Doklady of the National Academy of Sciences of Belarus, 2007, Vol.51, No.5
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Doklady of the National Academy of Sciences of Belarus, 2007, Vol.51, No.5

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
Emelichev V. A., Kuzmin K. G.
Stability measure of efficient solution of the vector problem on the integer linear programming with monotonic norm. pp. 57
Email: emelichev(at)bsu.by, kuzminkg(at)mail.ru
Summary: The formula of stability radius of Pareto optimal solution for the vector problem on integer linear programming is obtained in the case of the arbitrary monotonic norm determined in the criterion space.
Semenchuk V. N., Mokeeva O. A.
Characterization of some classes of finite groups using generalizedprimary subnormal subgroups. pp. 810
Email: mokeeva(at)tut.by
Zabreiko P. P., KrivkoKrasko A. V.
Common conditions for a local minimum of the smooth functions in two variables. pp. 1116
Email: zabreiko(at)mail.ru
Summary: The necessary and sufficient conditions of a local minimum of the real analytic function in two variables are given.
Radyna Ya. M., Radyno Ya. V., Sidorik A. G.
Characterizing the Hilbert spaces using Fourier transformation with respect to the field ofpadic numbers. pp. 1722
Email: yauhen_radyna(at)tut.by, radyno(at)bsu.by, anna_incognito(at)mail.ru
Summary: We give a new characterization of Hilbert spaces in the class of all Banach spaces. A Banach space is isomorphic to a Hilbert one if and only if the Fourier transform operator acting in a space of vectorvalued functions, which are squareintegrable in the Bochner sense and have their arguments in the padic field, is bounded.
Korolyova O. M., Matus P. P.
Stability of difference schemes for equations of weakly compressible liquid. pp. 2327
Email: korovyova(at)im.basnet.by
Summary: A priori estimates of the stability sense from the initial data of a linearized difference scheme approximating the equations of weakly compressible liquid in the Riemann invariants are obtained. The results of computational experiment confirming the theoretical conclusions are given.
Konyukh A. V.
Upper singular exponents and the Lyapunov and Bohl exponents of typical systems of linear differential equations. pp. 2832
Email: al3128(at)gmail.com
Summary: A complete description of the joint distribution of Lyapunov exponents, upper Bohl exponents and upper singular exponents of typical systems of linear differential equations is obtained.
Gabasov R., Dmitruk N. M., Kirillova F. M.
Optimal control of a hyperbolic system. pp. 3338
Email: dmitruk(at)im.basnet.by
Summary: An optimal control problem for a linear hyperbolic system is under consideration. The problem is reduced to an optimal control problem for a largescale system of ordinary differential equations, which is solved by an efficient constructive method based on a procedure of quasidecomposition. The optimal control of the initial system is performed by a discrete feedback representing a function of a finitedimensional state of the problem.
Yanchevskii V. I.
Cyclicity of central simple algebras of degree 4 over the fields with the uinvariant no more than 4. pp. 3943
Email: yanch(at)im.basnet.by
Zakrevskij A. D.
On solvability of Boolean equations. pp. 4446
Email: zakr(at)newman.basnet.by
Summary: It is shown that revealing the functional regularities in data is reduced to checking Boolean equations for solvability in regard to separate variables. The conditions of such solvability are formulated, and a method for testing the equations for satisfying them is suggested.
PHYSICS
Zhestkov S. V.
Existence of soliton solutions of a system of the coupled Schrodinger equations with the log law of nonlinearity. pp. 4751
Email: zhestkov_s(at)rambler.ru
Summary: New forms of soliton solutions of a system of the coupled Schrodinger equations are constructed. The effective conditions of propagation of these solitons are obtained.
Makarenko L. F., Korshunov F. P., Lastovsky S. B., Murin L. I.
Formation and annealing kinetics of metastable carbonoxygen complex in irradiated ptype silicon. pp. 5256
Email: makarenko(at)bsu.by
Summary: DLTS studies of transformation kinetics of different carbonrelated complexes in electron irradiated ptype oxygencontaminated silicon have been performed. It is shown that upon annealing of interstitial carbon a metastable state for interstitial carboninterstitial oxygen complex is formed. This state has an energy level of about Ev + 0.34 eV. The formation of the stable and metastable states takes place concurrently. The most probable model of the studied processes has been formulated. The found features of the carbonrelated complexes formation are likely related to the existence of different crystallographic orientation of the equiprobable pathways through which the interstitial carbon and oxygen atoms can approach each other.
Yearchuck D. P., Yerchak Y. D., Redkov V. M.
Quantum mechanical analogue of LandauLifshitz equation. pp. 5764
Email: dpy(at)tut.by, Jarchak(at)gmail.com, v.redkov(at)dragon.basnet.by
Summary: Quantum mechanical analogue of LandauLifshitz equation has been obtained. It has been established that LandauLifshitz equation is a fundamental physical equation underlying the dynamics of spectroscopic transitions and transitional phenomena. A new phenomenon is predicted: electrical spin wave resonance (ESWR) being an electrical analogue of magnetic spin wave resonance. It has been shown that the Raman spectrum of ESWR has to be characterized by a substantially different (approximately twice as large as) splitting constant in comparison with the ESWR spectrum formed by IRabsorbance or IRreflectance (by the frequencies of zero modes reduced to the same value).
Komarov F. F., Vlasukova L. A., Yuvchenko V. N. F., Volkov A. E., Borodin V. A.
Track formation in amorphous SiO_{2} under swift ions irradiation: simulation in terms of thermal spike. pp. 6570
Email: komarovF(at)bsu.by, vlasukova(at)bsu.by
Summary: The results of computer simulation of the track formation processes in amorphous SiO_{2} under the swift ions irradiation are presented. Numerical simulation is made using the model thermal spike. The radii and existence times of molten regions for nine types of ions with masses from 20 (Ne) to 209 a. m. u. (Bi) and energies from 6 to 710 MeV have been calculated. The possibility of molten regions formation in SiO_{2} irradiated with the comparative light and slow energy ions such as Kr (84 MeV) and Ar (40 MeV) has been demonstrated.
Bogush A. A., Dlugunovich V. A., Zhukovich S. Ya., Kurochin Yu. A., Snopko V. N.
Biquaternious and Mueller matrices. pp. 7176
Email: y.kurochin(at)ifanbel.basnet.by
Summary: It is shown that the presentation of the polarization density matrix of electromagnetic beams as biquaternion, which corresponds to the fourvector of the pseudoeuclidean space with the intensity and the Stokes parameters as components, opens the opportunities for introducing a group of transformations of such quantities. The general polarization properties of the electromagnetic beams, which follow from the above algebraic approach, and the geometry of the fourdimensional pseudo Euclidean space are discussed.
CHEMISTRY
Yurkova I. L., Shadyro O. L., Kisel M. A., Arnhold J. J.
Formation of ceramides under the action of dopamine and bivalent iron ions on cerebrosides. pp. 7779
Email: yurkovail(at)tut.by, shadyro(at)open.by
Summary: Using matrix assisted laser desorption ionization mass spectrometry it is established that the ceramides are formed under the action of the dopamine and Fe^{2+} mixture on cerebrosides.
BIOLOGY
Reshetnikov V. N., Kaler V. L., Bulko O. P., Usmanov P. D., Usmanova O. V.
Ratio of encoded in nuclear and chloroplast genomes chlorophyll native forms in leaves of Arabidopsis thaliana (L.) Heynh pigment mutants. pp. 8084
Email: biolog(at)it.org.by
Summary: Chlorophyll shares in each of its nine native spectral forms in leaves of two chlorophyll mutants and their initial race of arabidopsis plants were evaluated. Native forms with substantial differences in shares among the genotypes were revealed. The donor form containing only chlorophyll B was shown to link positive by and linear by with plastome encoded acceptorforms of photosystem 1 complex containing only chlorophyll A. These forms correlate negatively with donor and donoracceptor forms of photosystem 2 lightharvesting complex containing both chlorophyll A and B. The ratio of chlorophyll shares of individual forms is conditioned by the conformation of their protein carriers encoded in genomes of different cell organelles, that is why, the determination of the native chlorophyll forms correlations makes it possible to study genomeplastome interaction.
Prisyazhnenko O. K., Nikolaichik Y. A., Evtushenkov A. N.
Expression of harpin HrpN gene of Erwinia carotovora subsp. atroseptica in trangenic tobacco plants induces resistance genes. pp. 8589
Email: prisya(at)mail.ru
Summary: This article describes an affect of Erwinia carotovora subsp atroseptica hrpN_{Ec} gene expression in tobacco cells on the immune system of plant. The exogenous impact of this protein on plant induces an elevation of PR genes (pathogenesis related  PR) expression level and, accordingly the plant resistance to different pathogens. This research shows that the endogenous expression of hrpN_{Ec} gene leads to a constitutive change in PR genes expression. It is shown that at a positivegoing transition of PR transcripts level is seen in plants with a middle level of transgene expression, while a low level of transgene expression does not have a significant influence on PR level transition. A maximum amount of hrpN_{Ec} gene transcripts turns in reduction of PR expression in comparison with control, this may be due to a toxic effect of too high quantity of a synthesized product.
Galkovskaya G. A., Vezhnavets V. V., Molotkov D. V.
Diurnal changes of the Cladocera spatial distribution in a trophogenetic water layer of the littoral zone in stratified lakes. pp. 9094
Email: gal(at)biobel.basnet.by
Summary: The diurnal changes of the Cladoceran spatial structure were investigated in a trophogenetic water layer in two stratified lakes in July 2005 and 2006. It was shown that the total Cladoceran density at the sampling stations at night (24.00) exceeded 4 times the one by day (12.00). This is the result of strong exceeding (up to 22 times) of Bosmina spp at night at st. 1 (eulittoral). By day the structure of spatial Cladocera as a whole and that of Daphnia spp in particular, correlate with the temperature: the density index (ID) increases with decreasing temperature lowering (from 25 to 18°C). A special investigation of the factor causality of the revealed phenomenon is required.
Spivak S. G., Yaronskaya E. B., Vershilovskaya I. V., Davydov V. Yu., Trostyanko I. V., Dolgopalets V. I., Averina N. G., Kisel M. A.
Stimulative effect of lipophylic esters of 5aminolevulinic acid on the growth and development of barley plants. pp. 9599
Summary: A comparative study of the growth regulating activity of 5aminolevulinic acid (ALA) and its lipophilic hexyl ester (HALA) was performed. HALA was shown to stimulate the growth and development of barley plants as well as to increase the contents of photosynthetic pigments and proteins at much lower concentrations than ALA. The effect observed was determined to be due to facilitated transport of lipophilic derivatives of ALA into the plant cells.
Kushniarevich A. I., Sivitskaya L. N., Danilenko N. G., Kozhukh G. K., Tsybovsky I. S., Villems R., Davydenko O. G.
Y chromosome gene pool of Belarusians  clues from biallelic markers study (in English). pp. 100105
Email: kushniarevich(at)yahoo.com
Summary: Analysis of 25 Y chromosomal biallelic markers was performed on the sample of 574 Belarusians, living in various regions of the country. A revealed composition of the paternal gene pool is consistent with those in European populations and is presented by the following set of haplogroups: E^{*}, E3b, E3bl, F^{*}, G^{*}, I^{*}, I1a, I1b, I1c, J^{*}, J2, K^{*}, K2, P^{*}, N^{*}, N3, Q^{*}, R^{*}, R1^{*}, R1a, R1b3, R1b4. Haplogroups R1a, I1b and N3 are dominant and have frequencies of 50, 16 and 10%, respectively. Analysis of the gene pool of presentday Belarusians on the intrapopulation level allowed distinguishing subpopulations of southern Belarus (West and East Polesie) and the westnorthern region according to their compositions of biallelic haplogroups, which to some extent reflects the internal genetic heterogeneity. Belarusians show high genetic affinity with neighboring Slavs (Russians, Poles and Ukrainians) as well as with Baltic populations.
Dunai V. I.
Forming the distribution of the Noergic system of the brain of vertebrates in the process of phylogenesis. pp. 106109
Email: dunay_wal(at)bk.ru
Summary: The aim of this work is to study the distribution of NADFHd/CNO  positive nervous cells in the brain of fishes and amphibia such as representatives of anamnes and of birds and mammals such as representatives of amniots.
It has been established that in the process of phylogenesis, parallel with complication and perfection of the nervous system and as a consequence the adaptation to the environment, it is observed that the number of NOsynthesizing nervous cells in the intermediate brain increases.
MEDICINE
Sidorenko V. N., Labanok L. M., Mozhejko L. F.
Constrictor effects of the vessels of placenta at the pregnancy complicated with gestasis. pp. 110113
Email: zhmura(at)tut.by
Summary: Results of research on the contractile reactions of vessels of placenta at physiological pregnancy complicated with gestosis are presented. It is found that along with a decrease in the reactions of smoothmuscular cells under the action of vasoconstrictors there is an activation of endothelium, leading to the strengthening of contractile reactions for histamine, to the normalization of constrictor effects of serotonin and to an increase in the sensitivity of the isolated vessels of placenta to the action of hydrogen peroxide.
EARTH SCIENCES
Konishchov V. S.
Deposition rates and the prospects for oiland gasbearing basins of Belarus. pp. 114118
Email: vkon(at)igig.org.by
Summary: It is shown that only Devonian deposits of Pripyat depression have a high rate of deposition typical for oil and gas bearing complexes. Other deposits of Pripyat depression and all sedimentary rocks of Orsha and Brest depressions have a low rate of deposition not typical for oil and gas bearing complexes and have no prospects for searching oil and gas pools.
SOCIAL SCIENCES AND HUMANITIES
Myachikova I. I.
Archaic graphic symbolics of the eastern Slavs. pp. 119123
Email: myachikova(at)tut.by
Summary: The pagan graphic symbolics of the eastern Slavs is considered and the catalog of basic graphic symbols used for magic purposes is composed. The retrospective approach is proposed for studying the genesis of graphic symbols of the eastern Slavs. It is shown that the approach can be used for investigation of the ethnogenesis of the eastern Slavs.
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