# Доклады Национальной академии наук Беларуси, 2003, Том 47, No.2

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2003, Том 47, No.2

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Tikhonov S. V., Yanchevskii V. I.*
**Pythagorean numbers of function fields of conies defined over hereditarily Pythagorean field.** pp. 5--8

*Summary:* Pythagoras numbers of function fields of conies defined over hereditarily Pythagorean fields are computed.

*Bazylev D. F.*

**Quaternionity of W-algebras with special ramification.** pp. 9--11

*Summary:* The proof of the local Pfister conjecture for W-algebras 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 follow-up system.** pp. 12--14

*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 open-loop controls is used.

*Demidenko V. M.*

**Generalization of strong solvability conditions of the quadratic assignment problem with anti-Monge and Toeplitz matrices.** pp. 15--18

*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 anti-Monge 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. 19--22

*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. 23--25

*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. 26--28

*Summary:* Lower bounds for the number of rational points close to smooth manifolds are obtained.

*Benyash-Krivets V. V.*

**On the Tits alternative for some finitely generated groups.** pp. 29--32

*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. 33--36

*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. 37--39

*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 tree-point stencil and boundary conditions are done on the two-point one. Fundamental moment is connected with using only inner and external half-integer grid points.

*Kostyukova O. I.*

**Asymptotic properties of solutions of singular perturbed boundary-value problem.** pp. 40--43

*Summary:* For solutions of singular perturbed boundary-value problem, asymptotic expansion is obtained. Properties of limited solution are described.

*Balashchenko V. V., Vylegzhanin D. V.*

**Invariant generalized almost Hermitian structures on homogeneous F-spaces of finite order.** pp. 44--49

*Summary:* A vast class of invariant generalized almost Hermitian structures of arbitrary rank is presented. This is based on canonical *f*-structures on homogeneous F-spaces of order *k* (in other terminology, homogeneous *k*-symmetric 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 t-closed w-local formations.** pp. 50--53

*Summary:* All considered groups are finite. In this paper, we describe the elements of the height 3 of the lattice of all t-closed w-local formations of finite groups.

**ИНФОРМАТИКА**

*Batura M. P., Ptichkin V. A.*
**Study of accuracy of phase lock system by means of normalization and statistical linearization.** pp. 54--57

*Summary:* In order to improve accuracy of investigation of phase-locked-loop 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 higher-order 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. 58--60

*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.

**ФИЗИКА**

*Zhestkov S. V.*
**On the theory of "bright" solitons of simple form.** pp. 61--65

*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. 66--69

*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 cross-sections are obtained. It is ascertained that both the oscillatory regime of cross-section 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. 70--73

*Summary:* The continuous two-parameter 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 Seiberg--Witten and Freund's equations as well as some zero modes problem which are represented by universal form is established.

**ХИМИЯ**

*Krivoguz Yu. M., Pesetskii S. S., Pleskachevskii Yu. M.*
**Grafting of itaconic acid onto polyethylene over neutralizing agents.** pp. 74--78

*Summary:* Itaconic acid (IA) was grafted onto molten low-density 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.

**БИОЛОГИЯ**

*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. 79--82

*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. 83--85

*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 (1--54 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. 86--88

*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. 89--90

*Summary:* Our investigations have demonstrated biphasic pattern of growth and synthesis of glucose-oxidazing 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 b-D-glucone-d-lactone and b-D-gluconic 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. 91--93

*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*.

**НАУКИ О ЗЕМЛЕ**

*Astapenko V. N.*
**Plate tectonics and anomalies of electrical conductivity of the Earth's curst and the mantle.** pp. 94--97

*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. 98--104

*Summary:* Chalybeate mineral underground water within the Mikashevichi-Zhytkovichi 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. 105--111

*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. 112--116

*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 time-spectral 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.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Borodachyov N. M., Tarikov G. P.*
**On the Hertz problem taking into consideration heat generation.** pp. 117--119

*Summary:* The three-dimensional 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. 120--123

*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.

/ 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"