# Доклады Национальной академии наук Беларуси, 2003, Том 47, No.3

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2003, Том 47, No.3

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Sheinin S. A., Tuzikov A. V.*
**Areas and geometric moments of objects bounded by closed spline curve.** pp. 5--9

*Summary:* A new approach is proposed for computation of area and small-order 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. 10--13

*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.

*Benyash-Krivets V. V.*

**On free subgroups of certain generalized triange groups.** pp. 14--17

*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 Riemann--Liouville and Weyl fraction integrals.** pp. 18--23

*Summary:* Exact orders of rational approximation of functions representable as Riemann-Liouville and Weyl fractional integrals are found.

*Tykoun A. S.*

**On existence of the Conley index for ***n*-dimensional dynamic systems. pp. 24--27

*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. 28--32

*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 Chatelier--Samuelson theorems for infinite-dimensional Leontief matrix model.** pp. 33--37

*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. 38--41

*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. 42--45

*Summary:* A method of construction of optimal closable feedback for a linear dynamic system with bounded additive uncertainty is suggested.

**ФИЗИКА**

*Kozlov G. V., Burya A. I., Sviridenok A. I., Zaikov G. E.*
**Hierarchical systems in supermolecular organization of structure of polymer amorphous state.** pp. 46--48

*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. 49--51

*Summary:* A model of a scalar complex field with damping that describes the formation of topological defects at a first-order phase transition is considered. For spherical symmetry, a new solution of the nonlinear equation of motion is constructed in a thin-wall 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 second-order coupled nonlinear Schrodinger equations.** pp. 52--54

*Summary:* For the system of second order coupled nonlinear Schrodinger equations, the "dark" one-soliton solutions of complex form are constructed. The necessary and sufficient conditions of existence of these solutions are obtaned. The multiparametric form of "dark" two-soliton 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. 55--59

*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. 60--65

*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. 66--70

*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. 71--73

*Summary:* In the paper, we propose the functional diagrams of optical and electrooptical high-speed broadband switching elements based on fiber Bragg gratings with low cross-talk 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.

**ХИМИЯ**

*Sokolik G. A., Ovsyannikova S. V., Kimlenko I. M.*
**Behavior of plutonium and americium in the soil-water-carboxyl resin system.** pp. 74--77

*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. 78--80

*Summary:* Possibility of formation of not only graphite-like structures, but also fullerene-like polycojugation systems in peat organic matter has been investigated.

**БИОЛОГИЯ**

*Wasim T. V.*
**Cytoskeleton involvement in [**^{14}C]glutamate and [^{14}C]GABA neurotransmitter transport by brain nerve endings at osmotic swelling. pp. 81--84

*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 5--10%, 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. 85--87

*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.

**НАУКИ О ЗЕМЛЕ**

*Komarovsky M. E., Komarovskaya O. A.*
**Structure and genesis of the Sporitsa subglacial valley, northwestern belarus).** pp. 88--93

*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 ice-bed 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. 94--99

*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. 100--103

*Summary:* Riphean -- is time of the beginning of the formation of the East-European 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 Volyzhsk-Orsha 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. 104--107

*Summary:* The isotope composition of the methane carbon in the associated gas from inter-salt and under-salt 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 brine-dissolved 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 PVT-conditions of oil outgassing while the oil goes upwards the well of deep bore-holes.

*Mamchik S. O.*

**Jurassic deposit tectonics in the western part of the East-European platform.** pp. 108--112

*Summary:* The paper discusses some peculiarities of the structure and development of Jurassic deposits in the western part of the East-European 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.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Vereshchagin M..N., Ostrikov O. M., Zyukov D. B.*
**Modeling of stress state in shear band in amorphous material.** pp. 113--115

*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 water-cooled refrigerators at continuous steel casting.** pp. 116--120

*Summary:* Solution of the question of determination of the solid phase quantity freezing on the chilled surface of water-cooled refrigerators in continuous casting of steel is cited in this work. This shows that the use of water-cooled refrigerators allows the elimination of local segregation of admixtures.

*Dmitriev G. M.*

**Mathematical model of heat transfer in non-isotropic layer.** pp. 121--124

*Summary:* Formulaes for determination of thermohydrodynamic parameters of fluid flow in non-isotropic layer with heat generation are obtained in the paper.

/ Издания академии / Научные журналы / К началу страницы

Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: *15 ноября 2006 г.*

Создана при участии Игнатия И. Корсака

Копирайт © 2003-2008 Национальная академия наук Беларуси

Копирайт © 2003 Издательство "Беларуская навука"