Весці Нац. акадэміі навук Беларусі. Сер. фіз.матэм. навук, 2000, No.2
/ Выданні акадэміі / Навуковыя часопісы
Весці Нац. акадэміі навук Беларусі. Сер. фіз.матэм. навук, 2000, No.2

Весці Нацыянальнай акадэміі навук Беларусі
СЕРЫЯ ФІЗІКАМАТЭМАТЫЧНЫХ НАВУКВыдавец: Інстытут матэматыкі НАН Беларусі, Мінск, Рэспубліка Беларусь 
ЗМЕСТ
МАТЭМАТЫКА
Egorov A.D.
On multiple stochastic integrals in spaces with nongaussian quasimeasures. pp. 58
Summary:
A system of orthogonal polynomials on linear topological space with a nongaussian guasimeasure m is obtained. An approach based on L_{2}isomorphism from L_{2}(X, m) into L_{2}(Y, m^{^}) is used where Y = L_{2} (X, g), g be an arbitrary gaussian quasimeasure and m^{^} is a special gaussian measure on Y defined by m.
Bernik V.I., Trelina L.A.
Regular systems of algebraic numbers in the field of padic numbers. pp. 913
Summary:
The set of all nonzero algebraic numbers a in Q_{p} with the function H(a)^{n+1}(log H(a))^{5} at height values is a regular system in diophantine approximation theory.
Beresnevich V.V., Bernik V.I., Dicinson H., Dodson M.
On linear manifolds satisfying an approximation Khintchine theorem. pp. 1417
Summary:
A Khinchine type theorem for the linear manifolds is obtained.
Malyutin V.B.
Matrixvalued functional integral is represented by functional integral with respect to space of functions taking values ±l. pp. 1821
Summary:
Connection between matrixvalued functionail integrals and integrals with respect to space of functions taking values ± 1 is established.
Yanovich L.A., Ignatenko M.V.
Interpolation formulae for differentiable operators defined on cartesian product of functional spaces. pp. 2227
Summary:
Formulae of Lagrange and Hermite type interpolation with respect to twice multiple nodes which are deduced for differentiable operators defined on Cartesian product of functional spaces are constructed. The obtained formulae are exact for a number of classes of operator polynomials. The construction of the operator interpolation formulae based on the interpolation polynomials for functions.
Petrov V.A.
Approximation of Wiener functional integrals with employment of gaussian quadrature formulas. pp. 2831
Summary:
Composite approximate formula for evaluation of Wiener functional integrals is constructed. The estimate of remainder of approximation is obtained.
Zheleznaya T.M.
On some 3generated groups. pp. 3237
Summary:
The inductive systems (amalgams) of groups {G_{i}, G_{ij}} (i, j Î { 1,2,3 }), with respect to inclusions of G_{i}, in G_{ij} are considered. It is proved that if all G_{i} are cyclic of order 2 or 3, G_{ij} = á G_{i}, G_{j} ñ, and G_{ij} ¹ A_{4}, Z^{2}_{3}, S_{3}, Z_{3} x Z_{2} or Z^{2}_{2} for all {i,j}, then the inductive limit of this system (i.e. the universal closure of the corresponding amalgam) is infinite.
Emelichev V.A., Nikulin Yu.V.
The conditions of strong quasistability of a vector linear trajectorial problem. pp. 3841
Summary:
Such type of stability of the vector linear trajectorial problem that "small'' perturbations of parameters can leade to appearence of new efficient trajectories but at least one Pareto optimal trajectory preserves its optimality under the perturbations is considered. Necessary and sufficient condition of the stability of Pareto set in the vector trajectorial problem is obtained.
Gal'mak A.M.
Idempotent nary groups. pp. 4245
Summary:
The description of idempotent nary groups is obtained.
Kharin Yu.S., Akinfin A.V.
On robustness of Doptimal designs of regression experiments under functional distortions. pp. 4651
Summary:
The problems of Doptimal experimental design for the multiple linear regression under functional distortions in l^{n}_{2} and c^{n}metrics is considered. The following robustness characteristics are evaluated: supremum of the generalized variance of the LSestimator, design unstability coefficient and its upper bounds, dadmissible distortion level. The conditions are given under which the D^{*}_{+}robust design coincides with the exact Doptimal design. Results of computer experiments are presented.
Osinovskaya A.A.
Restrictions of irreducible representations of the Lie algebra sl_{3} to sl_{2}subalgebras and the Jordan block structure of nilpotent elements. pp. 5255
Summary:
Irreducible representations of the Lie algebra sl_{3} and their restrictions to sl_{2}subalgebras are considered. An explicit formula for dimensions of the so called "levels" is given and all irreducible factors of restrictions to all sl_{2} are found. This enables one to determine the Jordan block sizes of nilpotent elements in such representations and to solve this question for unipotent elements and irreducible representations of the group SL_{3}.
Kashevskii V.V.
Composition representation of the integraldifference operator and its kernel. pp. 5659
Summary:
A new integraldifference operator is considered.
ФІЗІКА
Pilipovich V.A., Esman A.K., Kuleshov V.K., Solonovich I.F.
An electromagnetic soliton generation by using a nonlinear transmission stripline. pp. 6063
Summary:
A coplanar waveguide electrical transmission stripline with controlled nonlinear component of a capacitance per unit length was designed, constructed, fabricated and tested. The stripline ensures generation of electromagnetic solitons with parameters permitting to use them for obtaining of spectrallimits pulse signals in an optical channel, i.e. optical enveloping solitons.
The developed nonlinear transmission stripline is adapted on characteristic impedance and amplitude of a signal to modulating electrooptical devices.
Gaiduk P.I., Tishkov V.S., Komarov F.F., Yakubenya S.N.
Electronmicroscopy study of a diamond film structure. pp. 6469
Summary:
The structure of the diamond films grown by CVD on silicon wafers were investigated by both planview and crosssection transmission electron microscopy. The structure quality of the diamond films was found which depend on the type of buffers layers. The possible mechanisms of diamond film growth are discussed.
Aleynikov D.V., Tolkachev E.A.
The dyogen atom: the selfadjoint Hamiltonian, the ambiguity of the spectrum. pp. 7075
Summary:
It is shown that the ambiguity of the dyogen atom spectrum caused by the nonuniqueness Hamiltonian selfadjoint extension is removed by description this system in terms of fourdimensional singular oscillator restricted by topological nontrivial condition of equivariance.
Red'kov V.M.
Porientation and spatial spinors. pp. 7681
Summary:
Transition from a 3dimensional vector space to a spinor spatial model is examined. It is shown that such a spinor model depends essentially on the preposition about the type of Porientation of the initial vector 3space: vector or pseudovector one. On this way two sorts of complex spatial spinors are determined, which correspond to an initial vector and pseudovector model respectively. These spinors differ in explicit expressions as functions of Cartesian coordinates. The paper investigates some continuity properties of the spatial 2spinor x(a) corresponding to the initial pseudovector geometrical model a = ( a_{1}, a_{2}, a_{3} ). The function x_{a}_{3}( a_{1} + ia_{2} ) is not an analytical function in the CauchyRiemann sense. As a characteristic of the continuity property of the spinor x(a) the derivations over directions (n_{1}¶_{1} + n_{2}¶_{2} )x(a) are found and the matrix differential equation Ñ_{n}x = A(a)x is given.
Kisel V.V.
The exact solutions of the Cox equation for particle with spin 0 in external electromagnetic fields. pp. 8285
Summary:
The exact solutions of the equation of Cox for a massive particle with spin 0 and extended charge in external electromagnetic fields of the following configurations are found: a constant homogeneous magnetic field, constant homogeneous electrical field.
Blinkouski A.A., Gorbatsievich A.K.
Classical cosmological tests in 5dimensional Projective Unified Field Theory. pp. 8692
Summary:
The classical observational cosmological tests (Hubble diagram, count of sources etc.) are considered for homogeneous and isotropic model of the universe in the framework of 5dimensional Projective Unified Field Theory in which the gravitation is described both with curvature of spacetime and with some hypothetical scalar field. It is shown that the presence of the scalar field can essentially influence on conclusions received from the cosmological tests. The surface brightness  redshift test can be the critical test for the scalar field effects. The available experimental data testify apparently to the scalar field decrease with time.
Andreev V.V.
Leptonic decays of mesons in Poincarecovariant quark model. pp. 9398
Summary:
Using a Poincarecovariant constituent quark model based on point form of relativistic quantum mechanics, the electroweak decays of the p and r mesons are investigated. All free parameters of quark model (the mass uquark and scale parameter) are fixed by using relevant experimental data.
Kachan S.M.
Plasmon resonances in doublelayered spherical metalline nanoparticles. pp. 99104
Summary:
The effect of a metal volume fraction in a particle on spectral dependence on the extinction efficiency factor of a nanosize doublelayer particle had been investigated with regard to the optical constants size dependence both a metal shell and a metal core cases. Dependence of resonance spectral positions and resonance absolute magnitudes on a metal volume fraction had been studied by the example of silver,
It was founded that nanosize doublelayer particles with a metal shell have two plasma resonance peaks in extinction spectra. Spectral positions of the peaks in contrast with absolute magnitudes in maximum depend only on a metal volume fraction and don't depend on a shell's thickness within a particle parameter range is investigated.
Kulak G.V., Hilo P.A.
Resonance acoustooptic interaction in niobates lithium diffusion optical waveguides. pp. 105108
Summary:
Peculiarities of resonance acoustooptic interaction in LiNbO_{3} diffusion optical waveguides with superlattice arc investigated.
Kurilkina S.N., Kovchur S.N.
Anisotropy of acoustooptic effect in the crystal of BaTiO_{3}. pp. 109112
Summary:
The estimation of influence of the indirect photoelastic effect and light polarization characteristics on anisotropy of acoustooptic effect in promising crystal BaTiO_{3} has been carried out. The configurations of light and acoustic interaction for which the piezoelectric effect has an influence on efficiency of acoustooptic transformation have been exposed.
Petrashko V.V., Novysh B.V., Mazovko A.V., Kurochkin L.A.
Synthesis and properties of (Bi,Pb)  (Sr,K)  Ca  Cu  O superconductors doped with silver. pp. 113116
Summary:
The influence of K and Ag additions on phase composition and superconducting properties of (Bi,Pb)  Si  Ca Cu  O system are investigated. It is shown that K and Ag increase the output of 2223 phase and superconducting fluctuations have a quasi twodimensional nature.
ІНФАРМАТЫКА
Korzyuk V.I., Kolyada A.A., Revinski V.V., Selyaninov M.Yu., Chernyavski Yu.A.
Parallel processing of the fingerprint images in the binaryvectorial packaging. pp. 117125
Summary:
The new tabular technology of the analysis of geometry, pattern and topology of lines on the fingerprint images (FI) introduced in the binaryvectorial packaging is offered. The methodology use socalled pseudodownlink sets. The procedure is synthesized based on this methodology. Mentioned procedure allows effectively to solve the problem of the linearizations of FI.
Naidenko V.G., Orlovich Yu.L.
Independent and dominated sets in K_{1,r}free graphs. pp. 126130
Summary:
It is shown that in K_{1,r}free graphs the maximum independent set problem, the minimum dominating set problem and the minimum independent dominating set problem are approximable up to constant factor r  1 by any maximal independent set.
Bakhanovich S.V.
Algorithm and systolic structure for an implementation of the modular multiplication. pp. 131135
Summary:
An algorithm and a linear systolic array for the modular multiplication is presented. The algorithm is based on the use of a set of precalculated values. The format of the representation of data provides the efficiency of the implementation of the algorithm by the developed systolic array.
КАРОТКІЯ ПАВЕДАМЛЕННІ
Demenchuk A.K.
On quasiperiodic solutions to linear differential equations of order n with trigonometric polynomial nonhomogeneous. pp. 136138
Summary:
Necessary and sufficient conditions of existence of quasiperiodic solutions for linear differential equations with a trigonometric polynomial at right hand are given.
/ Выданні акадэміі / Навуковыя часопісы / Да пачатку старонкі
Распрацавана і падтрымліваецца Мікалаем М. Касцюковічам. Апошняе абнаўленне: 8 снежня 2006 г.
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