Proc. of the Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 1996, No.1
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Proc. of the Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 1996, 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
Grudo E.I.
On quasinormal form of matrix of several variables. pp. 57
Summary: The method of reducing quadratic continuous matrix of several variables to quasinormal form is represented.
Zhavrid N.S., Yanovich L.A.
Quadratic interpolation of functionals in the spaces of the continuously differentiable functions of one and two variables. pp. 815
Summary: The quadratic interpolation formulas for functionals in the spaces of the continuously differentiable functions of one and two variables are derived.
Bobkov V.V.
On an approach to the construction of numerical methods for systems of ordinary differential equations. pp. 1519
Summary: A new approach to the construction of numerical methods for initial value problems for autonomous systems of ordinary differential equations (including stiff systems) is proposed. This approach is oriented to the procedure of linearization of the nonlinear system at each step of integration. The essence of the technique is the use of polynomial approximation of the matrix exponential function with respect to the matrix argument. It is important that the stability property holds for any degree of the polynomial and for any positive value of the discretization step.
Gorbuzov V.N.
On integrals and last multipliers of multidimensional differential systems with symmetries. pp. 2024
Summary: Construction of the last multipliers and the first integrals of the system (I) on the base of linear differential operators is carried out.
Brui I.N.
Trigonometric rows of L^{p}(T) classes and their regular means. pp. 2430
Summary: For the case when r^{(n)}_{m} = max(1  m(n + 1)^{1}; 0) theorem has been proved by W.H. and G.C. Young (1913).
Dubrovsky V.V.
Regulirized traces of selfadjoint operators. pp. 3033
Summary: Author proved the regularization of traces for discrete selfadjoint operators in sense of row Taylor.
Avdashkova L.P., Kamornikov S.F.
On normalizers of Freachable subgroups. pp. 3335
Summary: For Sclosed formation F it is shown that normalizer of each Freachable subgroup of finite group G contains Fresidual of socle of this group.
PHYSICS
Redkov V.M.
Existence of a spinor apace geometry and the concept of intrinsic fermion parity. pp. 3642
Summary: Some traditional approaches concerning the intrinsic fermion parity suffer from grave shortcomings. Analysing the fermion parity in the context of utilizing a spinor space geometry is proposed in this article. In such a space model, the 2 ¶rotation does not amount to the identical transformation I, and the whole problem of intrinsic fermion parities is to be solved by a classification of nonequivalent representations of the geometrical symmetry group. Extended according to E. Cartan the 2dimension unitary group {SU(2) + J) = SU^{~}(2) allows two types of nonrelativistic fermions. The 4dimension extended linear spinor group SL(2.C), covering the Lorentz group L_{+}^{} which contains P and Treflections, admits two types of relativistic fermions too. The concept of boson intrinsic parity is to be seriously revised in the spinor geometry framework.
Sergeenko M.N.
Isotropic oscillator in quasiclassical approach. pp. 4349
Summary: The question on the application of the quasiclassical approach for solution of multidimensional problems in quantum mechanics is investigated. The method of asymptotical quantization based on the solution of quasiclassical wave equation obtained by the correspondence principle and adiabatic one with classical HamiltonJacobi equation is proposed. The problem of isotropic oscillator is solved to demonstrate the efficiency of proposed quasiclassical method. Obtained after division of the variables the onedimensional equations (radial and angular ones) are solved by the proposed method that results in the wellknown exact eigenvalues of isotropic oscillator and correspondent eigenfunctions of standing wave type.
Revinsky A.F.
Calculation from the first principles of potentials of electron intervalley scattering on phonons. pp. 4952
Summary: The deformation potential for electron scattering between the equivalently oriented valleys (gtype intervalley scattering) is calculated for silicon using the density functional theory.
Tsvetkov I.V.
Calculation of functional integrals by the operator method. II. pp. 5257
Summary: In the framework of the Operator Method of the uniformly fitted estimation of functional integrals a simple and general procedure for calculating the terms of the expanding the Exponential is derived. With reference to the problem on nonrelativistic anharmonic oscillator a secondorder correction to the ground energy is obtained and compared with the tabulated numerical values. The agreement is excellent.
Dostanko A.P., Shiripov V.Ya., Fedosenko G.N., Yemelianov V.A., Maryshev S.P.
Analysis of diamondlike carbon film formation from laser plasma. pp. 5861
Summary: The characterization of laser plasma during diamondlike carbon film formation by pulsed laser evaporation is reported.
Bogatyrev Yu.V.
Current annealing of irradiated CMOS integrated structures. pp. 6165
Summary: Physical aspects and the current annealing method of irradiated CMOS integrated structures have been considered.
Sokolovsky T.D., Ryzhkovsky V.M.
Calculation of lattice and magnetic heat capacity of Mn_{2}Sb compounds. pp. 6569
Summary: Calculations of the bond energy, the dispersion relations and the specific heat of the manganese antimonide with account of anharmonicity at the temperature 0  850 K are fulfilled. The contribution of the electronic and magnetic specific heat is also calculated.
Akimov A.I., Yakimovich V.N., Rubtsov V.A., Savchuk G.K.
Production and analysis of new compound in the Ba  Cu  O system. pp. 6973
Summary: An unknown compound with the chemical formula BaCuO_{3x} was shown to be formed in the Ba  Cu  O system under oxygen pressure above 1 MPa and the temperature of 1000 °C. Parameters of this compound crystal lattice are  a = 11.43 A°, b = 12.86 A°, c = 14.58 A°. The compound is decomposed at heating up to 1170 K with formation of BaCuO_{2} and it loses some part of oxygen at heating up to 600 °C in the air without any crystal structure change.
Margolin L.N., Gontarev V.F.
Dielectric and polarization properties of triglycine sulfate doped by Lvaline. pp. 7477
Summary: The experimental investigation of dielectric and polarization properties of triglycine sulfate crystals doped with Lvaline was carried out. Doping of triglycine sulfate crystals with Lvaline reduces twice threshold, saturated and coercitive fields.
Sirota N.N., Vitkina Ts.Z., Shostak L.M.
Determination of kinetic parameters of cellulose thermal destruction. pp. 7783
Summary: Investigation of thermal destruction processes of microcrystalline cellulose has been carried out by a thermogravimetry method. The kinetic parameters of thermal destruction reactions of microcrystalline cellulose have been determined from thermal analysis data on the basis of the method developed.
Batishche S.A., Mostovnikov V.A., Nikitchenko V.M., Tarkovsky V.V.
Investigation of generation characteristics of new coumarin dyes under flashlamp pumping. pp. 8387
Summary: New coumarin dyes generating in the spectral range of 420  657 nm with energy efficiency up to 1% and photochemical stability 3  5 times as high as for Rodamin G are investigated.
Khilo P.A.
Generation of the second optical harmonic under its collinear diffraction by an ultrasound. pp. 8890
Summary: The influence of the sediment from Bragg synchronism at acoustooptic interaction on the SHG area phases being in agreement has been studied. Providing modified conditions of the phase synchronism the estimation of transformation efficiency has been done.
INFORMATICS
Kolyada A.A., Revinsky V.V., Selyaninov M.. Yu., Chernyavsky A.F.
Application of minimal redundant modular encoding for fast multiplication of complex numbers in the systems of digital signal processing. pp. 9197
Summary: A novel method of multiplication of Gaussian's numbers to fractional complex constants is designed. It is based on use of minimum redundant modular number systems (MNS) and strategy of symmetrization of error's range. The proposed method allows double decrease of code's redundancy in comparison with classical MNS just when the execution time of operation is minimized.
Likhoded N.A.
A method for constructing algorithm parallel forms for reducesize array processor implementation. pp. 97104
Summary: A formalized method for the construction of parallel forms of algorithms for implementation on reducesize array processors is proposed (reducesize array processors are twodimensional, the width of the arrays is fixed by preassigned number of processor elements). The method includes the partition of the dependence graph of algorithm and spacetime mapping of each part into computation graph. Proposed approach leads to array processors without global interconnections, the local memory of the processor elements is independent of the number of parts.
Dailyudenko V.F., Krot A.M.
Nervous pulse propagation modeling on the basis of digital filtration methods. pp. 104111
Summary: The article deals with the digital filtering method for kinetic model analysis of autowave processes. It is shown that the numerical model of nervous impulse propagation may be implemented by means of two linear filters construction. The main advantages of proposed method are the reduction of calculation complexity and increase of algorithm robustness.
Kravtsov M.K.
On unsolvability of discrete optimization vector problems by linear convolution algorithms. pp. 111116
Summary: It is proved that vector problems on graphs and a variety of boolean programming problems cannot be solved by means of linear convolution algorithms.
SHORT COMMUNICATIONS
Sheshko M.A.
Spectral ratios for singular integrals with Cauchy nucleus along the real axis. pp. 117119
Summary: The socalled "Spectral relations" for singular integrals with Cauchy kernel were revealed, the line of integration being the whole material axis and also their analogs for regular integrals.
ANNOTATIONS OF THE DEPOSITED ARTICLES
Basik V.A., Gladun O.M., Strezh A.I.
On composition of methods of complete reduction and matrix run. p.120
Strezh A.I.
On a variant of multigrid method of solving differential equations in combination with indistinct run. pp. 120121
Vorobiev G.N.
On conjugation of nsubgroups. p.121
Suprun V.P., Lichko Yu.V.
Resolution of elementary and monotone symmetric Bool functions into monotonically polarized ReedMuller polynomials. pp. 121122
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