Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 2002, No.2
/ Publications / Scientific Journals
Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 2002, No.2

Proceedings of the National Academy of Sciences of Belarus (Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICALMATHEMATICAL SCIENCESPublished by The Institute of Mathematics of NASB, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Kostyukova O. I.
Pathfollowing method for a family of semiinfinite programming problems. pp. 510
Summary: A oneparametric family of convex semiinfinite problems depending on a parameter t Î [0, t*] is considered. For fixed t = t_{0} Î [0, t*] rules of constructing the solutions of this family for t in a rightside neighborhood of t_{0} are described. Results on onesided derivatives of solution with respect to the parameter are presented. On the basis of the obtained results an activesetstrategy and a pathfollowing algorithm are suggested.
Zhuk E. E., Avramenko N. A.
Cluster analysis of autoregression time series in a space of MLestimators of autoregression parameters. pp. 1116
Summary: The problem of cluster analysis of observations described by the autoregression time series is considered. The clustering procedure in a space of MLestimators of autoregression parameters is proposed and its efficiency is analytically and experimentally investigated.
Zalesskii B. A.
Bayesian estimations of grayscale images by use of maximum network flow algorithms. pp. 1722
Summary: Two Bayesian models of grayscale images are described. The maximumaposteriori estimates of these models can be efficiently identified by parallel use of the maximum network flow methods.
Malyutin V. B.
Approximations of functional integrals with the Clifford values. pp. 2325
Summary: Functional integral with noncommuting Clifford values is approximated by functional integral where noncommuting values axe separated. It allowes to overcome the noncommuting values problem
Petrov V. A.
Approximations functional integrals on some Gaussian measures. pp. 2629
Summary: Composite approximate formulas for evaluation some Gaussian functional integrals are constructed. The estimates of remainders of these approximations are obtained.
Rusak V. N. Tolmasheva M. S.
Hermitetype interpolation and quadrature formulas which are exact for rational functions. pp. 3033
Summary: Gausstype quadrature formulas for rational functions with simple poles has been investigated.
Tykun A. S.
On the the Conley index evaluation for 3D dynamical systems. pp. 3438
Summary: The 3D dynamical system without singular points is considered. The existence of the bounded solution is proved using the Conley index. For an arbitrary compact area in three dimensional space the sufficient condition of being an isolating area is proved.
Galmak A. M.
Manyfolds of polyadic groups. pp. 3940
Summary: The varieties of naxy groups of the M*(n) form are defined and considered, where M is variety of groups.
Hodalevich A. D.
Projectors of soluble universal algebras. pp. 4143
Summary: The following result is proved. Let A be a finite soluble universal algebra containing some oneelements subalgebras, then A has at least one Fprojector for any nonempty saturated formation F Í m.
Benediktovitch I. I.
About the structure of the Specht's module. pp. 4445
Summary: The set of all homogeneous products of commutators in the free associative algebra over field of characteristic 0 is called a Specht's module. It is a natural module over the symmetric group S_{n}. We have obtained its structure as S_{n}module. Namely, it is isomorphic to the sum S^{n}_{i=2} (1)^{i}[1^{i}] n where [1^{i}] is an Young table corresponding to the one dimensional alternating representation and [1^{i}] n denotes a module induced from S_{i} to S_{n}.
Silaeva N. A.
Simultaneous approximations of zero by values of normal curves in different metrics. pp. 4652
Summary: The extremality of plane curves with positive curvature in the space R x C x Z_{p} is proved.
Sarazhinskii D. S.
Invariant cones and eigenvectors for the PerronFrobenius operator in spaces of the Holder functions. pp. 5356
Summary: The strong invariant cone for the PerronFrobenius linear operator generated by the shift mapping on a space of sequences is constructed. Existence of the cone was allowed to define ergodic invariant measures on the space of sequences, to prove probability limit theorems and to obtain presize asymptotics for large deviations.
Akinfina M. A.
Estimation of a spectrum of a discrete stationary symmetric astable process in case of using Bartlett's periodogram. pp. 5760
Summary: A consistent estimate of spectral density of a symmetric stationary astable casual process is being designed in case of using Bartlett's periodogram. Its convergence in probability to spectral density is established. The rate of convergence of the considered estimate is investigated in case of using polynomial kernel Jekson's type and depending on a smoothness of a spectral density.
PHYSICS
Bogush A. A., Kisel V. V., Tokarevskaya N. G., Red'kov V. M.
Nonrelativistic limit in generally covariant theory of a vector particle. pp. 6166
Summary: The known procedure of obtaining the nonrelativistic limit in the Duffin  Kemmer theory of a vector particle in flat Minkowski spacetime is generalized to a possible nonEuclidean spacetime geometry. It is shown that the generally covariant Duffin  Kemmer equation permits such a limit if a metric tensor satisfies the relations g_{00}(x) = 1, g_{0i}(x) = 0. In the frames of the Tetrode  Weyl  Fock  Ivanenko tetrad formalism a generally covariant equation for 3component wave function describing the vector particle is produced. It is correct in presence of an external electromagnetic field and of a curved 3space background with the metric of the form dS^{2} = (dx^{0})^{2}  g_{ij}(x^{0}, x^{k})dx^{i}dx^{j}.
Pilipovich V. A., Esman A.K., Goncharenko I. A., Kuleshov V. K., Sergienya S. A.
Dynamic of the generation frequency tuning of singlefrequency fibre and waveguide lasers with controllable Bragg grating. pp. 6771
Summary: The dynamic of radiation wavelength tuning of fibre and waveguide lasers by the use of Bragg grating on the base of waveguide electrooptical modulator is analysed. Dependence of the switching time on the power of signal remaining on the wavelength into which the radiation is tuned, on concentration of doping elements, reflectivity of cavity output mirror and optical pump power is estimated. It is shown that lasers with output mirror reflectivity around 95% possess the minimal tuning time and maximal generation efficiency. In lasers with cavity length 1 cm and optimal characteristics the time of switching to another wavelength does not exceed 0.7 ns in all region of spectral tuning.
Kudryashov V. V., Vanne Yu. V.
Quasiuniform approximation for powerlaw potentials. pp. 7276
Summary: Analytical solutions of the Schrodinger equation with powerlaw potentials are obtained in the framework of the new quasiuniform approximation based on explicit summation of the constituent WKB series. The detailed numerical verification of the proposed method is performed.
Kurilkina S. N., Shuba M. V.
Bistability of acoustooptic interaction in gyrotropic crystals with electroinduced anisotropy. pp. 7781
Summary: It has been shown that conditions and peculiarities of bistable regimes by acoustoelectrooptic interaction in cubic noncentrosymmetrical crystals are determined by presence of gyrotropy. It has been established that more essentially the latter is displaying i doubling of number of bistable regions and in appearance of dependence of conditions for realization of bistable regimes on polarization of incident light wave. It has been obtained the opportunity of change of switching character by reversion of external electric field.
Makovetskii G. I., Galyas A. I., Demidenko O. F.
Obtaining and magnetic properties of Mn_{1x}Ti_{x}Se (0 £ x £ 0.2) and Mn_{1x}V_{x}Se (0 £ x £ 0.15) solid solutions. pp. 8284
Summary: Under the high pressure and the high temperature conditions theMn_{1x}Ti_{x}Se (0 £ x £ 0.2) and Mn_{1x}V_{x}Se (0 £ x £ 0.15) solid solutions were synthesized. All samples have the cubic lattice like MnSe. The magnetic susceptibility for all the investigated samples was determined in temperature interval 77  900 K. The antiferromagnetic ordering have been observed for all the solid solutions at T < 130  150 K.
Akimov A. I., Savchuk G. K., Rubzov V. A., Letko A. K.
Research of influence of cationic and anionic deficiency on the crystal structure of lead titanate. pp. 8590
Summary: Usung by the Rietveld method parameters of crystal structure of lead titanate were refined in depending on a degree anionic and cationic defectiviti. XRay difractometer DRON4 (CuK_{a}, 20° < 2q < 70°, step 0.01°, exposition in a point  ten sec.) was used. All accounts are carried out by using the program "GSAS" in the framework of space group P4mm. The refinement of parameters of structure is carried out in isotropic approximation R_{p} 5.0  6.0.
Gusakov V. E.
On anomalous temperature behaviour of HTSC compounds elastic properties. pp. 9196
Summary: It was established that experimentally observed anomalous (hysteretic) temperature dependencies of elastic properties of YBa_{2}Cu_{3}O_{7d} crystals are related to the hysteretic behavior of the elastic modulus C_{3333} and are caused temperaturedependent renormalization of force constants of O(4) (apex) oxygen atoms with copper atoms.
Nupriyonok I. S., Shibko A. N.
Phase changes of composition Zr  Si under UVirradiation. pp. 97101
Summary: Phase transformations of thin films Zr and composition of Zr  Si under vacuum stacionary annealing with simultaneous UVirradiation have been investigated. Phase changes, change of the boundary metal  semiconductor cause change in contact electrophysical characteristics. The simultaneous treatment of the Zr  Si compositionmakes it possible to form a rectifying contact with given parametes depending on light irradiation power.
Brinkevich D. I., Lukashevich M. G., Petrov V. V., Prosolovich V. S., Skripka D. A., Yankovskii Yu. N.
Giant magnitoresistance in rareearth doped silicon. pp. 102104
Summary: Negative magnitoresistance at liquid nitrogen temperature was found in silicon doped by rareearth elemets Er, Gd and Ho at the concentrations 3 • 10^{15}  2.3 • 10^{17} cm^{3}. It cause by giant magnitoresistance consist of rareearth clusters magnetic moments orientation by external magnetic field that charge carriers scattering decrease.
INFORMATICS
Tikhonenko O. M.
The analysis of processor sharing queueing system with nonhomogeneous demands. pp. 105111
Summary: The sum tags vector characteristics for M/G/1/¥ and M/G/1/m processor sharing queues are determined taking into account the dependence between tags values and service time of the demand. The stationary probability of demand's losing is estimated for the case of restricted summarized volume.
Naidenko V. G.
The complexity of finding a second solution to a NPcomplete problem. pp. 112113
Summary: The NPcomplete problem is constructed. Every instance of the problem contains either no solution or at least two solutions. There is no polynomialtime algorithm which for given example of the problem and its solution could find the second solution with the following condition NP Ç coNP ¹ P.
Zaika V. A., Vankovich G. R., Lopareva N. V., Povarov A. A.
Method of information "section" in study of electromagnetic complex technical system compatibility. pp. 114118
Summary: The method of constraction of the information "sections" of multichannel data, which make it possible to decrease the number of measuring channels under the carrying out of the electromagnetic compatibility tests of the complex technical systems is proposed and analysed.
Bakhanovich S. V.
The synthesis of onedimensional scheduling function generated by the multidimensional scheduling. pp. 119122
Summary: The method of onedimensional scheduling function synthesis is presented. The method is considered in the frameworks of multidimensional scheduling and spacetime mapping of ndimensional algorithms with uniform dependences onto (n  rdimensional parallel architectures.
ABSTRACTS OF DEPOSITED PAPERS
Shishkevich A. A.
Finite represented semi aspherical propgroups. p. 123
Pavlov L. I.
Photodiod electric optical measuring instrument for the lengthy micro objects. p. 123
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