Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2010, No.2

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

MATHEMATICS

Lazakovich N. V., Khmyzov А. К.
Systems of quasi-differential equations in the direct product of algebras of mnemonic functions. pp. 5--11.

Summary: The Cauchy problem for systems of quasi-differential equations with the generalized right hand-side is investigated. The associated solution of the initial problem is considered in the direct product of algebras of mnemonic functions.

Shchukin M. V.
n-Homogeneous C*-algebras with the space of primitive ideals being homeomorphic to a compact two-dimensional oriented manifold. pp. 12--17.

Summary: The structure of the algebraic bundles over two-dimensional compact oriented manifoldsis considered. We describe the criteria for two algebraic bundles over two dimensional compact oriented manifolds to be isomorphic.

Zhuk E. E.
Investigation of the covariance properties of pseudo random sequences transformed based on the empirical distribution function. pp. 18--22.

Summary: The covariance properties of pseudo random sequences transformed based on the empirical distribution function is investigated. The case of this transformation optimal in the sense of covariance properties, which provides passing the basic statistical tests, is proposed.

Budarina N. V., Kukso O. S.
Simultaneous approximations of zero by values of quadratic irrationalities in R ´ Q_p with non-monotonic right-hand sides of inequalities. pp. 23--25.

Summary:

Kalosha N. I.
Finding the best constant for the approximation of zero by values of second degree polynomials. pp. 26--29.

Summary: A lower estimate has been obtained for the value d such that the inequality |P(x)|>dQ^-2 holds for any integer polynomial of the second degree satisfying H(P) £Q, where H(P) is the height of P.

Malyutin V. B.
Exact and asymptotic formulas for some functional integrals over discrete variables. pp. 30--34.

Summary: The functional integrals of the exponential with a linear and quadratic functional in the exponent defined on a set of the functions q(s)=±1, sÎ[0,T], are considered. Exact and asymptotic formulas as T ® µ со for these functional integrals are obtained.

Lucenko Ju. V., Skiba A. N.
Finite groups with X-permutation second and third maximal subgroups. pp. 35--40.

Summary: The article is devoted to studying finite groups in which every i-maximal subgroup, 1 £ i £ 3, is X-permutable with all Sylow subgroups of G, where X is a soluble normal subgroup with a fixed nilpotent length.

Erofeenko V. T.
Modeling boundary conditions on composite screens for electromagnetic fields of axial symmetry. pp. 41--45.

Summary: Bilaterial boundary conditions linking electromagnetic fields on the both sides of a biisotropic plane layer are developed. Boundary conditions for cylindrical fields with a harmonic dependence on the azimuth angle are obtained. Boundary relations are presented by cylindrical coordinates in a special basis, and can be used for solving boundary-value problems of mathematical physics.

Zhestkov S. V., Romanenko A. A.
Existence of new forms of wave solutions of nonlinear equations of mathematical biology. pp. 46--51.

Summary: A direct method of constructing wave solutions of nonlinear equations of mathematical biology is developed. Necessary and sufficient conditions for existence of wave solutions are obtained.

PHYSICS

Tolkachev E. A.
Analysis of the Born-Infeld electrostatics equations in the Helmholtz representation. pp. 52--55.

Summary: The basic vector equation of Born-Infeld electrostatics is derived taking into account a vortex part of electric induction. It is shown that for the two point electric charges, it reduces to one nonlinear equation for a scalar function which is not a potential.

Baryshevsky V. G., Shyrvel A. R.
Effect of incoherent scattering on the birefringence of high energy deuterons. pp. 56--65.

Summary: Consideration of elastic incoherent scattering of deuterons on a thin target leads to a necessity of taking into account a single scattering contribution to the birefringence effect. The amount of these corrections depends significantly on a particular geometry of experiment. Namely, it depends on the angular opening of a detector collimator. It is shown that the full compensation of contributions to the rotational angle of deuteron polarization vector coming from conditional interference of Coulomb and nuclear interactions is possible only in the case of 4p- geometry of experiment.

Degtyareva E. A., Timoshin S. L.
Spin structure of the nucleon from the lp — DIS with charged weak current. pp. 66--70.

Summary: The possibilities of determination of quark contributions to the nucleon spin based on observable asymmetries of lp -semi-inclusive deep inelastic scattering with the charged weak current of the p-, K - meson production are considered.

Korshunov F. P., Gurin P. M., Gurinovich V. A., Zhdanovich N. E.
Annealing of silicon epitaxial n⁺-p-structures irradiated with fast electrons. pp. 71--75.

Summary: Static (forward voltage drop and barrier capacitance) and dynamic (minority charge carriers lifetime in p-base) parameters changes of n⁺-p-structures irradiated with electrons (6 MeV) have been investigated. It is established that the forward voltage drop and the barrier capacitance of n⁺-p-junction recover during annealing at about 623 K, but the minority charge carriers lifetime recovery occurs at annealing temperatures above 773 K. The recovery of a forward voltage drop and barrier capacitance is related with annealing of radiation complexes of divacancy-oxygen (V₂0) and boron-carbon (B_iC_s). The recovery of minority charge carriers lifetime in structures is related mainly with annealing of radiation complex of carbonoxygen (С_iО_i).

Tikhomirov V. V., Sytova S. N., Cherkas S. L., Siahlo S. E.
Simulation of internal electrical voltages in the magnetic flux compression generator. pp. 76--82.

Summary: A simple method of evaluation of local voltages arising in the flux compression generator allowing the generation of a short electric power pulse is suggested. A method of reducing both internal voltage and electric field strength is considered and tested using numerical simulations.

Kolchevsky N. N., Petrov P. V.
Spectral properties of an adiabatic microcapillary lens. pp. 83--88.

Summary: In 1996, the idea of using compound refractive lenses for focusing hard X-rays was presented. An adiabatic lens is a kind of short-focal X-ray compound refractive lenses. An adiabatic lens consists of lenses with variable radius. As a kind of the adiabatic lens the adiabatic microcapillary lens is proposed. The microcapillary X-ray lens is developed as a row of bubbles in the shaped glass capillaries. Each bubble has a refractive surface for X-rays. The shape of the capillary defines the radius of the bubbles or refractive surfaces. Compound refractive surfaces define the optical properties of the adiabatic microcapillary lens. Spectral distributions of the focal spot of the adiabatic microcapillary lens are calculated. The possibilities of using the adiabatic microcapillary lens a X-ray filter are discussed.

Tochitskii T. A., Grabchikov S. S., Dmitrieva A. E.
Investigation of the mechanism of formation of the transition layer structure in the electrodeposited Ni-W alloy films on copper. pp. 89--93.

Summary: The structure of electrodeposited Ni-W alloy films with a thickness of about 30-50 nm depending on the cathode current density and the chemical composition was investigated. The mechanism of formation of the film-substrate» transition layer structure was suggested.

Chernyshev A. V.
Determination of reversible and irreversible magnetization components for the asymmetric minor loop with branches of parabolic shape. pp. 94--99.

Summary: Determination of increases in reversible and irreversible components of magnetization for the asymmetrical minor loop, whose branches are shaped as parabolas, is examined. It is shown that for such a minor loop the increase in the reversible component of magnetization depends parabolically on the increase in the strength of the external magnetic field.

Nazim F. A., Lukashevich M. G., Nyzdin V. L., Chaibullin R. L, Odzaev V. B.
Peculiarities of the electrontransport properties of polyimide films implanted with copper and cobalt ions. pp. 100--105.

Summary: Thin polyimide foils were implanted with 40 keV Co⁺ and Cu⁺ ions at fluencies of 2.5×10¹⁶—1.25×10¹⁷ cm^-2 and at ion current densities of 4, 8 and 12 mA cm^-2. Surface dc electric resistance of the implanted polymer samples have been measured in the temperature range 40 -- 300 K. Metal implantation results in decreasing polymer resistance with the dose and current density increasing for the both kinds of metal ions. The decrease of dc electric resistance is caused by radiation-induced carbonization and metal nanoparticle formation in the implanted region of polymer. The transition from the insulating to metallic regime of conductivity is observed in cobalt implanted samples for critical doses above D_c = 1.25×10¹⁷ cm^-2 at an ion current density of 8 mA cm^-2. In the contrary, high-fluence implantation in the polymer with Cu⁺ ions for the same regimes does not result in the transition. The dominating mechanisms of charge carrier transport and the origin of insulator-to-metal transition in the metal implanted polymer are discussed.

INFORMATICS

Likhoded N. A., Ogeiko A. E.
Vector scheduling functions for generalized fusion of multidimensional loops. pp. 106--111.

Summary: A new method of obtaining transformations, witch specify generalized loop fusion, was developed. The method is applied to multidimensional loops with arbitrary nesting structure and allows external variables to be take into account parametrically.

Kostyukova O. L., Fedartsova N. M.
Guaranteed control strategy for linear systems with disturbances in a class of bounded controls. pp. 112--119.

Summary: For linear optimal control systems with bounded disturbances and bounded controls, a problem of constructing a guaranteed optimal control strategy is solved. The control strategy can be corrected at the given time moments during a control process. Available control strategy guarantees that for all admissible disturbances, cost functional does not exceed a calculated value that approximates the optimal value.

SCIENTISTS OF BELARUS

Nikolai Mikhailovich Olekhnovich (On the occasion of the 75th birthday). pp. 120--121.
Click here to read this article in Belarusian (Win 1251)

Viktor Ivanovich Korzyuk (On the occasion of the 65th birthday). pp. 122--123.
Click here to read this article in Russian (Win 1251)

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