(Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICAL-MATHEMATICAL SCIENCES
Published by The Institute of Mathematics of NASB, Minsk, Republic of Belarus
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Proceedings of the National Academy of Sciences of Belarus (Vestsi Natsiyanalnai Akademii Navuk Belarusi) SERIES OF PHYSICAL-MATHEMATICAL SCIENCES Published by The Institute of Mathematics of NASB, Minsk, Republic of Belarus |
Summary: The necessary and sufficient conditions of solvability of the matrix equation AX - XA = C are given.
Rovba E.A.
Rational interpolation of differentiated functions with r-derivative of limited variation. pp. 8--13
Summary: We developed a method of approximation of functions, differentiated by Rimann--Louiville technique, and having r-derivative of limited variation (r > 0). The approximation is achieved by means of interpolative rational functions in the areas of Bernstein knots.
Benyash-Krivets V.V.
Classes of characters in free groups with rank 2. pp. 14--19
Summary: We consider the problem of determining when two elements u, v in the free two generator group F2 = < g, h > have the same characters under all representations of F2 into SL2(K), i.e. u, v belong to the same character class. We proved that if the syllable length of a cyclically reduced word u Î F2 is £ 3 and v Î {u} then v can be obtained from u with the help of the sequence of "so called" standard transformations. Two series of examples show that this does not hold for words of syllable length ³ 4.
Garist Yu.E., Palchik E.M.
On finite groups which admit the co-simple automorphism. pp. 20--22
Summary: In the paper are proved the following results. Theorem 4. Let X be a finite group admitting automorphism y of order r, (|X|, r) = 1, B = Cx(y). Let P be a y-invariant S2-subgroup of X, |B| is odd order and PB = BP. Then is P D X. Theorem 5. Let X,y,B are defined as in theorem 4. Let P be a y-invariant Sp-subgroup of X, B is a p'-group. IfP Í Nx(B), then is X = P x Xp'. Theorem 6. Let X, y, B, P are defined as in theorem 5, p > 2. If B DD < P,B >, then X has a normal p-complement.
Safonova I.N.
On minimal w-local non-H-formations. pp. 23--27
Summary: The goal of this paper is to describe minimal w-local non-h-formations, where h is an arbitrary formation of classical type.
Malyutin V.B.
Interpolation formula for functional integrals defined by differential equation with noncommuting values. pp. 28--32
Summary: Interpolation formula for functional integrals defined by a transitional function taking noncommutative values is constracted.
Astrovskii A.I.
Positive observability of linear time-varying systems. pp. 33--39
Summary: The observability problem of linear time-varying systems with positive output functions is considered. The necessary and sufficient conditions for positive observability and positive nonobservability are proved. In terms of the observability matrix the sufficient conditions are obtained for linear time-varying system to be positive observable.
Blinova E.I., Zalessky B.A.
On precision of maximum-a-posteriori estimation of binary functions (images) in the Ising model. pp. 40--45
Summary: We study the maximum a posteriori estimator properties in the case of the well-known Ising prior distribution for binary images degraded with independent Bernoullian noise. We prove that in general the maxinaum-a-posteriori estimator does not converge to the original image.
Bielawski S.S., Mulyarchik S.G., Popov A.V.
About convergence linear iterative methods for cyclically reduced linear system with nonsymmetric matrix. pp. 46--49
Summary: Estimates of the the spectral radius of iteration matrix of linear iterative method for solving cyclically reduced system of linear equations is obtained. Given system of linear equations approximate two dimensional boundary value problem for non-self-adjoint convection-diffusion equation.
Shilin A.P.
Infinite algebraic systems with power multipliers. pp. 50--53
Summary: Two new discrete convolution equations are solved.
Prohorovich T.N.
The linear Fuch system of three equations. pp. 54--57
Summary: The Fuch system of three equations with the special monodromy group is studied.
Dmitruk N.M.
Positional solution for the problem of optimal dynamics of the firm. pp. 58--63
Summary: An optimal control problem originated from the dynamic theory of the firm is under consideration. On the base of the sufficient optimality condition the positional solution of the problem is given.
Summary: The structure of multilayer optical fibre which permits to suppress the radiation on the definite wavelength a proposed. Fibre lasers and optical pulse amplifiers for wavelength 1.3 µm can be designed on the base of such fibres which are made from usual Nd-doped silica glasses.
Sirota N.N., Vitkina Ts.Z., Berezina G.M.
Influence of mechanical pounding, ultrasonic excitation and g-radiation on magnetic properties of microcrystalline cellulose. pp. 69--71
Summary: The temperature dependence of magnetic susceptibility of microcrystalline cellulose subjected to various energy excitations is investigated. It is established that an anomaly is observed irrespective of the type of the external effects and preparation technique at temperatures close to 300 K. In this case the energy excitations bring about the shift of phase transition temperature. It is shown that the Van Vleck paramagnetism enhances when affected by the energy excitations.
Zhestkov S.V., Kuvshinov V.I.
On existence of quasi-soliton solutions for multidimensional analogs of Landau--Ginzburg equation. pp. 72--76
Summary: On the basis of common approach to development of mathematical theory of multidimensional waves for nonlinear Landau--Ginzburg equation two multidimensional models possessing quasi-soliton solutions are build,
Babenko V.A.
New approach to T-matrix calculation of light scattering and absorption by spheroidal particles. pp. 77--82
Summary: The new algorithm for computations of the T-matrix integral elements for electromagnetic wave scattering and absorption by spheroidal particle is suggested. The algorithm is based on the expansion the Ricatti--Bessel and Legendre functions into finite power series and the construction of recurrence relations for expansion coefficients. It is shown that this approach has great advantage for calculation of light scattering by great and/or highly aspherical scatterers.
Valevaty N.A., Zakharov I.L., Predko K.G.
Transfer functions of an aperture in form of regular polygon. pp. 83--87
Summary: Analytical expression for the calculation of the point spread function (PSF) for ideal pupil in form of the regular polygon with arbitrary number of sides has been found. The calculation method for optical transfer function (OTF) for such pupil has been offered. The analytical expression for OTF has been received for polygonal pupil with the even number of the sides. Received expressions have been applied to the calculation of PSF and TF in case of a hexagonal aperture.
Volkov V.P., Skiba P.A.
The glass crystallization under the condition of the arising of phase macro boundary at the laser heating. pp. 88--92
Summary: It is shown that the degree of crystallization of titanium containing glass is nonmonotone dependent on the density of the light power during the local exposing laser irradiation. The growth of a new phase in this glass film is accompanied by the spreading of a nonlinear temperature wave. the front of the wave coincides with the macroscop boundary as glass and crystallized glass.
Belyatskaya L.N., Chigarev A.V.
Propagation of nonstationary surface waves in inhomogeneous elastic media with random scattering of parameters. pp. 93--99
Summary: The approach based on the use of Markov approximations for the description of wave propagation processes along a free boundary of a stochastically inhomogeneous elastic body is developed. The problem of the behavior of a non-stationary surface wave in a random inhomogeneous linear elastic medium is considered. The investigation of surface wave fronts is made on the basis of ray representations about a wave as a line of break of derivatives of displacements, propagating along boundary surface.
Summary: The special form of partitioning and spatial mapping of the algorithms onto three-dimensional array processors are considered. Fixed size of the arrays and the locality of interconnections between processor elements are ensured due to the development of a special formalized technique.
Suzdal S.V., Tyshkevich R.I.
Towards Beineke's theorem on line graphs. pp. 106--110
Summary: A new proof of Beineke's theorem characterizing the line graphs of simple graphs in terms of forbidden induced subgraphs is obtained. The proof is based on the algorithmic approach and Krausz coverings technique.
Orlovich Yu.L.
Contribution to extending cycles in graph classes. pp. 111--116
Summary: The graph G is almost K1,3-free by Ryjacek if the vertices that are centers of induced K1,3 in G are independent and their neighborhoods are 2-dominated. Let Zi be the graph obtained by identifying the center-vertex of K1,3 and an end-vertex of Pi. We show that every connected, locally connected, almost K1,3-free graph on n ³ 3 vertices having no induced Z3 is fully cycle extendible.
Moshchensky V.A.
Some properties of on-line Turing machine computations and lower bound of computation complexity of multiplication. pp. 117--122
Summary: Some properties of on-line Turing machine computations are established. After that it is proved that "school" method of multiplication is optimal for such machines with one working tape.
Kravtsov M.K., Krachkovskii A.P.
Asymptotic approach to deciding of the p-index axial assignment problem. pp. 123--126
Summary: The algorithm for finding asymptotically optimal plan of the p-index axial assignment problem is developed.
Mel'nikov O.I., Levin.Yu.G.
The outpoints of hypergraph realizations. pp. 127--131
Summary: The necessary and sufficient conditions of the existence of cutpoints in realizations of hypergraphs by graphs are formulated and proved. Checking algorithm of the existence of cutpoint in the realizations of hypergraph H is presented. The complexity of this algorithm is O(n2m).
Kiselyov A.A.
Some comments to the paper "On nonreachable cardinals". p. 132
Ostrikov O.M.
Duplication of crystals by influence of radiation and electrical fields. p. 133
Niculin Yu.V.
About two types of stability of a vector trajectorial discrete optimization problem. p. 133
Zverovich I.E.
Methods for characterization of hereditary classes. Part 1. pp. 133--134
Zverovich I.E.
Methods for characterization of hereditary classes. Part 2. Classes of perfect graphs and classes of intersection graphs. p. 134
Olekhnovich N.M., Korshunov F.P., Sokol V.A.
Vladimir Arkhipovich Labunov (On the occasion of the 60th Birthday Anniversary). pp. 138--139
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