Doklady of the National Academy of Sciences of Belarus, 2003, Vol.47, No.3
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Doklady of the National Academy of Sciences of Belarus, 2003, Vol.47, No.3

DOKLADY OF THE NATIONAL ACADEMY OF SCIENCES OF BELARUS
(Doklady Natsionalnoi Akademii Nauk Belarusi)Published by The Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Sheinin S. A., Tuzikov A. V.
Areas and geometric moments of objects bounded by closed spline curve. pp. 59
Summary: A new approach is proposed for computation of area and smallorder geometric moments for a plane object with a spline curve boundary. The explicit formulas are obtained for calculation of areas and moments for curves having a cyclic sequence of spline control points. These formulas can be used widely.
Yablonskii O. L.
Stochastic integrals for random processes with independent increments. pp. 1013
Summary: The new classes of stochastic integrals are defined in the paper. Use of these integrals limiting behavior of sums of generalized processes with independent increments is investigated.
BenyashKrivets V. V.
On free subgroups of certain generalized triange groups. pp. 1417
Summary: The Tits alternative holds for generalized triangle groups of type (2, k, 2), where k > 6, k ¹ 10, 12, 15, 20, 30, 60.
Starovoitov A. P.
Speed of rational approximation of RiemannLiouville and Weyl fraction integrals. pp. 1823
Summary: Exact orders of rational approximation of functions representable as RiemannLiouville and Weyl fractional integrals are found.
Tykoun A. S.
On existence of the Conley index for ndimensional dynamic systems. pp. 2427
Summary: A problem of determining an isolating property for compact domains (if domain is an isolating neighborhood) is considered. A sufficient condition for domain to be an isolating block is obtained. The result is extended on the domains with a piecewise smooth boundary. Also, a necessary condition of an isolating property is found.
Minchenko L. I., Volosevich A. A.
On differentiability of maximum function on strong differentiable multifunctions. pp. 2832
Summary: Differentiability of maximum function on strong differentiable multifunctions is studied. The estimates of the derivatives of the maximum function are investigated in case when objective function is regular regarding to Clarke.
Shevelevich K. V.
The Hicks and Le ChatelierSamuelson theorems for infinitedimensional Leontief matrix model. pp. 3337
Summary: The paper deals with analogues of Hicks and Le Chatelier  Samuelson theorems for nonnegative infinite matrices. In particular, it is proved that analogues of these theorems hold for decomposable nonnegative infinite matrices.
Zakrevskii A. D.
Optimization problems in linear Boolean space. pp. 3841
Summary: Three combinatorial optimization problems over systems of linear logical equations are regarded, which have useful applications in the theory of finite automata and logic circuits as well as in information transmission and security. Connection between them is established and methods for solving them are suggested.
Balashevich N. V.
Synthesis of optimal closable feedback. pp. 4245
Summary: A method of construction of optimal closable feedback for a linear dynamic system with bounded additive uncertainty is suggested.
PHYSICS
Kozlov G. V., Burya A. I., Sviridenok A. I., Zaikov G. E.
Hierarchical systems in supermolecular organization of structure of polymer amorphous state. pp. 4648
Summary: Hierarchical organization of supermolecular (supersegmental) structure of polymer amorphous state is confirmed. Physically, this organization mediates between weak and strong hierarchical systems.
Knyazev M. A.
Expansion of domain structure with constant velocity. pp. 4951
Summary: A model of a scalar complex field with damping that describes the formation of topological defects at a firstorder phase transition is considered. For spherical symmetry, a new solution of the nonlinear equation of motion is constructed in a thinwall approximation. This solution describes such a regime of domain structure expansion where thickness and velocity of a domain wall are exactly determined by the model parameters alone.
Zhestkov S. V.
On "dark" soliton solutions of complex form for system of secondorder coupled nonlinear Schrodinger equations. pp. 5254
Summary: For the system of second order coupled nonlinear Schrodinger equations, the "dark" onesoliton solutions of complex form are constructed. The necessary and sufficient conditions of existence of these solutions are obtaned. The multiparametric form of "dark" twosoliton solutions is suggested.
Rogovtsov N. N., Karpuk V. V.
Analytical expressions for average and integral characteristics of radiation fields in dispersion media of different configurations. pp. 5559
Summary: Some analytical expressions and asymptotical formulas are obtained for average intensities and integral characteristics of the radiation fields in nonconcave dispersion media.
Sotsky A. B.
On the theory of prism excitation of channel optical waveguides. pp. 6065
Summary: Approximate analytical solution of the diffraction problem of prism excitation of channel optical waveguides is obtained. Possibilities of optimization of the excitation and reconstruction of propagation constants of waveguide modes are.
Matyuk V. F., Churilo V. R., Strelyukhin A. V.
Computer simulation of finite size ferromagnetic field in inhomogenous constant magnetic field. pp. 6670
Summary: The numerical method is substantiated. The computation of the magnetic state of isotropic ferromagnetic disc in the inhomogeneous constant field of solenoid, located on one of its end faces, taking into account its dimensions and magnetic properties, is carried out. The magnetic properties of the material were assumed to be isotropic and were specified in the main magnetization curve.
Pilipovich V. A., Esman A. K., Goncharenko I. A., Kuleshov V. K.
Optical and electrooptical switches based on fiber Bragg gratings. pp. 7173
Summary: In the paper, we propose the functional diagrams of optical and electrooptical highspeed broadband switching elements based on fiber Bragg gratings with low crosstalk and flexible routing. The switching of optical data streams is completed using spatial and/or spectral channels. It is shown that the architecture of matrix commutator for communication networks and data processing systems can be easily created from such basic switches.
Operating speed of the proposed fiber commutators corresponds to the one of the modem element base. Therefore, the use of these commutators makes it possible to achieve peak performance of the processor elements composing matrix parallel computer.
CHEMISTRY
Sokolik G. A., Ovsyannikova S. V., Kimlenko I. M.
Behavior of plutonium and americium in the soilwatercarboxyl resin system. pp. 7477
Summary: Distribution of plutonium and americium between components of the soil  water  carboxyl resin system for soil samples with different sorption systems has been studied. It has been shown that content and qualitative composition of soil humus determine the TUE state in solution and influence significantly the sorption of plutonium and americium by resin.
Dudarchik V. M., Prokhorov S. G., Smychnik T. P., Strigntsky V. P., Strigutsky L. V.
On structure of polyconjugation systems in peat. pp. 7880
Summary: Possibility of formation of not only graphitelike structures, but also fullerenelike polycojugation systems in peat organic matter has been investigated.
BIOLOGY
Wasim T. V.
Cytoskeleton involvement in [^{14}C]glutamate and [^{14}C]GABA neurotransmitter transport by brain nerve endings at osmotic swelling. pp. 8184
Summary: The aim of this paper was to investigate the role of cytoskeletal elements such as microtubules and microfilaments in [^{14}C]GABA and [^{14}C]glutamate transport at osmotic swelling of nerve endings (synaptosomes). Treatment of synaptosomes by colhicyn (0.1 mM) did not influence neurotransmitters transport. Swelling of synaptosomes under hypoosmotic condition stimulates [^{14}C]GABA (~ 30%) and [^{14}C]glutamate (~ 34%) release into incubation medium. Depolymerisation of microfilaments network by cytohalasin B in isotonic medium, under condition excluding the effect of changing Na^{+} ions concentration by tetrodotoxin, imitates [^{14}C]GABA and [^{14}C]glutamate ralease observed in nerve endings exposed to osmotic stress. Cytohalasin B increases neurotransmitters ralease in hypotonic medium by about 510%, that is point to a fact that skeleton of cells exposed to hypotonic stress is destroyed incompletely.
Synaptosomes treatment by cytochalasin B+TTX did not eliminate inhibition of neurotransmitters reuptake by synoptosomes at swelling.
Nesterova O. L.
Biology of sibling species of Oulema Des Gozis (Coleoptera, Chrysomelidae) as cereal pests in Belarus. pp. 8587
Summary: Biology of the sibling species Oulema melanopus (L.) and Oulema duftschmidi (Redtb.) was investigated in Belarus for two years. Certain differences in the life history of these species were found out. Changes in phenology of O. melanopus during extraordinarily hot season of 2002 were discovered.
EARTH SCIENCES
Komarovsky M. E., Komarovskaya O. A.
Structure and genesis of the Sporitsa subglacial valley, northwestern belarus). pp. 8893
Summary: The Sporitsa subglacial valley in northwestern Belarus (Postavy District) with the occurrence of subglacial ridges and hills, tunnel valley and depressions with lakes suggest significant role of glacial exaration and erosion of pressure subglacial meltwater during the Poozerie glaciation in this area. Four phases of the valley formation in subglacial conditions can be identified: (1) glacial exaration; (2) water tunnel erosion of icebed deposits; (3) water tunnel erosion of glacier bed; and (4) glacial accumulation.
Yakubovskaya T. V., Anoshko Ya. I.
Deposits and flora of the second part of the miocene in belarus. pp. 9499
Summary: Structure and occurrence of the deposits of the second part of the Middle Miocene and the later part of the Upper Miocene  Antopol super horizon of the Neogene of Belarus are discussed. The age of deposits is proved by fossil fruits and seeds.
Shkuratov V. I., Makhnach A. S.
Paleogeographical conditions of sedimentation in Belarus during the Middle and Late Riphean. pp. 100103
Summary: Riphean  is time of the beginning of the formation of the EastEuropean platform mantle. Maximum of transgression was during the middle Riphean (the Pinsk time), when on the territory of Belarus and adjacent territory of the Ukraine and Russia the vast VolyzhskOrsha Paleotrough occupied with shallow continental sea basin formed. It was arise sedimentation basin in the Late Riphean the basin is reduse.
Voitov G. I., Kudelsky A. V., Gusev A. S., Murogova R. N., Yakovleva M. P.
Isotope composition of carbon in associated gas of the Alexandrov and Barsukov oil fields (the Pripyat Trough). pp. 104107
Summary: The isotope composition of the methane carbon in the associated gas from intersalt and undersalt oils of the Alexandrov (s^{13}C 41 ¸ 44.4) and Barsukov (s^{13}C 40.3¸ 44.9) oil fields is very similar to the isotope content of the carbon of the natural gas deposits in the Russian Federation, as well as to that of the water and brinedissolved gas mixtures of the Pripyat Trough. It is found out that fluctuations of the isotope composition of the carbon in associated gas within the studied deposits are conditioned by physical and chemical effects of PVTconditions of oil outgassing while the oil goes upwards the well of deep boreholes.
Mamchik S. O.
Jurassic deposit tectonics in the western part of the EastEuropean platform. pp. 108112
Summary: The paper discusses some peculiarities of the structure and development of Jurassic deposits in the western part of the EastEuropean platform in the context of the main geological processes in Europe. The formations have been distinguished and the geodynamic conditions of their accumulation have been traced.
TECHNICAL SCIENCES
Vereshchagin M..N., Ostrikov O. M., Zyukov D. B.
Modeling of stress state in shear band in amorphous material. pp. 113115
Summary: Stress fields in shear Band in amorphous material are determined.
Samoilovich Yu. A., Timoshpolsky V. I., Anisovich G. A., Klimovich G. A.
Use of watercooled refrigerators at continuous steel casting. pp. 116120
Summary: Solution of the question of determination of the solid phase quantity freezing on the chilled surface of watercooled refrigerators in continuous casting of steel is cited in this work. This shows that the use of watercooled refrigerators allows the elimination of local segregation of admixtures.
Dmitriev G. M.
Mathematical model of heat transfer in nonisotropic layer. pp. 121124
Summary: Formulaes for determination of thermohydrodynamic parameters of fluid flow in nonisotropic layer with heat generation are obtained in the paper.
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