СЕРИЯ ФИЗИКО-МАТЕМАТИЧЕСКИХ НАУК
Издатель: Беларуская навука, Минск, Республика Беларусь
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Известия Академии наук Беларуси СЕРИЯ ФИЗИКО-МАТЕМАТИЧЕСКИХ НАУК Издатель: Беларуская навука, Минск, Республика Беларусь |
Summary: It is shown that integer polynomials under the condition |P(Z)| < H(P)-n/2+1/2+g, where 0 < g < 1/2, have the big modulus of the derivative |P'(Z)| > H1 - g - e, e > 0, for almost all z ª C.
Zabrejko P.P., Marchenko V.V.
On the average of superposition operators. pp. 11--17
Summary: This paper deals with the description of the continuous functions f(s,u) for which the mean of the function f(s,x(s)) is defined by the mean of the function x(s). It turns out that under natural suppositions the correspondent relation is affine. In case, when the function f(s,u) is w-periodic with respect to t the function f(s,u) itself is affine with respect to u.
Sheshko M.A.
Approximate solution of singular integral equations with Cauchy kernel on the material axis. pp. 18--21
Summary: Two calculation schemes on the base of the so-called "spectral relations" for singular integrals with Cauchy kernel on the material axis and also their analogues for regular integrals are built taking into account the equation index
Lazakovich N.V.
Finite-difference approximations with stochastic differentiaI equation in Ito form. pp. 22--29
Summary: The approximation of solutions of stochastic differential equations by difference ones is considered.
Zuev N.M.
Estimates of the convergence rate in the central limit theorem for random fields satisfying the Cramer's condition and the strong mixing condition. pp. 29--34
Summary: 
Semenkova E.A.
On analytical representation of hemispaces in finite-dimensional vector spaces. pp. 35--40
Summary: In this paper we obtain the analytical representations in the form of V.Klee for hemispaces (convex sets whose complements are also convex) of finite-dimensional vector space.
Shilin A.P.
Convolution integral equations with two kernels and conjugation. pp. 41--47
Summary: Two new integral equations on the real line are solved in a closed form.
Bruj I.N.
Trigonometric series of Loo (T) class and their conservative means. pp. 48--52
Summary: 
Summary: Preliminary analysis of the capability of VLEPP-1 (s1/2=500 GeV) has been carried out with respect to the direct search for the Z'-bosons in eg-collisions. It is shown that there is good perspective for the search and investigation of the Z'-bozons if their masses do not exceed 500 GeV.
Tunyak Y.M.
Tetrad gravitation theory without cosmological singularity. pp. 58--61
Summary: A non-singular solution of the field equations of the tetrad theory of gravity is given for the case of an universe filled with radiation and vacuum energy. The early cosmology behaves kinematically in a good approximation like the Einstein -- Cartan -- Sciama -- Kibble model with spinning fluid.
Baryshevsky V.G., Cherkas S.L.
On the connection of the P-odd neutron resonance elastic scattering amplitude on nucleus with weak N-N interaction. pp. 61--70
Summary: The expression for the P-odd, neutron elastic scattering amplitude is derived proceeding from N-N weak interaction. The amplitude depends on weak N-N interaction through the matrix elements from some operator. The above operator contains weak interaction in the form of direct exchange and polarization terms. The last term is the strong interaction perturbated by weak one.
Pilipovich V.A., Yesman A.K., Goncharenko I.A., Posiedko V.S., Solonovich I.F.
Controlled optical fibre processor for matrix/vector multiplication. pp. 70--73
Summary: The structure of controlled optical fibre processor for operation of matrix/vector multiplication is proposed. Such processor could be used for calculation of a large number of data in optical image and information processing. The processor consists of an array of elementary processors. Each elementary processor is a combination of an optical fibre amplifier and coupler. The method of processor operation is discussed.
Bely V.N., Kulak G.V., Ropot P.I.
Interaction between electromagnetic and acoustic waves in gyrotropic cubic crystals with electrically induced anisotropy. pp. 74--77
Summary: Application of slowly changing amplitude method, Bragg diffraction in gyrotropic cubic crystals with electrically induced anisotropy are considered. Analytical expressions which give the possibility for calculation of energy and polarization characteristics of diffracted waves in regime of strong interaction are obtained. It has been shown that the influence of the external electric field in the case of diffraction by the shear acoustic wave under the longitudinal electrooptical effect makes it possible to control selective properties of acoustooptical interaction.
Korshunov F.P., Murin L.I., Prokhorenko T.A.
On determination.of compensation degree in GaAs of n-type. pp. 78--83
Summary: It has been shown that Brooks--Herring formulae is not applicable for determination of the compensation factor K in highly compensated n-GaAs crystals. The areas of validity of Brooks--Herring and Conwell--Weiskopf approximations for n-GaAs with different doping level and compensation degree are found.
Novysh B.V., Dorozhkin N.N., Gololobov E.M., Anishchik V.M.
Calculation of effective one-electron potential for superconductor Y1Ba2Cu3O7. pp. 83--88
Summary: The effective one-electron potential of high-temperature superconductor Y1Ba2Cu3O7 has been calculated in Fourier representation for a crystal potential.
Ges A.P., Solovykh T.K., Shapovalova A.F.
Linear magnetooptical effect in the spin reorientation region. pp. 88--90
Summary: Orthoferrites are weak ferromagnetics with large Faraday effect. The Faraday effect is related to magnetic properties of crystal. The nature of large Faraday effect is not cleared up. The obtained experimental data are important, especially in spin-reorientation region. Not only ferromagnetic vector but antiferromagnetic one contributes mainly to Faraday effect in spin-reorientation transition region as it was experimentally demonstrated.
Prishchepa S.L.
Temperature dependence of the pinnting potential in HTSC films. pp. 90--95
Summary: On the basis of theoretical analyses the formula, related to the pinning potential U determination from the resistive transition curves of superconductor in the case of isolated vortex, is derived. The importance of U versus temperature T dependence is shown. The conclusion about two possible values of the exponent value n in the U(T) dependence is drawn. The experimental results simply reveal the case n = 3, that gives us an opportunity to estimate the pinning potential energy at zero temperature.
Akimov A.I., Shushlebin I.M., Chernyakova A.P.
Lower critical fields in superconductor TI-Ra-Ca-Cu-O. pp. 95--100
Summary: The results of the investigation of the magnetic flux penetration in Tl-based HTSC-material are presented.
Summary: The polynomial algorithms for solving the recognition problem "G Î L(H)", where L is the multiform mapping "line hypergraph", and H is a hypergraph with certain property P, are proposed. According to the algorithms an element of complete prototype L-1(G) is constructed.
Gorelik A.O.
Graphical System based on relations. pp. 105--111
Summary: The article deals with the construction principles of the graphical system GCAD based on the relations between the object structural elements. The algorithm for the coordinate parameters calculation of the graphical object by its model based on the relations is proposed.
Butkin G.A., Konchak V.S.
Procedure of vibrating state control of multicoherent object. pp. 111--115
Summary: The task of vibrating state control of multicoherent object is considered. Some iterative matrix procedures are proposed as a solution of this task.
Likhoded N.A., Tsurko V.A.
Iterative solution of two-dimensional elliptic equations by systolic processor. pp. 115--120
Summary: Systolic array for the implementation of successive overrelaxation method for the iterative solution of linear systems with sparse five-diagonal matrices is proposed.
Matalytsky M.A.
Study on the networks of mass service with random choice of applications for servicing. pp. 121--125
Summary: Queueing networks with random selection for service of different classes customers in service system queues are investigated.
Summary: Using the properties of the harmonic motion equation necessary and sufficient conditions of an isochronism of the center of the two-dimensional holomorphic autonomous systems of the ordinary differential equations are obtained.
Kiselev A.A.
On elimination of subunreachability. pp. 129--130
Podenok L.P., Sadykhov R.Kh.
Information protection in automatic systems of data processing. p.130
Datsik V.T., Semenchuk N.P.
Asymptotic formulae of Voronovskaya type for generalized means of Fourie conjugate integral. pp. 130--131
Borisoglebsky L.A., Polegenky V.V.
Method of nucleus effective charge in calculations of bounded atom characteristics. p. 131
Rudnitsky A.S.
Investigation of polarization properties of kaleidoscope form optical element. pp. 131--132
Krushevsky A.E., Naumovich S.A.
Solution of the problem on equilibrium of periodontium as a membrane bounded by two composite elliptic hyperboloids. p. 132
Krushevsky A.E., Naumovich S.A.
Study on a stressed state of periodontium junction region with a root of a tooth. pp. 132--133
Yetimchik N.E., Ramazanov A.B.
On error of gradient extremum of a strictly convex function of discrete variable. p. 133
Shilin A.P.
Integral equations with difference kernels. p. 134