Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 2003, No.1
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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 2003, No.1

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
Alekhno E. A., Zabreyko P. P.
Quasipositive elements and nondecomposible operators in ideal spaces. II. pp. 510
Summary: The class of nondecomposable linear integral operators in ideal spaces is studied. The positiveness of spectral radius of these operators is proved, their basic spectral properties are described and the theorem about general form of a kernel of the imprimitive nondecomposable operator is obtained.
Kharin Yu. S., Pashkevich M. A.
Statistical Estimation of the parameters of the betabinomial distribution in the case of distortions of binary observations. pp. 1117
Summary: The robustness problems of estimation of parameters for the beta binomial distribution (BBD) in the case of distortions of binary observations is considered. It is proved that the moment estimator and the maximum likelihood estimator are inconsistent in the case of binary data distortions. A new consistent moment estimator of the BBD parameters in the case of known distortion levels is developed. An iterative algorithm for joint estimation of BBD parameters and distortion levels is also proposed. Computer simulation results are also given,
Malyutin V.B.
Evaluation of functional integrals with respect to space offunctions with finite number of values. pp. 1821
Summary: The class of functional integrals with respect to space of functions taking values ±l is evaluated,
Beresnevich V. V.
On the construction of regular systems of points with real, complex and padic algebraic coordinates. pp. 2227
Summary: The method of constructing regular systems of algebraic points in the space of R x C x Q^{p} is proposed.
Shabalina I. P.
On the lattice of tclosed nmultiply wlocal formations of finite groups. pp. 2830
Summary: It is proved that the lattice of tclosed nmultiply wlocal formations is modular for all natural n.
Kuzmenkova I. A.
Radical ideal subgroup functors and Fitting classes. pp. 3133
Summary: The concept of radical tideal subgroup functor is introduced. Isomorphism of both lattices of all radical tideal subgroup functors and of all Fitting classes is established.
Yudin M. D.
About indispensable conditions of convergence of distributions of the sums of dependent random vectors. pp. 3437
Summary: The indispensable conditions of convergence of distributions of the sums of dependent random vectors to is boundless to divided distributions are considered.
Primicheva Z. N.
Coefficient conditions of dichotomy for triangular systems. pp. 3844
Summary: The sets of L^{p}dichotomic, p w 1, or exponentially dichotomic linear systems with supplementary projections E and O are considered. Coefficient conditions of the dichotomy for linear triangular systems are established.
Krasovskaya T. G.
The structure of the set of lower Perron exponents of infinitely differentiable linear system. pp. 4549
Summary: It is proved that the set S Î R is the set of lower Perron exponents of the linear differential system x^{.} = A(t)x, x Î R<>n, t ³ 0, with infinitely differentiable bounded coefficients and their bounded derivatives of any order, if and only if the S is a bounded Suslin set and sup S Î S.
Tretyakova N. N.
Limit correlations between some integral transforms in Euclidean space. pp. 5055
Summary: Two new types of integral transforms which are generalize Fourier, Fourier  Bessel, Hankel transforms are introduced. The conditions of their convergence are established. The limit relations between transforms introduced are obtained. This result has many interesting consequences.
Audoshka I. V.
Asymptotic integration of the dynamical equations of shallow shells subjected to external forces. pp. 5661
Summary: By using the complex WKBmethod, the formal asymptotic solution of the Cauchy problem for a set of partial differential equations describing motion of thin shell of arbitrary form is found. It is supposed that initial displacements and velocities of surface points are localized near some point on a shell surface.
PHYSICS
Bogush A. A., Kisel V. V., Tokarevskaya N.G., Red'kov V. M.
On equations for the spin2 particle in external electromagnetic and gravitational fields. pp. 6267
Summary: 30component, of the first order, equation by Fedorov  Krylov  Regge for the spin 2 particle, equivalent to the second order Pauli  Firz one, is generalized to presence of an external electromagnetic field as well as a curved background spacetime geometry. The essential property of the generally covariant wave equation obtained is that here from the very beginning, in accordance with requirement of the Pauli  Firz approach, a set of additional relations on 30component wave function for eliminating complementary spin 0 and spin 1 fields is present at the starting equation.
Pilipovich V. A., Esman A.K., Goncharenko I. A., Kuleshov V.K., Sergienya S.A.
Parallel optical adder based on fibre logic elements with Bragg reflectors. pp. 6871
Summary: Gaussian's functions are used to consider properties of optical spatialtemporal solitons propagating in inhomogeneous elliptical waveguide with Kerr local nonlinearity. It is shown that the same as in the spherically symmetrical case both transverse dimensions and temporal duration of the light bullet oscillates along with the pulse propagating in the waveguide.
Blinkouski A. A., Gorbatsievich A.K.
Construction of exact cosmological solutions in the fivedimensional Projective Unified Field Theory. pp. 7275
Summary: In the framework of the fivedimensional Projective Unified Field Theory in which gravitation is described by both spacetime curvature and some hypothetical scalar field, we propose a method for construction of exact solutions for homogeneous and isotropic cosmological models when the time dependence of mass density is given. General consequences of this approach are investigated and new exact solutions are produced.
Komarov F.F., Vlasukova L.A., Mironov A. M., Komarov A. A., Yuvchenko V. N.
Redistribution of indium implanted in silicon under the influence of thermal treatment and superhighenergy ion irradiation. pp. 7680
Summary: The layer of supersaturated solid solution with uniform concentration of introduced In atoms up to ~ 5 at. % and thickness up to ~ 150 nm had been created in Si by polyenergetic implantation. It has been observed close correlation of experimental In distribution profile along the depth of implanted crystal and computer calculations. The implanted samples had been annealing at 550°C during 35 minutes and then had been irradiated by 710 MeV  Bi with fluences 1 x 10^{11} and 1 x 10^{12} cm^{2}.
The introduced atoms redistribution under the postimplanted annealing and followed irradiation by swift Bi ions had been investigated by means of Rutherford backscattering/channeling. The significant redistribution of indium concentration at subsurface and peripheral regions of profile has been observed both after annealing and after additional irradiation by superhigh energy Bi ions. The effect is increased with the growth of Bi ions dose.
Tsionenko D. A.
The DiracKahler equation in a nonEuclidean spacetime. pp. 8185
Summary: The matrix formulation of the DiracKahler equation in a curved spacetime is constructed. The Lagrange formulation is given. The conservation laws and symmetries of the theory in a nonEuclidean spacetime are investigated.
Shipilo V. B., Dutov A.G., Shipilo N.V., Comar V. A., Kurilovich N. Ph., Azarco I. I., Shempel N. A.
Crystallization of diamonds in a melt of metal at use of graphite irradiated with gammaquantums. pp. 8690
Summary: The influence of an irradiation a gammaquantums of reactionary mix material for synthesis of diamonds in a system Mn  Ni  C  Cu on a mass fraction and speed of transformation of graphite in diamond is investigated at P = 5.5 GPa, T = 1620 K and t = 150 s, grit size and admixture makeup of diamond.
It is shown that an irradiation of mix material the gammaquantums diminishes an exit and speed of transformation of graphite in diamond and also contents in diamonds of manganese and nickel. Thus the density of paramagnetic imperfections is essentially augmented. The obtained experimental data are considered from a point of view of the colloidal theory of synthesis of diamonds and contact to features of shaping of structure of carbon complexes in a melt of metal.
Solovyh T. K., Truhanov S. V., Troyanchuk I. O., Kasper N. V., Shimchak G., Berner K.
Magnetic phase transformations in anion deficit manganite La_{0.7}Ca_{0.3}MnO_{3g}, with structure of perovskite. pp. 9196
Summary: The crystal structure, magnetic and electrical properties of the La_{0.70}Ca_{0.30}MnO_{3g} (0 £ g £ 0.20) oxygendeficient manganites have been studied. It is found that the compounds La_{0.70}Ca_{0.30}MnO_{3g} show a longrange ferromagnetic order up to g = 0.06 and a cluster spin glass behavior at 0.06 < g < 0.20. The strongly reduced samples exhibit a large magnetoresistance below the temperature, at which the spontaneous magnetization develops. The magnetic phase diagram of La_{0.70}Ca_{0.30}MnO_{3g} system has been constructed. We argue, that the oxygen vacancies are disordered in the La_{0.70}Ca_{0.30}MnO_{3g} system in the studied region of oxygen vacancies concentration (0 £ g < 0.20).
Kazakevich L.A., Lugakov P.F.
Recombination of charge carriers on radiationinduced defects in silicon doped by transition metals impurities. pp. 97100
Summary: It has been studied the peculiarities of recombination of nonequilibrium charge carriers on radiationinduced defects in received according to Chohralsky method psilicon (p » 3  20 Ohm • cm), doped by one of the impurities of transition metals of the IVth group of Mendeleev table (titanium, circonium, hafnium). Experimental results are obtained out of the analysis of temperature and injection dependence of the life time of charge carriers. The results are explained taking into consideration the influences of elastic stress fields created by the aggregates of transition metals atoms on space distribution over the crystal of oxygen and carbon background impurities as well as on the migration of movable radiationinduced defects during irradiation.
INFORMATICS
Bakhanovich S.V., Likhoded N. A.
Mapping algorithms onto fixed dimension and fixed size parallel architecture. pp. 101108
Summary: The problem of spacetime mapping of algorithms with uniform dependencies onto the given dimension parallel architecture with given number of processors is researched. The investigations is developed in the framework of locally parallel globally sequential strategy. This paper extends previous investigations: the dimensions n and p of algorithm and parallel architecture, respectively, are arbitrary, but p < n.
Evdokimovich V. E.
The closed queueing networks with dynamic routing and dynamic probability rounds of nodes by the customers. pp. 109113
Summary: The closed exponential networks with routing matrix depending on their state are considered. The customers arriving in a node, irrespective of other customers with probability depending on a network state, join queue, or with additional probability instantly round a node. After detour of a node customers move according to stochastic matrix depending on a network state and, generally speaking, distinct from routing matrix. The sufficient condition of an ergodicity is installed with certain restrictions on model parameters and the final stationary distribution is founded.
SHORT NOTES
Bogush A. A.
On two kinds of the vector parametrization of the threedimensional rotation group. pp. 114117
Summary: The basic relations obtained in the framework of two different vector parametrizations of the rotation group (1958, 1977, Fedorov; 2001, Engo) are compared.
ABSTRACTS OF DEPOSITED PAPERS
Lukshin E.V.
About the types of (3n  3) nonintegral vertices of polyhedral of three indexed, axial assignment problem. p. 118
SCIENTISTS OF BELARUS
Andrey Markovich Goncharenko (On the occasion of the 70^{th} birthday). pp. 119120
Click here to read this article in Russian (Windows 1251)
Anton Nikiforovich Sevchenko (On the occasion of the 100^{th} birthday). pp. 121123
Click here to read this article in Russian (Windows 1251)
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