Весці Нац. акадэміі навук Беларусі. Сер. фіз.матэм. навук, 2003, No.3
/ Выданні акадэміі / Навуковыя часопісы
Весці Нац. акадэміі навук Беларусі. Сер. фіз.матэм. навук, 2003, No.3

Весці Нацыянальнай акадэміі навук Беларусі
СЕРЫЯ ФІЗІКАМАТЭМАТЫЧНЫХ НАВУКВыдавец: Інстытут матэматыкі НАН Беларусі, Мінск, Рэспубліка Беларусь 
ЗМЕСТ
МАТЭМАТЫКА
Gorokhovik V. V.
On secondorder optimality conditions for solutions of the optimization problem with inequality constraints. pp. 510
Summary: The paper presents a straightforward proof of the primal second order sufficient optimality condition for solutions of the optimization problem with inequality constraints. This proof does not use any dual variants of optimality conditions.
Demenchuk A. K.
On the existence of almost periodic solutions of linear differential systems in noncritical case. pp. 1116
Summary: The existence problem for almost periodic partially irregular solutions of the system x = A(t)x + j(t), mod (A) Ç mod (k) = {0} in noncritical case is considered. The conditions for existence of such solutions are obtained.
Lyalikov A. S.
Approximation of continuous functions of bounded variation by rational operators of Vallee'Poussin type. pp. 1722
Summary: Continuous functions f having bounded variation on the given segment are considered. Rational operator of Vallee'Poussin type is built, with poles being chosen depending on distribution of variation of f. Deviation of such operator from f is estimated.
Al'sevich L. A., Kastritsa O. A.
Explicit Calculation of ShiftPeriodMapping for Linear Systems with Blockreflectivematrix. pp. 2325
Summary: The set of linear systems with blockreflectivefunction is constructed. For such systems a shiftperiodmapping is given. The results apply to twopoint boundary problem.
Makaruk S. F.
Boundary value problem on jump for a multiply connected domain with optimtimally situated internal domains. pp. 2629
Summary: It is considered jump boundary value problem for multiply connected domains with unknown internal domains (inclusions). Distribution of the inclusions is determined by the optimality of the functional of effective conductivity and the constancy of their complete area. The solution is given in form of sums depending on centers of inclusions. For two and three inclusions optimal configurations are described, and the closed form solution is found in the important for application particular case.
Egorov A. D.
On the system of orthogonal polynomials on linear topological space with a nonGaussian quasimeasure. pp. 3033
Summary: The system of orthogonal polynomials on linear topological space with a nonGaussian quasimeasure defined by arbitrary homogeneous (2p)forms is constructed. Some special cases are considered.
Malyutin V. B.
Approximation for expectation from solution of nonlinear stochastic differential equation with anticommuting coefficients. pp. 3437
Summary: The approximation for expectation from solution of nonlinear stochastic differential equation with anticommuting coefficients is obtained.
Zherelo A. V.
On convergence of functional quadrature process for integrals on Poisson measure. pp. 3842
Summary: The convergence conditions of functional quadrature process for continual integrals on Poisson measure in given class of functionals are obtained.
Bliznets I. M.
On the one of the class of the distributive lattices of tclosed wsaturated formations. pp. 4345
Summary: It is established, that if the formation F is an element of height 3 of the lattice of all tclosed wsaturated formations, then its lattice of tclosed wsaturated subformations is distributive.
Semenchuk V. N., Mokeeva S. A.
Finite groups with Fsubnomal and Faccessible subgroups. pp. 4648
Summary: All groups considered are finite. In the paper we obtain a description of soluble hereditary saturated formations F such that the following condition holds: in any group G for any its two permutable Fsubnormal subgroups H< and K the subgroup HK is also Fsubnormal in G.
Sabuts A. V.
Criterions of existence of even integral positive definite quadratic forms. I. pp. 4953
Summary: It is established that nary even integral positive definite quadratic forms with invariant factors 1,. . ., 1, d exist if only if the values of n and d satisfy one of the following conditions. First, d º +1(mod 4), d is not square, and n º 0(mod 4).
Second, d = (2c  1)^{2}, c = 1,2 , . . . , and n º 0 (mod 8).
Third, d º 1(mod 4), n º 2 (mod 4).
Fourth, d = 0(mod 2), 2d is not square, and n º 1(mod 2);
Fifth, d = 2c^{2}, c = 1, 2, ..., and n º ±l(mod 8).
Kavalenok N. N.
Optimal control of dynamic systems with bangbang functions. pp. 5459
Summary: The optimal control problem with bangbang principle is considered. Taking into account the specific structure of bangbang controls the optimality condition is proved and an optimization algorithm is justified.
ФІЗІКА
Bogush A. A.
On the quantum parameters and generators of the hdeformed group GL_{h}(2.C). pp. 6067
Summary: The description of the quantum (hdeformed) group GL_{h}(2.C) in terms of the introduced quantum fourdimensional vectorparameters is given. The simple composition rules for these vectorparameters and, as a consequence, the related linearity relations are established and used. On this basis, it is shown that the realization of the transition GL(2.C) ® GL_{h}(2.C) (gl(2.C) ® gl_{h}(2.C) ) may be reduced to the simple linear transformation of the group vector parameters (generators of the Lie algebra).
Ryabushko A. P., Nemanova I. T., Zhur T. A.
The relativistic translational motion of two rotating bodies comparable masses in the gravitational medium. pp. 6873
Summary: In the postNewtonian approximation the equations of the translational motion of two rotating bodies comparable masses in the gravitating medium have been integrated. Some novel relativistic effects due to the proper rotation of the bodies and the gravitational field of medium are detected.
Matsukovitsh S. M., Gavrilovich A. B.
The polarization characteristics of the radiation received from the diffusion spot source in the repeated dispersion conditions. pp. 7478
Summary: Experimental research of the polarization characteristics of emanation in the disperse medium received from the spotted diffuse source have been carried out. The normal intensity angle distributions and polarization degrees with optic thickness that varies from 2.0 to 11.0 has been found. Positive and negative polarization changes with medium parameters variations have been analyzed.
Kamlyuk A. N., Nemtsov V. B.
Rotation of the plane of polarization for transverse waves propagating along the axis of biopolymers (like DNA). pp. 7982
Summary: It is shown in the framework of the simple elastic rod with spiral structure model that the transversal wave propagation along the axis of biopolymers (like DNA) is followed by the rotation of the wave polarization plane.
Goncharenko E. A.
Coupled states of kinks for macroscopic chains. pp. 8386
Summary: In the model with two real scalar fields of the fourth order potential an application of two and three solitonlike objects for description the macroscopic chains of atoms and clusters is considered.
Akimov A. I., Lebedev S. A., Letko A. K., Ivanova T. A.
The structure properties of the mixture Pr_{2y}Sr_{y}Ni_{x}Al_{1x}O_{4}. pp. 8791
Summary: The effect of Ni/Al substitutions has been investigated for PrSrNi_{x}Al_{1x}O_{4} (0 £ x £ 0.7) compounds produced by conventional solid state reaction. Structural data for this system are reported. The unit cell parameter a increases when Al atoms are progressively replaced by Ni atoms but the parameter c decreases. A Rietvcld analysis of the roomtemperature powder Xray diffraction data showed that the tetrahedral distortion of the NiO_{6} increases with increasing x for 0 £ x £ 0.7 but the Pr(Sr)  O(2) bond length decreases in the same interval.
Belevich N. N.
The obtaining of ZnSe films, their structural and optical properties. pp. 9294
Summary: ZnSe films are obtained by method of thermal evaporation of the compound. Their structural and optical properties are explored at room temperature. It is shown that films have cubic structure. The width of a forbidden gape determined from optical absorption is equal 2.6 eV. On interference features of a transmission coefficient the refractive coefficient of films is explored, which is equal 2.90 ± 0.05 in the region of wavelengths from 500 to 1100 nm.
Mahnach V. I., Shved O. L.
Initial conditions of plasticity at the finite strains. pp. 9599
Summary: It is shown that the plasticity function for the isotropic material represents the Cauchy task solution for an ordinary differential equation, which initial condition is defined by the experiment. For the particular case the solution has been obtained in the finite tensorinvariant form depending on the characteristics of the stress state. The plasticity curve is piecewise regular, concave, the normal to this curve in the singular points are orthogonal.
ІНФАРМАТЫКА
Tiunchik A. A.
Matching graph models of systoliclike algorithms on the basis of matrix representation of data structures. pp. 100105
Summary: The formal approach for the construction of the spatial transformations for uniting decomposed graph models is proposed. This approach is based on the formalization of the description of input and output domains in graph models. The algorithms are split into the separate blocks and simpler graph models for the blocks is constructed. Matrix representation of the data structures that are to be transmitted between different blocks allows us to solve the problem of the spatial connection of different blocks in a systematic way. The existence of an appropriate spatial connection in a number of important cases is proven. Algebraic tools provide easy constructing complicated graph models.
Orlovich Yu. L.
Characterizations and recognition of some subclasses of wellcovered modulo m graphs. pp. 106114
Summary: The graph G is wellcovered modulo m ³ 2 if I_{1} º I_{2} (mod m) for all maximal independent sets I_{1}, I_{2} Í V(G). (The class of all such graphs is denoted by Z_{m}W.) Characterizations of some hereditary subclasses of a class Z_{m}W are obtained and the wellcovered modulo m products of graphs are characterized. The polynomial solvability of a recognition problem G Î Z_{m}W is proved for the following graphs: acyclic, clawfree, bounded maximum vertex degree.
Matskevich A. N.
Mathematical models casual nonstationary influences in the class of regular processes. pp. 115117
Summary: The technique of synthesis and mathematical models of random nonstationary perturbations in the class of regular processes is represented.
ВУЧОНЫЯ БЕЛАРУСI
Николай Александрович Борисевич (К 80летию со дня рождения). С. 118120
Націсніце тут, каб прачытаць артыкул
Борис Борисович Бойко (К 80летию со дня рождения). С. 121123
Націсніце тут, каб прачытаць артыкул
/ Выданні акадэміі / Навуковыя часопісы / Да пачатку старонкі
Распрацавана і падтрымліваецца Мікалаем М. Касцюковічам. Апошняе абнаўленне: 8 снежня 2006 г.
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