskaya I. S.
Cauchy problem for the hyperbolic thirdorder equation. pp. 5057
Summary: The Cauchy problem with a nonsmooth boundary for a thirdorder 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. 5865
Summary: The existence, uniqueness and continuous dependence theorem of strong solutions of the Cauchy problems for generalized Euler¾Poisson¾Darboux operatordifferential equation with variable domains of operator coefficients, which are discontinuous on a finite or countable set of the points, is proved.
PHYSICS
Sotsky A. B., Glasunov E. V., Chudakovsky P. J., Primak I. U.
Inverse problem of waveguide spectroscopy with a bounded prism coupler. pp. 6674
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 prismwaveguide 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. 7580
Summary: The phaseintegral 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 quarkantiquark interaction.
Korshunov F. P., Marchenko I. G., Zhdanovich N. E., Gurin P. M.
Cyclic radiationthermal processing impact on speed performance of p^{+}nn^{+}structures in silicon. pp. 8185
Summary: The results of experimental study of cyclic radiationthermal impact on processes of accumulation and annealing of structural defects, charge carriers recombination in silicon diode I>p^{+}nn^{+}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 tradeoff of static and switching parameters of power diodes as compared with traditional radiationthermal 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 highenergy ions: recearch by indentation method. pp. 8690
Summary: Defect formation processes in silicon implanted with highenergy 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 ~5×10^{14} sm^{2}, but it did not reach the saturation even at the maximal doze of 1×10^{16} 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. 9195
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 highfrequency dielectrics in the BaOРr_{2}0_{3}ТiO_{2} and ВаОРr_{2}0_{3} ТiO_{2}Та_{2}0_{5} systems. pp. 96101
Summary: The (Ва_{1a}Рb_{a})_{4}(Рr_{1yz}Bi_{y}Sm_{z})_{9 + 1/3}Тi_{18}O_{54} compound in the ternary ВаОРr_{2}0_{3}ТiO_{2} system and the Ва_{2}Рr_{4}Ti_{6}Ta_{4}0_{30}, Ва_{3}Рr_{3}Ti_{5}Ta_{5}0_{30}, Ва_{4}Рr_{2}Ti_{4}Ta_{6}0_{30}, and Ва_{5}Рr_{1}Ti_{3}Ta_{7}0_{30} compound in the quaternary ВаОРr_{2}0_{3} ТiO_{2}Та_{2}0_{5} system are obtained by the solidphase 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 10^{2}, 10^{3}, 10^{4}, and 10^{6} Hz in the temperature range from 20 to 100 ^{0}C. 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 » 100110 and the dielectricloss angle tg d » 0,00150,003 are synthesized. In the quaternary system, the compounds with FONT FACE="Symbol">x » 100150 and tg d » 0,00150,003 are obtained.
Galias A. I., Demidenko O. F., Makovetskii G. I.
Crystal structure and magnetic properties of the system of MnSe_{1x}Sx solid solutions. pp. 102104.
Summary: The continuous series of the system of MnSe_{1x}Sx (x = 0.01.0) solid solutions with the NaCltype 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 m_{B} for Mn^{2+} 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 Мn_{1,2}Zn_{0,8}Sb alloy. pp. 105108
Summary: The existence of the crystal structure transformation d®x in the Мn_{1,2}Zn_{0,8}Sb alloy at T>800 K was shown by neutron diffraction method. The transformation is accompanied by a change in the composition of the main dphase with the precipitates of the hexagonal xphase NiAstype. The transformation is described by the scheme: Mn(Zn)_{2}Sb (dphase) ® Mn(Zn)_{1+D}Sb (xphase) + Mn(Zn)_{2+D}Sb (d_{1}phase).
INFORMATICS
Likhoded N. A., Tolstikov A. A.
Formalization of communication operations of multidimensional loops. pp. 109112
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.
Noncrossing perfect matching in geometric complements. pp. 115121
Summary: In this article some sufficient conditions of existence of a noncrossing perfect matching in the geometric clique K_{2n} after removing n edges have been found.
SHORT NOTES
Goncharenko A. M.
To the theory of propagation of optical solitons in absorbing media. pp. 122123
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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