Proc. of the Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 1997, No.1
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Proc. of the Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 1997, No.1

Proceedings of the Academy of Sciences of Belarus (Vestsi Akademii Navuk Belarusi)
SERIES OF PHYSICALMATHEMATICAL SCIENCESPublished by The Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Petrov V.A.
Diagram method based evaluation of functional integrals on the Poisson measure. pp. 58
Summary: An approximate formula for functional integrals on the Poisson measure is constructed. This formula takes consideration the contributions of special form Feynman diagrams.
Gaiduk S.I.
Problem about impact caused traversal oscillations of an elastoviscous beam with the supported ends. pp. 914
Summary: Solvability of mixed problem on traversal oscillations of a homogeneous finite elastoviscous beam is investigated for the case when the beam was subject to an impact by some load which after the impact keeps contact with the beam.
Prusov A.I.
Elastic state of anisotropic strip lying on rigid base. pp. 1518
Summary: New formulas of elasticity theory for anisotropic strip are obtained. Problem of rigid punch invasion into anisotropic strip, lying on rigid base, is considered as an example. There is no friction between the punch, stip and the base.
Krushevski A.E., Boiko N.Ya.
A technique for constructing solutions of elastic parallelepiped equilibrium problems with consistent conditions on the bounds based on the Lagrange variational principle. pp. 1923
Summary: The threedimensional elastic parallelepiped equilibrium problem is reduced to onedimensional one on the base of Lagrange variational principle with use of the Fourier series with supplementary terms in the form of Legendre polynomials. In this connection the boundary value conditions on four facets are precisely fulfilled. Some examples with consistent boundary value conditions are considered.
Dubrovski V.V.
Asymptotics for eigenvalues of Gegenbauer type singular differential operators. pp.2428
Summary: Asymptotics for eigenvalues of Gegenbauer's differential operator is calculated up to the terms that converge when summing up.
Minchenko O.Yu., Zhivitskaya E.N.
On sensitivity of discrete control systems with respect to perturbations of parameters. pp. 2932
Summary: We consider a discrete system with perturbations in the righthand side and in the initial conditions. We investigate differential properties of the optimal value function. In particular, we obtain estimates of generalized gradients for the optimal value function and prove its directional differentiability.
Lazakovich N.V., Stashulionok S.P.
Approximations in Ito's and Stratonovich's form of integrals and equations of point stochastic processes. pp.3339
Summary: Approximations in form of Ito and Stratonovich of stochastic integrals and equations for point stochastic processes are considered.
Lazakovich N.V., Stempkovskaya T.V.
Approximations of stochastic differential equations in Stratonovich's form by difference ones. pp.4045
Summary: Approximations of solutions to stochastic differential equations by difference ones are considered.
Mateiko O.M.
Linear two dimensional representations of the free product of two finite cyclic groups. pp.4649
Summary: Complex linear two dimensional representations of the free product of two finite cyclic groups are described. Faithfulness and nonfaithfulness of such representations are investigated.
Belko I.V.
Characteristic homomorphism of the Lie algebroid. pp. 5055
Summary: We can construct the Chern  Weil characteristic homomorphism for the principal bundle that aubstitutes this one for its Lie algebroid. On this base we construct characteristic homomorphism of transitive Lie's algebroid. The domain attached is the cohomology of the Lie algebroid. The range is the De Rham cohomology of the base space.
Novic A.A., Fedosenko V.S.
Nonstationary internal waves in a flow of inhomogeneous fluid. pp. 5660
Summary: It is considered the problem about internal waves generated by initial perturbations or surface pressures in a twolayer flow. Exact solution of problem is obtained in the form of combinations of Bessel's functions. As a special case it contains the solution of the Cauchy  Poisson problem.
Korzan L.A.
An explicit solution to a special case of mixed problem of elasticity theory for the plane with sections lying on the real axis. pp. 6167
Summary: Solution to a special case of the mixed problem of elasticity theory for the plane with sections lying on the real axis is given. A feature of this problem is that for its solution it does not need solving the auxiliary Jacobi's problem.
Gladyshev M.T.
Some problems of fluid mechanics. pp. 6874
Summary: Break and asymptotic solutions of the equations of open and close flows are considered.
PHYSICS
Fiodorovych A.M.
Formulation ot electrodynamics in terms of relativistic vector algebra. pp. 7579
Summary: An algebraic formulation of electrodynamics (Maxwell  Lorentz equations, the Lagrangian, energymomentum conservation law) is given in terms of the operations of relativistic vector algebra extending the ordinary treedimensional vector algebra to the relativistic case. This formulation is compact and explicitly relativistically covariant. A solution of inhomogeneous Maxwell equations in the form of harmonic plane wave is found in algebraic way.
Minkevich A.V., Polozov M.N.
On sphericalsymmetric fields in gauge theory of gravity in the WeilCartan spacetime. pp. 8083
Summary: Gravitational equations for sphericalsymmetrical fields in the framework of gauge theory of gravity in WeylCartan spacetime based on sufficiently general gravitational Lagrangian including both scalar curvature and terms quadratic in the curvature and torsion tensors are obtained. It is shown that under certain conditions some known solutions of general relativity for the metric (the vacuum Schwarzschild solution, the ReissnerNordsrom solution and others) satisfy obtained gravitational equations as the torsion vanishes and nonmetricity holds.
Baryshevski V.G.
Phenomenon of T noninvariant rotation of the polarized waves in diffraction gratings under violating invariance with respect to the inversion of the time T. pp. 8489
Summary: We show that Tnoninvariant interaction of electromagnetic waves with atoms leads to the effect of polarization plane rotation and circular dichroism of electromagnetic waves in diffraction gratings.
Belov V.V.
Equations for balance of distribution functions of systems with orientational degrees of freedom. pp. 9094
Summary: Within the framework of functional expansion method a closed system of equations for one and twoparticle distribution functions of a system of nonspherical particles is derived. Generating functional is chosen to be a linearrational combination of exponential functions with oneparticle direct correlational function in the exponent.
Mityanok B.B.
Field equations and lagrangian corresponding to nonlinear superposition. pp. 9598
Summary: The field equations on assumption of existence of nonlinear superposition of the scalar and vector fields are found. The appropriate lagrangians are given too.
Razvin Yu.V., Kovaliov A.A., Potachits V.A.
Electrooptical characteristics of liquid crystal matrix modulators on fibre optic faceplates. pp. 99102
Summary: Results of investigation of liquid crystals matrix modulators on fibre optical faceplates are obtained.
Kulak G.V., Kulak V.I., Ropot P.I.
Acoustooptical filtering with sideband suppression of interference maxima in planar lithium, niobate optical waveguides. pp. 103104
Summary: Some peculiarities of acoustooptical filtering with sideband suppression of interferential maxima in planar lithium niobate optical waveguides are considered. A new scheme of acoustooptical filter using the consecutive (TETM and TMTE) mode conversion of a guided optical wave by an acoustic surface wave is proposed. Fundamental characteristics of the tunable acoustooptical filer are found under the conditions of effective sideband suppression.
Kulak G.V., Hilo P.A.
Bragg's back scattering on phase superlattices of photoelasticity. pp. 105107
Summary: Properties of the Bragg back scattering on phase superlattices of photoelasticity, created with using trigonal, tetragonal and cubic crystals, are studied. The possibility of effective back scattering on low frequency ultrasound is shown.
Batishche S.A., Tarkovski V.V.
Generation of microsecond laser pulses by an YAG: Nd^{3+} laser. pp. 108111
Summary: It is shown that YAG: Nd^{3+} laser produces smooth microsecond pulses under dye or Al_{2}O_{3} laser pumping with energy efficiency up to 36%.
Rudnitski A.S., Voropai Ye.S.
On a method to extend reflection anglewidth. pp. 112116
Summary: Maximum reflection angles and apertures in kaleidoscopical prism are obtained and investigated. Retroreflective surface from these prisms returns light for any angle of illumination in certain plane.
Korshunov F.P., Zhdanovich N.E., Marchenko I.G., Troshchinski V.T.
Influence of nonuniform distribution of radiation defects in silicon pnstructures on their characteristics. pp. 117121
Summary: The possibility of forming nonuniform distribution of radiation defects in silicon structures with pn junctions using electron irradiation is shown and influence of this distributions on the characteristics of the devices is considered.
Shipilo V.B., Orlova N.S., Rapinchuk T.V., Kochkarik O.E.
Xray study of structural variation in aluminium nitride ceramics under thermobaric conditions. pp. 122125
Summary: Variation of the structural characteristics in the aluminum nitride ceramic samples sintered at high temperature (2120 K) under high pressure (5 GPa) daring 1  90 s are studied using the Xray powder diffractrometry method. It is found that this thermobaric treatment of fine powder AIN causes the lattice compression along hexagonal axe and intensive annealing of defects during 5  10 s. All the structural characteristics almost do not change during 15  60 s.
INFORMATICS
Vasilevich L.N., Kolyada A.A., Revinski V.V.
Highspeed modular realization of finite impulse response adaptive digital filters. pp. 126131
Summary: A modular arithmetic based technique is presented to implement the adaptive digital FIRfilters of high order (up to 16). New highspeed table method for multiplying data is described and the errors of the method are studied.
Oleinik L.F.
Simulation of marked point processes. pp. 132135
Summary: An algorithm for marked point process simulation is described. It is assumed that an allocation of given points in the plane is known. The problem is to assign marks to every point in accordance with specified semivariogram.
ABSTRACTS OF DEPOSITED PAPERS
Podkopaev D.P.
On sensitivity radius of effective solutions with respect to perturbation of one parameter for the multicriteria trajectory problem. p. 136
Datsyk V.T., Semenchuk N.P.
On a certain integral equation in the class L(¥, ¥). pp. 136137
Yudov A.A.
Group model of submanifold of homogeneous space. Invariant polynomial, ordered point submanifolds of homogeneous space. Classification of isotropic curves of space ^{2}R_{4}. p.137
CHRONICLE
International Conference "Diophantine Analysis and its Applications" in Honour of Academician V.G. Sprindzhuk (1936  1987). p. 138
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