Doklady of the National Academy of Sciences of Belarus, 2003, Vol.47, No.2
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Doklady of the National Academy of Sciences of Belarus, 2003, Vol.47, No.2

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
Tikhonov S. V., Yanchevskii V. I.
Pythagorean numbers of function fields of conies defined over hereditarily Pythagorean field. pp. 58
Summary: Pythagoras numbers of function fields of conies defined over hereditarily Pythagorean fields are computed.
Bazylev D. F.
Quaternionity of Walgebras with special ramification. pp. 911
Summary: The proof of the local Pfister conjecture for Walgebras defined over R ((t))(x) is obtained in case where points of ramification have roots of special type.
Gabasov R., Kirillova F. M.
Synthesis of regulator of reference governors for followup system. pp. 1214
Summary: A new method of solving the synthesis problem for regulator of reference governors is suggested based on positional solutions of auxiliary optimal control problems. At constructing positional solutions (optimal feedback controls) the procedure of correction of optimal openloop controls is used.
Demidenko V. M.
Generalization of strong solvability conditions of the quadratic assignment problem with antiMonge and Toeplitz matrices. pp. 1518
Summary: The conditions of strong solvability of the quadratic assignment problem, guaranteeing attainment of the minimum of its functional on permutation of the given form, are described. The proposed conditions are generalization of all previously received results regarding strong solvability of the quadratic assignment problem with antiMonge matrix and Toeplitz matrix, including the known theorem of rearrangement of three systems.
Kalosha N. I.
Simultaneous approximations of zero by values of integral polynomials in RxQ_{p}. pp. 1922
Summary: It is proved that the inequality P_{n}(x) P_{n}(w)_{p} < H^{n} ln^{g}H in integral polynomials P_{n}(x) holds infinitely often only for the set of points (x, w) (RxQ_{p}) of measure zero.
Demenchuk A. K.
Criterion of existence of almost periodic solutions of linear differential systems in critical case. pp. 2325
Summary: The existence of necessary and sufficient conditions of almost periodic partially irregular solutions are given for linear ordinary differential systems in certain critical case.
Bernik V. I.
Khinchine's transference principle and lower bounds for the number of rational points close to smooth manifolds. pp. 2628
Summary: Lower bounds for the number of rational points close to smooth manifolds are obtained.
BenyashKrivets V. V.
On the Tits alternative for some finitely generated groups. pp. 2932
Summary: We prove the Tits alternative for some finitely generated groups with periodic relations. We apply this result to prove, in some special cases, an old conjecture that generalized triangle groups satisfy the Tits alternative.
Dymkov M. P.
Optimization of linear composite control systems. pp. 3336
Summary: The operator approach is proposed for solving the linear quadratic optimization problem for the linear nonstationary repetitive control system. It is shown that in the stationary case, the optimal control can be represented as optimal feedback control law.
Matus P. P., Matus O. P., Martsynkevich G. L.
Monotone schemes for differential problems with boundary conditions of the third type. pp. 3739
Summary: By the example of ordinary differential equation with boundary conditions of the third type
(k(x)u')'  q(x)u = µ(x), 0 < x < l, ku'  su = µ, x Î µ, (1) we suggesta fundamentally new approach for construction of monotone difference schemes of the second order of approximation and accuracy on the minimal stencils without using the equation on the boundary. Thus, for the problem (1), differential equation is approximated on the treepoint stencil and boundary conditions are done on the twopoint one. Fundamental moment is connected with using only inner and external halfinteger grid points.
Kostyukova O. I.
Asymptotic properties of solutions of singular perturbed boundaryvalue problem. pp. 4043
Summary: For solutions of singular perturbed boundaryvalue problem, asymptotic expansion is obtained. Properties of limited solution are described.
Balashchenko V. V., Vylegzhanin D. V.
Invariant generalized almost Hermitian structures on homogeneous Fspaces of finite order. pp. 4449
Summary: A vast class of invariant generalized almost Hermitian structures of arbitrary rank is presented. This is based on canonical fstructures on homogeneous Fspaces of order k (in other terminology, homogeneous ksymmetric spaces). Some general and particular examples including homogeneous spaces of semisimple and solvable types are considered in more detail.
Bliznets I. M.
On the elements of the height 3 of the lattice of tclosed wlocal formations. pp. 5053
Summary: All considered groups are finite. In this paper, we describe the elements of the height 3 of the lattice of all tclosed wlocal formations of finite groups.
INFORMATICS
Batura M. P., Ptichkin V. A.
Study of accuracy of phase lock system by means of normalization and statistical linearization. pp. 5457
Summary: In order to improve accuracy of investigation of phaselockedloop frequency control system by moments equation method, modification of this method is proposed. It consists in application of error signal moments of higher order than moments determined by moments equation system. This result is obtained using expression of higherorder moments in terms of moments determined under the assumption of Gaussian distribution of error signal.
Zakrevskii A. D.
Decomposition methods of finding the shortest solution of system of linear logical equations. pp. 5860
Summary: Two new combinatorial methods are suggested for finding a shortest solution of a system of linear logical equations. They are based on changing one canonical form of the system to several ones, which allows lowering substantially the level of search for solutions, and whence reducing the whole runtime.
PHYSICS
Zhestkov S. V.
On the theory of "bright" solitons of simple form. pp. 6165
Summary: Common system of second order coupled nonlinear Schrodinger equations is solved in case of "bright" solitons of simple form.
Goncharenko A. M., Shapovalov P. S.
On interaction of circular Guassian light beams in nonlinear media. pp. 6669
Summary: Interaction of two circular Gaussian light beams of equal power in cubic nonlinear medium is considered with the aid of variation method. Analytical forms of beam crosssections are obtained. It is ascertained that both the oscillatory regime of crosssection changing and the monotonic one can be observed for two beams. The critical power of beam collapse and upper limit of the oscillatory regime are determined.
Aleinikov D. V., Tolkachev E. A.
Contraction of SO(3), SO(2,1) and E(2) groups in terms of SO(3,1) and SO(4,2) groups representations. pp. 7073
Summary: The continuous twoparameter contraction of SO(3), SO(2,1) and E(2) groups as the subgroups of Lorentz group and conformal group of Minkovsky space is constructed. In this framework, the connection between particular solutions of SeibergWitten and Freund's equations as well as some zero modes problem which are represented by universal form is established.
CHEMISTRY
Krivoguz Yu. M., Pesetskii S. S., Pleskachevskii Yu. M.
Grafting of itaconic acid onto polyethylene over neutralizing agents. pp. 7478
Summary: Itaconic acid (IA) was grafted onto molten lowdensity polyethylene over neutralizing agents (oxides and hydroxides of Zn and Mg). It is shown that partial or complete neutralization of carboxyl groups occurs in the grafted monomer along with the reactions of grafting and crosslinking. In the order of their neutralizing activity, the neutralizing agents can be arranged as follows: Zn(OH)_{2} > ZnO > Mg(OH)_{2} > MgO. The addition of a neutralizing agent to the initial reaction mixture increased the yield of the grafted product.
BIOLOGY
Voitovich A. M., Afonin V. Yu., Krupnova E. V., Trusova V. D., Ogurtsova S. E.
Level of aberrant cells in bone marrow in bank vole depending on doses and radionuclide balance in the body. pp. 7982
Summary: Regression analysis shows the direct linear relation between ^{137}Cs accumulation in rodents and the level of aberrant cells (R = 0.30; P < 0.05). For ^{90}Sr, this trend was negative (R =  0.23; P < 0.05). The dose relationship was the same with ^{137}Cs. The trends were negative 1 month after keeping animals on clean food. Correspondingly, the dose relationship was also negative. The levels of cells with apoptosis characters were different in animals in control from radiocontaminated sites.
Trifonov O. V., Ostapenya A. P.
Periphyton growth on artificial substrates in secondary settling tanks of sewage water biological purification station. pp. 8385
Summary: The growth of periphyton on artificial substrates in secondary settling tanks of the Minsk purification station was studied. Peritricha were prevailed in quantitative relation. The growth of periphyton biomass during investigation period (154 days) is described by exponential curve. Maximal periphyton biomass was 440 g/m^{2} (dry matter).
Rudenok A. N., Belyanovich L. M., Nekrashevich N. I., Konev S. V.
Comparative efficiency of inhibitors of oxidized form of cytochrome oxidase. pp. 8688
Summary: Inhibitory activity of different ligands of oxidized form of cytochrome oxjdase has been studied. It is suggested that efficiency of these inhibitors depends largely upon maintenance of the protonated form of their molecules.
Shishko Zh. F., Mikhailova R. V., Yasenko M. I., Lobanok A. G.
Mechanisms of extracellular glucose oxidase by penicillium adametzii H penicillium funiculosum. pp. 8990
Summary: Our investigations have demonstrated biphasic pattern of growth and synthesis of glucoseoxidazing enzyme in P. adametzii and P. funiculosum.
Constitutive synthesis of glucose oxidase in the fungi was found to be not subjected to catabolite repression and repression by end products of glucose oxidation reaction. Stimulating effect of bDgluconedlactone and bDgluconic acid on fungal glucose oxidase synthesis and effect of FAD, FMN, and riboflavin on enzyme production by P. adametzii and P. funiculosum are established.
Padutov V. E., Baranov O. Yu.
Levels of genetic diversity and differentiation in Betula L. in Belarus. pp. 9193
Summary: Natural populations of silver birch, hairy birch, and dwarf birch are studied by isozyme. analysis. It has been found that of the three birch species in Belarus, B. pubescens shows the highest heterozygosity level, B. pendula demonstrates a moderate level of genetic variation, while B. nana exhibits the lowest level of genetic diversity. The study of genetic distance coefficients among the three birch species showed that there is the least differentiation between silver and hairy birches placed into a single section Betulae. Major differences were revealed between silver and dwarf birches united into the section Nanae.
EARTH SCIENCES
Astapenko V. N.
Plate tectonics and anomalies of electrical conductivity of the Earth's curst and the mantle. pp. 9497
Summary: Anomalies of electrical conductivity of the Farth's crust and the mantle are described in terms of plate tectonics. Results of electromagnetic soundings in 46 regions of the Earth show that anomalies of the electrical conductivity are attribute of tectonically active zones.
Kudelsky A. V., Kapora M. S., Pashkevich V. L, Korkin V. D.
Chalybeate mineral water in Belarus: localization, origin, and prospects of use. pp. 98104
Summary: Chalybeate mineral underground water within the MikashevichiZhytkovichi Uplift of the crystalline bedrocks is indentified and characterized comprehensively as balneal one for the first time. It is recommended to use this water in the balneal and therapeutic practice in Belarus for the purposes of treatment of patiens with iron deficiency.
Aksamentova N. V.
Sedimentological interpretation of granulite complexes alumina gneisses in the East European Craton. pp. 105111
Summary: The initial mineral composition of the granulite complexes alumina gneisses in the East European Craton has been reconstructed using lithochemical calculations of chemical data. It has been concluded that the considered rocks represent originally pelagic and semipelagic aleuropelitic and pelitic sediments and products of redeposition of the mature crust of chemical weathering.
Loginov V. F., Kuznetsov G. P., Mikutsky V. S.
Analysis and modelling of climatic processes in Belarus. pp. 112116
Summary: Experience in using mathematical methods in the study of the climate in Belarus is presented. Among these methods, statistical methods and mathematical modelling are selected. The questions of smoothing of time series and extraction of trends on the basis of calculation of splines and other methods, research of time series amplitudes using apparatus of Fourier transformation, modern methods of spectral analysis, such as timespectral analysis and wavelet methods, are considered. The models of the boundary layer of the atmosphere and results of the application of experiments on models of general atmospheric circulation applied to regional conditions in Belarus with solution, on this basis, of different applied problems are also described.
TECHNICAL SCIENCES
Borodachyov N. M., Tarikov G. P.
On the Hertz problem taking into consideration heat generation. pp. 117119
Summary: The threedimensional contact problem of the theory of elasticity taking into consideration heat generation is esteemed at a sliding friction.
Dorozhkin N. N., Klimenko S. E., Khudoley A. L.
Porosity change during radial distribution of powder strata. pp. 120123
Summary: In this paper, dependences allowing to determine current values of porosity for any rone of work area of calibrating element of punch and final porosity of powder stratum after its radial distribution are presented.
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Created with assistance of Dr. Ignatii I. Korsak
Copyright © 2003 The National Academy of Sciences of Belarus
Copyright © 2003 The Belaruskaya Navuka Publishing House