Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 1998, No.3
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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 1998, No.3

Proceedings of the National Academy of Sciences of Belarus (Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICALMATHEMATICAL SCIENCESPublished by The Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Grudo Ye. I. †, Demenchuk A. K.
Relations for solving linear algebraic systems in one critical case. pp. 56
Summary: Formulas of solutions are given for a systems of linear algebraic equations in one critical case.
Blinova E. I.
A hierarchical algorithm for image denoising. pp. 711
Summary: The paper is devoted to recovering of images sampled with random noise. The images are interpreted as functions on the unit square that can take values from the set A = {i/n, 0 £ i £ n}, where n is fixed, only. The hierarchic algorithm consists in detecting parts of the square in which the function is constant, from large parts to small ones. The L^{s}risks of recovering are estimated in terms of Besov spaces norms. This estimates can not be improved up to logarithmic factor. The result for ddimensional case is formulated, too.
Tiounchik A. A.
Minimizing the height of parallel forms of algorithms by the branching method. pp. 1217
Summary: A method for the construction of the efficient parallel forms of algorithms is proposed. The method generalizes known strategies of partitioning and mapping of the graph models of algorithms onto array processors and provides the minimization of time requirements for the implementation of the algorithms by the processors.
Tuzik A. I.
On the index of a singular integral equation with a finite commutative group of Carleman's direct and reverse shifts. pp. 1820
Summary: A simple relation for calculating the index of a singular integral equation with a finite commutative group of Carleman's direct and reverse shifts is obtained.
Tishchenko K. I.
On approximation to integer padic numbers by algebraic numbers having a bounded degree. pp. 2124
Summary: The padic analog of Wirsing's theorem is obtained.
Ignatenko M. V., Yanovich L. A.
Newton type formulas for the operator interpolation on the spaces of many variable functions. pp. 2530
Summary: The Newton interpolation formulas for differentiable and nondifferentiable operators defined on the sets of functions of many variables are constructed.
Rovba E. A.
On one orthogonal system of rational functions and the Gauss type quadratures. pp. 3135
Summary: Quadrature formulas generalizing the classical Gauss formulas of Jakobi nodes with a = b = 1/2 are given.
Radyno A. Ya.
Degree of convergence of rational approximation depending on the order and type of a function to be approximated. pp. 3641
Summary: Relation between the rate of rational approximation of an analytic function f and its order and type are established. The corresponding theorems are proved.
Egorov A. D., Zherelo A. V.
Approximate formulas for the class of functional integrals on quasimeasure based on interpolating the measure. pp. 4245
Summary: Approximate formulas based on interpolation of quasimeasure are constructed for functional integrals w.r.t. quasimeasures.
Vabishchevich P. N., Chuiko M. M.
Difference schemes for one class of systems of convectiondiffusionreaction equations. pp. 4651
Summary: The boundary value problem for system of two convectiondiffusionreaction equations is considered. For nonstationary differential problem the maximum principle is formulated, a priory estimates are given and a monotonic difference scheme is constructed. It is shown the convergence of difference solution to the exact solution with the first order in the grid norm L_{1}(w).
Shilin A. P.
A singular integral equation with the conjugation in the regular part. pp. 5254
Summary: A new singular integral equation is solved.
Sobolevski S. L.
On one method of representation of singlevalued analytic functions with a discontinuous set of singular points. pp. 5560
Summary: A singlevalued analytic function can be represented in a neighborhood of an isolated singular point with the help of the Lourent series. In particular, if the function has no other singularities, the Lourent series represents it in the whole domain where the function is defined. V. P. Khavin obtained a similar representation by the way of integral series of a special type for singlevalued analytic functions with a bounded continuous singular set. In the present paper we obtain necessary and sufficient conditions for the existence of the similar expansion for singlevalued analytic functions with a bounded discontinuous singular set.
Tsegelnik V. V.
Selfsimilar solutions of some systems of partial differential equations. pp. 6163
Summary: Selfsimilar travellingwave solutions expressed in terms of elementary functions, in terms of elliptic functions or as integrals of the latters for some systems of special nonlinear evolution equations are obtained.
PHYSICS
Korshunov F. P., Zhdanovich N. E., Marchenko I. G., Troshchinskii V. T.
Investigation of radiationthermal defects and their influence on the characteristics of silicon diffused pnstructures. pp. 6468
Summary: Investigation results about the nature of effective recombination centers induced in diffused pnstructures on Si after the electron irradiation and subsequent annealing in the temperature range 400600 °C and their influence on the parameters of these structures in the operation temperature range 77400 K are presented. It is shown that the recombination in these structures is controlled by the defect with level E_{c}  0.32 eV and electron capture crosssection s_{n} > 1· 10^{14} cm^{2} which contains, seemingly, Al or B.
Hmyl A. A., Anisimovich V. G., Dostanko A. P., Uhov V. A., Boiko L. D.
Physicalmechanical properties of a solid surface treated by electrolyte plasma. pp. 6974
Summary: Contact resistance, microhardness, brightness and microroughness parameters of steel and brass surfaces were investigated after various polishing techniques. The most smooth surfaces and better physical and mechanical properties are produced by plasmaelectrolytical treatment. Mechanism of improving operation performance is proposed on the base of experimental data obtained with the help of Auger Electron Spectroscopy (AES), Xray, Scanning Tunnelling Microscope (STM) and Scanning Electron Microscope (SEM).
Vlasov R. A.
Formation of tilted femtosecond solitons in a cubic medium: diffractiondispersion higherorder effects. pp. 7577
Summary: The soliton propagation of tilted femtosecond pulses in cubic media is analysed, taking into account the higherorder dispersiondiffraction effects, including the specific "dispersion of diffraction". The latter is shown to exert the crucial influence on the formation of the phase and envelope of a tilted soliton.
Soroko A. V.
Atomicoptic holograms. pp. 7881
Summary: An analytical solution for off resonant density matrix is presented in such a form, that allows at certain physical conditions to interpret the interaction of ultracold atomic beam with inhomogeneous laser radiation as a passage through a threedimensional hologram.
Zhur T. A.
Relativistic rotation of a particle in a medium. pp. 8285
Summary: A system of differential equations, which describes the rotational movement of a particle in postNewtonian approximation of general relativity, is introduced and integrated. The system was derived on the basis of Papapetrou's equations with some additional conditions on S^{ab} : S^{0i} = K S^{ij} u_{j}. Numeric estimates for some peculiarities of rotational movement of a particle are obtained.
Akimov A. I., Karpei A. L., Savchuk G. K.
Investigation of atomic defects influence on reflection spectra of HTSphases in thallium based compounds. pp. 8690
Summary: We report on measurements of far infrared reflection spectra of Tlbased superconducting ceramics with different content of oxygen. Phases 1212, 1223, 1234, 2201, 2212, 2223 are investigated. Phonon modes and their frequencies are determined. It is shown that the phonon near 360 cm^{1} is sensitive to the concentration of oxygen in CuO_{2} plane for the sample with 2201 phase.
Savenko V. S., Ostrikov O. M.
Calculating the strain fields near a twinning duplicate. pp. 9194
Summary: A method for calculation of the strain fields around two doubles is proposed.
Tishkov V. S., Gaiduk P. I., Shirjaev S.Yu., Larsen A. N.
Structural transformations in alloys Si_{0.6} Ge_{0.4} implanted with Ar^{+} under rapid thermal annealing. pp. 9599
Summary: Structural transformations produced in strainrelaxed, lowdislocationdensity Si_{0,6} Ge_{0,4} films by As^{+} implantation and rapid thermal annealing were studied by transmission electron microscopy and Xray microanalysis. The type of residual defects was found to be strongly dependent on annealing temperature. Only perfect dislocation loops were observed in implanted layers after annealing at 800 °C. Annealing at higher temperature (900 °C) results in complete removal of irradiation damage accompanied by the formation of GeAs precipitates of monoclinic phase and spherical shape. The results show that the behavior of As in SiGe alloys during thermal processing is remarkably different from that in Si. In particular, precipitation of As atoms in Si_{0,6} Ge_{0,4} was found at an As concentration of 9 · 10^{20} cm^{3} which is at least one order of magnitude lower than the critical As concentration for As precipitation in Si.
Kazakewich L.A., Lugakov P. F.
Recombination properties of grownin microdefects in silicon. pp. 100102
Summary: The temperature and injection dependencies of the chargecarrier lifetime in dislocationfree nSi were analysed. This allows one to make conclusion about the recombination activity of microdefects of various types. The parameters of the main recombination centres connected with microdefects of A and Btype were determined.
INFORMATICS
Kolyada A. A.. Revinskii V. V., Selyaninov M. Yu., Chernyavskii A. F.
Minimal redundant polynomial scalar modular number systems pp. 103106
Summary: A mathematical formalization of minimum redundant polynomialscalar modular number systems is given and arithmetics methods for this class of new systems are considered.
Belov D. I., Sadykhov R. Kh.
An algorithm for removing invisible surfaces for the laminated models of threedimensional objects by approximation with the use of simple polyhedra. pp. 107110
Summary: An algorithm for removing invisible surfaces for the laminated modes of threedimensional objects by approximation with the use of simple polyhedra is developed. A new class of simple polyhedra containing convex and starshaped ones is considered and results of testing and comparative analysis are given.
Lipnitskii S. F., Shibut M. S., Yarmosh N. A.
A hypertext expert training system. I. Data and knowledge model. pp. 111114
Summary: A conception of experttutorial system is proposed that combines quality of a computer adviser, an expert and a handbook. Mathematical models of hypertext database and knowledge base are considered for the control of navigation in hypertext when computeraided learning is being realized.
Fedyanin D. V., Tikhonenko O. M.
The total demand volume and waiting time distributions for an unreliable queueing system with an infinite number of servers. pp. 115117
Summary: Summarized demands volume and waiting time characteristics of M/M/¥ queue with simultaneous breakage and renewal of all the servers are determined for the case of service time proportional to the demand length.
Krylenko A. V.
Insensitivity of the stationary distribution of closed queueing networks with rounds of nodes, nonexponential service and several types of customers. pp. 118122
Summary: Closed networks with N simply nodes with M types of customers and with rounds of nodes are considered. A round of a node depends on the state of the node and the type of a customer. The stationary state distribution is found in multiplicative form and is not dependent on the functional form of service durations of the customers with fixed expected values.
ABSTRACTS OF DEPOSITED PAPERS
Kiselev A. A.
On generation of subnonattainability. p. 123.
Kiselev A. A., Lebedev A. V.
On information properties of reduced matrices over subnonattainable cardinals. pp. 123124.
Kiselev A. A.
On nonattainable cardinals. p. 124.
Savenko V. C., Uglov V. V., Ostrikov O. M.
Twinning of bismuth single crystals irradiated with hydrogen ions. p. 124.
Savenko V. C., Ostrikov O. M.
Impurity distribution near twins boundary. p. 125.
In Belarusian Mathematical Society. pp. 126131.
SCIENTISTS OF BELARUS
Basov N.G., Burakov V.S., Voitovich A.P., Olekhnovich N.M., Tolkachyov V.A.
Nikolai Aleksandrovich Borisevich (On the occasion of the 75th birthday anniversary). pp. 132134.
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Olekhnovich N.M., Apanasevich P.A., Goncharenko A.M., Petrov N.S., Soika A.K.
Boris Borisovich Boiko (On the occasion of the 75th birthday anniversary). pp. 135136.
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Apanasevich P.A., Voitovich A.P., Olekhnovich N.M., Kozulin A.V., Korzyuk V.I., Kukharchik P.D.
Aleksandr Fyodorovich Chernyavskii (On the occasion of the 60th birthday anniversary). pp. 137138.
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