Doklady of the National Academy of Sciences of Belarus, 2007, Vol.51, No.1
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Doklady of the National Academy of Sciences of Belarus, 2007, Vol.51, No.1

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
Borukhov V. T.
Lyapunov's bases of vector spaces. pp. 58
Summary: Lyapunov's bases of infinite vector subspaces are considered. The property of the nonexstensibility of these bases is investigated. Some applications to the theory of asymptotic expansions in the sense of Poincare are considered.
Zakrevskij A. D.
Sequential decomposition of the Boolean function: search for a suitable partition on a set of arguments. pp. 911
Summary: A new heuristic algorithm for Boolean functions decomposition is suggested. The problem is reduced to the random search for a suitable simplest partition on the set of arguments and its successive expansion.
Tuzik S. A.
One scheme of constructing iteration methods for solution of operator equations. pp. 1215
Summary: A new form of Kantorovich's iterations theorem is proved. New sufficient conditions are obtained for convergence of nonstationary iteration methods for solution of operator equations.
Navakhrost V. G.
Differential equations with a generalized righthand side in the algebra of mnemofunctions. pp. 1621
Summary: Differential equations with the discontinuous and generalized righthand side are investigated. It is shown that the associated solutions of the corresponding differential equations in the algebra of mnemofunctions coincide with those of equations under consideration that are understood in the sense of differential inclusions.
Minyuk S. A., Metelskii A. V.
Criteria for complete constructive identifiability and complete controllability of linear autonomous systems of neutral type. pp. 2226
Summary: For systems of differentialdifference equations of neutral type the parametric criteria for complete constructive identifiability and complete controllability are proved, when the system solution is understood as a continuous function.
Legchekova H. V., Skiba A. N., Titov O. V.
Finite groups with the given weakly quasinormal subgroups. pp. 2733
Summary: Let G be a finite group, H be a subgroup of G. Then we say that H is weakly quasinormal in G if G has a quasinormal subgroup T such that HT = G and TÇH is quasinormal in G. In this article we use the weak quasinormality to obtain new characterizations for some classes of finite soluble groups.
PHYSICS
Shirko A. V., Kamluka A. N., Nemtsov V. B.
Research of the configuration of the DNA macromolecule ring by the methods of the elasticity theory. pp. 3439
Summary: The change in the form of a DNA macromolecule and the redistribution of bend and twist energies depending on an external force are investigated.
Gusak N. A.
Kinetics of spatial charge gratings in photorefractive crystals in the presence of an external electric field. pp. 4045
Summary: A correct description of buildingup charge gratings excited by standing light in a photorefractive crystal in the presence of an external electric field is given. It is shown that the process is set forth by the fourthorder equation. The particular solutions of the obtaind equation are found, and a general solution satisfying the given initial condition is built.
Privalchuk A. N., Tolkachev E. A.
Algebraic reduction of the Dirac equation in R^{2.1}. pp. 4649
Summary: The reduction of the biquaternionic Dirac equation in R^{2.1} was done. The developed algebraic formalism gives the possibility to embed the solutions of the (2 + l)dimensional of Dirac equation into the physical space  time.
CHEMISTRY
Kouznetsova T. F., Agabekov V. E., Ratko A. L., Karpinchik E. V., Eremenko S. I.
Preparation and the physicochemical properties of silica nano sol (IV). pp. 5052
Summary: The properties of stable silica nanosol prepared using the ionexchange method including the particle growth and concentration are described. A specific surface area was determined by means of hydroxide ion adsorption at the SiO_{2}/ water interface. Sol obtained had a specific surface area of 230 m^{2}/g, a particle diameter of 11.9 nm, a SiO_{2} mass concentration of 30.0% and a pH value of 9.3. It is shown that the stability of silicanano sol stabilized by an aluminum silicate ion increased with decreasing pH value.
Mozheiko F. F., Korshuk E. F., Potkina T. N., Goncharik I. I.
Preparation of suspensions of fertilizers containing phosphorite flour. pp. 5358
Summary: Differentkind compositions based on phosphorite flour and salt solutions have been prepared. It has been shown that their properties depend on an initial blend composition, a solid particle size, viscosity, density, a sedimentation degree of the solid phase, a pH value, fluidity.
Yegorova O. M., Zlenkovsky V. M., Soldatov V. S.
Fe(III) sorprion complexes structure in a werakbase anion exchanger with amidoamine groups. pp. 5962
Summary: The processes bringing to the formation of composite ironbearing sorbent FIBANAs were studied. The optimal conditions of its preparation were determined. The computer analysis of Fe (III) salt solutions composition was carried out. The structures forming in the polymer matrix of an amidoamine ion exchanger after Fe_{2}(SO_{4})_{3} adding were calculated using the simulation package GAMESS.
Potkin V. I., Maier N. A., Rudakov D. A., Zalesskaya E. G., Shirokii V. L.
Halogenation of monoanion [5,6Br_{2}7,8C_{2}B_{9}H_{10}] salts. pp. 6366
Summary: The chlorination of monoanion [5,6Br_{2}7,8C_{2}B_{9}H_{10}]^{} by Nchlorosuccinimide and the iodination by elementary iodine are found to lead to the corresponding B(9) substituted derivatives [9X5,6Br_{2}7,8C_{2}B_{9}H_{9}]^{} (X = Cl, I). The bromination of anion by Nbromosuccinimide proceeds with the introduction of two bromine atoms in the B(9, 11) sites and ends with the formation of tetrabromo substituted compound [5,6,9,11Br_{4}7,8C_{2}B_{9}H_{8}]^{}.
BIOLOGY
Galkovskaya G. A., Vezhnovets V. V., Vlasov B. P., Majsak N. N., Molotko D. V.
Comparative analysis of the zooplakton taxonomic structure in the littoral zone of stratified lakes. pp. 6771
Summary: The species richness and the ratio between the taxonomic groups of a higher rank (genus, family) in the total density of littoral zooplankton were studied in connection with the geomorphological features of the littoral zone. Essential differences in the species similarity indices and the dominance structure peculiarities in Rotifera and Crustacea taxonomic groups were revealed by comparing the sampling stations. The formation of subcommunities in the littoral plankton community was substantiated by the geomorphological specificity of the littoral zone of the lakes considered.
Semenchenko V. P., Razlutskij V. I.
New multimetric index for determination of the trophic status and the ecological condition of lentic waters. pp. 7274
Summary: A new multimetric index (MI) based on the data of the pelagic cladocerans community structure and species composition is proposed. MI is an average value of the sum of species decimal, Margalef index and quantitative similarity of the Sorensen index between investigated and reference lakes. A strong relation (R^{2} = 0.727) was obtained between MI and trophic states (Carlson Index) of 21 lakes from the same region. Additional data on 25 water bodies (lake, reservoirs, pounds) confirmed such a relation (R^{2} = 0.641). Thus, MI can be used for determining the trophic status and the ecological water quality of lentic waters.
Kulahava T. A., Semenkova G. N., Kvacheva Z. B., Mikhadzionak M. N., Koran S. V., Cherenkevich S. N.
Menadioneinduced reactive oxygen species generation by C6 glioma cells. pp. 7578
Summary: To establish the mechanisms of oxygenactivated menadione action on C6 glioma cells in a monolayer, the investigation of diverse reactive oxygen species and NOgenerating enzymes contribution to this process was realized using the lucigeninenhanced chemiluminescence method. It was shown that superoxide basically and, to a certain extent, hydrogen peroxide, nitric oxide and singlet oxygen make a contribution to menadioneinduced chemiluminescence of astroglial cells. It was determined for the first time that NOsyntheses and mainly neuronal isoform of this enzyme participate in the reactive oxygen species formation in C6 glioma cells under the menadione action. The ability of nNOS to generate O_{2}^{.} depends on the enzyme conformation which is regulated by substratum Larginine concentration.
Kushniarevich A. I., Sivitskaya L. N., Danilenko N. G., Tsybovsky I. S., Davydenka A. G., Villems R.
Mitochondrial DNA diversity in the ethnic Belarusians. pp. 7983
Summary: Sequencing of the first hypervariable segment of mitochondrial DNA in combination with the RFLPanalysis of a coding region was performed on 292 samples of the belorassians from six different geographic regions of Belarus. Haplogroups H, J, K, Nl, T, U4, U5, V, X, W (European type) are around 90% of the mitochondrial pool of the ethnic Belarusians. Analysis of the haplogroup distribution among Belarusian subpopulations has shown the intrapopulation heterogenety according to frequencies of haplogroups J, U, V, T.
EARTH SCIENCES
Veretennikov N. V., Laptsevich A. G.
First carnonatite finding in the platform cover of Belarus. pp. 8488
Summary: The results of investigation and petrographic diagnosis of volcanic rocks from the section of the borehole 772 drilled within the Luchin group of the Zhlobin diatreme field are presented. For the first time in Belarus this borehole has exposed carbonatites that are represented by their chromiumrich (up to 1,000 g/t) tetraferriphlogopitecalcic variety and are associated with pyroxenefree olivine melilitites and their tuffs. These rocks form a volcanic pipe or infill the cratervent part of a small LateDevonian palaeovolcano.
Konischev V. S.
Geothermal criteria and the prospects for oil and gas deposits of the basins of Belarus. pp. 8993
Summary: It is was established that as a result of low heat flow and temperature, the deposits of Orsha and PodlesseBrest depressions did not generate oil and gas and do not have oil and gas pools.
Aronova T. I.
Seismotectonic deformations according to the data on group mechanisms of earthquake foci in the northwestern part of the Pripjat yield. pp. 9499
Summary: The analysis of the dynamics of spatiotemporal migration of the annual zone positioning of earthquake foci in the northwestern part of the Pripjat yield has been conducted. Group mechanisms of earthquake foci have been constructed. The key elements of the focal earthquake mechanisms have been estimated and the types of their seismic dislocation have been defined. The data on spatial orientation of the compression axis and the axis of stretching taken from the solutions of focal mechanisms of earthquake foci have been used to characterize the stress field. The major axis of tension has been determined, and a summary diagram of focal earthquake mechanisms has been plotted.
TECHNICAL SCIENCES
Shapovalov V. M., Bochkaryov D. I., Pleskachevsky Yu. M.
Influence of modifiers on the physicochemical properties in composite bitumenmineral materials. pp. 100103
Summary: The efficiency of application of differentnature modifying additives in a composite bitumenmineral material system, which provide a temperature displacement of basic phase transformations of bitumen to a highertemperature area and the expansion of the temperature range of its plastic condition, is established. All this taken together enables one to purposefully control technological and service properties of composite mixtures based on the best system.
Chorny A. D.
Numerical modeling of interaction between aturbulent jet and a coflow in the cylindrical channel. pp. 104110
Summary: Numerical results on the modeling of interaction between a turbulent jet and a coflow of liquid in the cylindrical channel of round crosssection are presented. The standard k  e turbulence model has been adopted for computations. Two flow regimes: with a recirculation zone developed near the channel walls and without it are considered. The standard k  e turbulence model is verified by the available experimental data. The use of different sets of constants of the above model known from free turbulent j et studies has shown that the modification of constants C_{µ} =0.06, C_{e2} = 1.87 had given the best results as compared to the experimental data on the considered flow regimes.
Zhukova Yu. V.
Influence of guide plates on heat transfer of a circular cylinder (laminar flow at Pr >> 1). (The article is presented in English). pp. 111115
Summary: The present article is concerned with numerical results on heat transfer enhancement of a circular cylinder by means of installing guide elements  plates. Computations have been made for the case of laminar crossflow past a heated cylinder in an inhomogeneous viscous medium when its thermal and physical properties depend essentially on temperature. In our case, turbine oil MS20 has served as an inhomogeneous medium. Numerical results on local heat transfer, thermohydrodynamic efficiency and total Nusselt number are presented as a function of length of the installed plates. The data obtained are compared with the identical results for a single cylinder.
Ilyuschenko A. Ph., Akimov A. I., Fedotova J. A., Letsko A. I., Bonnet G., Dubois S., Talako T. L., Belyaev A. V.
Hightemperature oxidation effect on the microstructure and phase composition of powered alloy Fe_{3}Al. pp. 116122
Summary: The effect of the initial microstructure of Fe_{3}Al samples sintered by high isostatic pressing on the kinetics of the alumina formation during hightemperature oxidation in the controlled atmosphere at 900°C, 1000°C and 1100°C has been studied.
It has been observed that the formation of a surface oxide layer started with the islandlike growth of transition aluminium oxides and finished with the precipitation of finestructure stable >aAl_{2}O_{3}. The lamellar structure and inhomogeneous chemical composition of lamellars of the initial mechanoactivated FeAl mixture were the dominating factors influencing the kinetics of Fe_{3}Al hightemperature oxidation.
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Designed and maintained by Dr. Nikolai N. Kostyukovich. Last updated: February 23, 2007
Created with assistance of Dr. Ignatii I. Korsak
Copyright © 2007 The National Academy of Sciences of Belarus
Copyright © 2007 The Belaruskaya Navuka Publishing House