Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2009, No.2

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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2009, 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, 2009

MATHEMATICS

Troush N. N, Charnavoki A. L.
Numerical simulation of stochastic differential equations driven by a-stable motion. pp. 5--10

Summary: In this article we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to a-stable Levy motion. Two examples of financial mathematics are presented.

Mukha V. S.
Convergence of vector random sequences and their vector functions. pp. 11--16

Summary: The theorems on convergence of vector random sequences and vector functions of such sequences are proved.

Stelmakh S. N.
Unification of numerical methods to the three-point grid equations. pp. 17--23

Summary: A three-point grid problem is considered. For such problems hybrid numerical method is constructed and justified.

Urbanovich T. M.
Solution to the Riemann boundary-value problem with power factors of non-integer order in the coefficient. pp. 24--35

Summary: The Riemann boundary-value problem for a half-plane in the exceptional case with non-integer powers is solved for a class of Sato's hyperfunctions whose components are vanishing at infinity and possibly have power-type singularities in the neighbourhood of a finite number of real points.

Malyutin V. B.
Evaluation of functional integrals generated by some electromagnetic field models. pp. 36--41

Summary: The method of decreasing the number of linear independent components is presented. This method is based on decreasing the multiplicity of a functional integral. The approximate formulas for evaluation of functional integrals generated by the electromagnetic field model are constructed.

Mironenko V. V.
Periodic solutions of the non-autonomous differential system with a quadratic right hand-side. pp. 42--45

Summary: The conditions for a quadratic non-autonomous differential even-odd system are given. The set of periodic solutions of such a system is investigated.

Rasolko G. A., Alsevich L. A.
Decomposition of Chebyshev's polynomials of a singular integral with the logarithmic singularity and Cauchy's kernel. pp. 46--51

Summary:

Palchik E. M.
Finite factorable groups with the nilpotent Hall factor. pp. 52--56

Summary: In the article the finite simple groups with proper subgroups H and B, where H is a nilpotent Hall subgroup of odd order and = H • B , are described. As a consequence the following is obtained. Corollary. Let = H • B , where H is a nilpotent Hall subgroup of odd order and B is a proper 2-supersolvable subgroup. Then X is a solvable group.

PHYSICS

Bogush A. A., Red'kov V. M., Krylov G. G.
Quantum particle in a uniform magnetic field on the background of the spherical Riemann space. pp. 57--63

Summary: Schrodinger equation in the spherical Riemann space has been solved in the presence of an external magnetic field, being an analogue of a uniform magnetic field in the flat space. Generalized Landau levels have been found, which have been modified by the presence of the space curvature. The energy spectrum is discrete, energy levels depend on the magnitude of a magnetic field B, a curvature radius p, and two quantum numbers.

Triguk V. V., Feranchuk I. D.
Zero approximation for the Hamiltonian of the multielectron atom. pp. 64--70

Summary: The model Hamiltonian of atom (MHA) is developed. It allows one to analytically calculate electron density, total energy, radius, ionization potential, and other atomic characteristics and provides the accuracy comparable with the results of the Har-tree-Fock model. The effective one-electron potential of MHA doesn't include free parameters and corresponds to the electrostatic distribution of the atomic electrons. MHA can be used for constructing a density functional and for the operator method of solving the Schrodinger equation.

Karolik A. S., Lukhvich A. A., Sharando V. I.
Contribution of dislocations to the thermoelectric power of aluminum. pp. 71--75

Summary: The contribution of dislocations to the thermoelectric power of aluminum per unit dislocation density DS_d / N_d = (2.0 ± 0.2) • 10^-19 V &$149 cm² / K. is determined for the first time on the basis of direct measurement the thermopower induced by plastic deformation and indirect estimation of the induced dislocation density. The partial-wave method is used to calculate the value DS_d / N_d in the free-electron approximation on the basis of the dislocation model designed earlier. The model takes into account both the dilatation of a lattice in the dislocation core and the existence of the localized quasi-stationary electronic state on dislocations near the Fermi level. The results of calculation agree well with the experiment.

Esman A. K., Kuleshov V. K., Zykov G L., Zalesski V. B.
Influence of the geometry of a ring waveguide on the basic parameters of a microresonator IR detector. pp. 76--81

Summary: The basic results of research and development of a microresonator IR detector based on silicon waveguide ring resonators of micron size for thermovision systems of new generation are presented. A new design of an uncooled infrared integrated array silicon IR detector and a principle of its operation are described. The influence of the geometrical sizes of the design of the IR detector manufactured usung the silicon technology on its basic parameters are analyzed.

Poklonski N. A., Siahlo A. I., Gardey A. P., Gorbachuk N. I., Shpakovski S. V., Vlassov A. T.
Current simulation in the circuit (p⁺n-junction + resistor) and lifetime determination of minority charge carriers. pp. 82--93

Summary: A method for simulation of the circuit "p⁺n-junction + resistor" response to an input arbitrary-shape voltage signal is proposed. Agreement of the responses measured and obtained by simulation is shown. Approximate analytical expressions for the response signal are obtained. Simulations are used to determine the lifetime of minority charge carriers in diodes irradiated with various fluences of electrons with an energy of 3.5 MeV.

Akimov A. I., Savchuk G. K., Letko A. K.
Conditions of formation and dielectric properties of the microwave materials on the basis of the Zn-Ti-O system. pp. 94--99

Summary: Dielectric properties of ceramic materials of the Zn₂TiO₄--TiO₂ binary system are studied. The influence of the Sn⁺², Sb⁺³, Bi⁺³ doping ions on dielectric properties of ceramic samples of the Zn₂TiO₄--TiO₂ system is investigated. It is found that the SHF materials with e < 30 and tgd of about 0.0001 can be prepared by modifying the Zn₂TiO₄--TiO₂ ceramics. It is shown that the modified ceramics of the Zn₂TiO₄--TiO₂ system have great potential for development of microwave devices including compact ceramic-based antennas.

INFORMATICS

Malinkovsky Yu. V., Korobeinikova E. M.
Steady distribution in the form of displaced geometric distributions of the product for network with batch arrival and service. pp. 100--105

Summary: An exponential network with independent Poisson customer batch input flows arriving a finite number of the nodes is considered in this paper. Service times of the customer batches at nodes are independent and have exponential distributions. The sizes of arriving and leaving customer batches are independent positive random variables. The sizes of arriving customer batches have a geometric distribution. The served customer batches move at other nodes or leave the network according to some routing matrix. The sufficient condition for equilibrium network state distribution in the product form of the displaced geometric distributions is obtained.

Ovsiannicov A. V.
Statistical inequalities in superregular statistical experiments of the theory of estimation. pp. 106--110

Summary: In the article, statistical inequalities in the conditions of regular statistical experiment are considered. It is shown that when amplifying the regularity conditions (superregular) a system of inequalities, which is the generalization of the inequality of Cramer -- Rao -- Frechet can be obtained. The system obtained expands a theoretical basis for determination of qualitative limiting performances of the arbitrary moments of estimations errors. It is noted that the definition of values of the moments of error estimations of higher order allows one to take into account the non-gaussian form of the error distribution.

Mitsianok V. V.
Determination of numerical characteristics of high-frequency sounds of speech by the harmonic function approximation. pp. 111--118

Summary: The approximation problem-based method of finding the frequencies and movable amplitudes of almost periodical signals is proposed. This method is applied for 8 high-frequency sounds of human speech. The basic mode frequencies for 8 respondents and for 8 high-frequency sounds is established, unique for every person.

SCIENTISTS OF BELARUS

Vitalii Antonovich Tolkachev (To the 75th Anniversary of Birthday). pp. 119--120
Click here to read this article in Russian (Win 1251)

Fedor Pavlovich Korshunov (To the 75th Anniversary of Birthday). pp. 121--122
Click here to read this article in Russian (Win 1251)

Anatolii Nikolaevich Rubinov (To the 70th Anniversary of Birthday). pp. 123--124
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