Doklady of the National Academy of Sciences of Belarus, 2011, Vol.55, No.3
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Doklady of the National Academy of Sciences of Belarus, 2011, Vol.55, No.3

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
Kovalkova D. P., Skiba A. N. L. A.
Shemetkov's problem for maximal chains of subgroups. pp. 58.
Email: dina.kovalkova@gmail.ru; skiba@gsu.by
Summary: Let G be a finite group, H a subgroup of G. Then we say that H is Squasinormal in G if H permutes with all Sylow subgroups of G. The article is devoted to the description of the precise structure of finite groups in which every maximal chain of length 3 contains a proper Squasinormal subgroup. Moreover, we constructed the example showing that the class of groups with such a condition is wider than the class of groups in which all 3maximal subgroups are Squasinormal.
Yanchevskii V. I.
On abelian factors of special unitary groups of anisotropic forms. pp. 911.
Email: yanch@im.basnet.by
Summary: It is announced that there exist homomorphisms of factor groups of special unitary groups of anisotropic skewHermitian forms by the commutator subgroups of unitary groups on the corresponding reduced unitary Whitehead groups.
Tatsiy R. M., Mazurenko V. V.
Conditions of solvability of a multipoint problem for the generalized differential system. pp. 1216.
Email: mazvic@ukr.net
Summary: By using the concept of a pseudoinverse matrix, the conditions of existence and uniqueness for solutions of a multipoint problem for the generalized differential system are obtained. Statements of equivalent to it problems for the quasidifferential equation with distributions as coefficients, including the case when the order of the equation and the number of additional conditions do not coincide, are considered.
Serine Aliou Lo, Moussa Ould Ahmed Salem.
Algebraicity conditions for weighted shift operators generated by potentially periodic mapping. pp. 1720.
Email: losa2006@gmail.com
Summary: Let X be a compact topological space and a be a given continuous mapping from X into X. Weighted shift operator B in C(X) is a linear operator of the form (Bu)(x) = a(x)u(a(x)), uÎС(X), where a is a given continuous function. The necessary and sufficient conditions for B to be algebraic are obtained and the characteristic polynomial is given.
Likhoded N. A., Sobolevsky P. I., Tolstikov A. A.
Parallel algorithm communication operations generated by uniform dependences. pp. 2126.
Email: likhoded@im.basnet.by; sobolevsky@im.basnet.by
Summary: A method for generation of communication operations in parallel grained algorithm is developed for the case of operations to be determined by uniform information dependences. Propositions to formalize the communication operations of sending and receiving data arrays are stated and proved.
Кnyazhishche L. B.
Stabilization and disturbance parry for delay systems. pp. 2730.
Email: klb@im.basnet.by
Summary: New asymptotic stability tests are stated for delay systems. New estimates of the disturbances, which influence the delay system and do not destroy the stabilizing control, are given.
Lomovtsev F. E., Motsevich A. V.
New smoothing operators of the Goursat problem for the hyperbolic operatordifferential equation with variable domains. pp. 3136.
Email: lomovcev@bsu.by; anton.motsevich@gmail.com
Summary: The new existence, uniqueness and continuous dependence theorems of strong solutions of the Goursat problem for the hyperbolic secondorder operatordifferential equation with variable domains of the operator coefficients are proved. The existence of strong solutions of hyperbolic operatordifferential equations by means of new smoothing operators is established.
Benediktovich V. I.
Geometric graphs with rational edge lengths. pp. 3742.
Email: vbened@im.basnet.by
Summary:
PHYSICS
Ovsiyuk E. M., Tokarevskaya N. G.
Quantummechanical particle with spin 1 in the uniform magnetic field: nonrelativistic limit. pp. 4348.
Summary: On the basis of the 10dimensional matrix DuffinKemmer formalism in cylindrical coordinate
Email: e.ovsiyuk@mail.ru; tokarevskaya@tut.bys and tetrad, exact solutions of the equation for a spin 1 particle in the uniform magnetic field are constructed in the nonrelativistic limit. Three types of linearly independent solutions are found, in each case the energy spectrum is determined.
Makarenko L. F., Korshunov F. P., Lastovskii S. B., Murin L. I., Moll M.
Features of selfinterstitial diffusion in ptype silicon. pp. 4954.
Email: makarenko@bsu.by
Summary: Deep level transient spectroscopy has been used for studying the defects induced in ptype silicon by irradiation with alpha particles at room temperature (RT). The stability of the Si selfinterstitials (Si_{i}) in pSi at RT is confirmed. It is revealed that the rates of the Si_{i} disappearance and formation of the interstitial carbon related defects in the temperature range 300370 К depend inversely on the free hole concentration in the samples studied. The phenomenon is suggested to be associated with an extremely strong charge state dependence of the Si, diffusivity.
Zhestkov S. V., Romanenko A. A.
Existence of the wave solutions of the twodimensional Fisher equations with differenttype nonlinearity. pp. 5558.
Email: zhestkov_s@rambler.ru
Summary: A direct method of constructing the wave solutions of the twodimensional Fisher equations with Neumann's zero boundary conditions at infinity is developed. Sufficient conditions of existence of the wave solutions are obtained.
Artukhina N. K., Shkadarevich A. P.
Calculation methods of new compositions of twomirror anastigmatic systems. pp. 5963.
Email: art49@mail.ru
Summary: This article presents the methods of calculating twomirror anastigmats. Aberration factors of astigmatism correction are determined. Design resources by a refresh extension list of computer methods are noted. The calculation of the plane field anastigmat design factors has been done.
CHEMISTRY
Lakhvich F. A., Antonevich I. P., Katoк Y. M., Nesterova S. V.
Cleavage of 5,6oxiranylcyclopenta[d]isoxazolines by hydrobromic acid. pp. 6469.
Email: ipantonevich@rambler.ru
Summary: The cleavage of 5,6oxiranylcyclopenta[d]isoxazolines by hydrobromic acid led to 5bromo6hydroxicyclopenta[d]isoxazolines which were then transformed to the corresponding acyl derivatives. The reaction proceeded with high regio and stereoselectivity.
Andrianov A. M., Anishchenko I. V., Kisel M. A., Nikolaevich V. A., Eremin V. F., Kucherov I. I., Tuzikov A. V.
Design of the HIV1 replication inhibitors based on bgalactosylceramide by molecular modeling and chemical synthesis. pp. 7078.
Email: andrianov@iboch.basnet.by; anishchenko.ivan@gmail.com
Summary: Computeraided design of the watersoluble analog of bgalactosylceramide (bGalCer), which presents a potential HIV1 entry inhibitor, was implemented by the analysis of intermolecular interactions of bGalCer with the central region of the virus V3 loop followed by synthesis of this glycolipid derivative and testing for antiviral activity. As a result, interactions of overlapping пorbitals of the side chain of the conserved phenylalanine, which resides in its immunogenic tip GlyProGlyGln/ArgAlaPhe, with the XH (X designates C or O) sugar groups was suggested to play a key role in forming the structural complexes of glycolipids with the HIV1 V3 loop. At the same time, hydrogen bonds between galactose hydroxyl groups and polar atoms of the V3 backbone were also illustrated to greatly contribute to the stabilization of the complexes of interest. Using binding energy simulations carried out for the glycolipids and V3 loop peptides, the high probability of exhibiting the antiviral activity was predicted for the designed bGalCer analog. The data of molecular modeling were confirmed by those of medical trials of the synthesized compound.
Hloba N. I., Zelenkovsky V. M., Prokopchuk N. R., Krutko E. T.
Soluble block polyimides. pp. 7982.
Email: orion2308@yandex.ru
Summary: Fragmentary polyamicacids on the basis of industrially made poly(4,4'diaminodipheniloxide)piromellitamicasid and oligoamidoacid, received by polycondensation of 4,4'diaminodiphenyloxide and dianhydride 4,8diphenil1,5diazodicyclic/3,3,0/octane2,3,6,7tetracarboxylic acid has been synthesized with their subsequent chemical imidization. Unlike initial poly(4,4'dipheniloxide)piromellitimide synthesized block polyimides possess solubility in polar aprotic solvents. For explanation of their solubility calculations of parameters of conformation of constitutional repeating units of macromolecules by computer modeling has been carried out.
BIOLOGY
Katlinskaya Y. V., Katlinski K. V., Doroshenko T. M., Akalovich S. T., Voitenok N. N.
Role of metalloproteinases in the expression regulation of interleukine8 receptor CXCR2 on human neutrophils. pp. 8387.
Email: katlinskaya@bcht.by
Summary: Interleukin8 (IL8) plays a central role in polymorphonuclear neutrophils (PMN) chemotaxis during the inflammatory response to the invasion of pathogenic microorganisms. PMN react to IL8 by transmembrane receptors CXCR1 and CXCR2. The expression of CXCR2 is about twice reduced in patients with sepsis as against healthy donors, while CXCR1 remains unaltered. We have previously showed that phagocytic stimuli or tumor necrosis factor [da (TNF) caused a sharp decrease in the expression of CXCR2 on PMN membrane and the appearance of a soluble CXCR2 antigen (sCXCR2) in the culture supernatants. In the current study, we examined the effect of matrix metalloproteinases inhibitors on the generation of sCXCR2 during the activation of purified PMN or whole blood in vitro by lipopolysaccharide or TNF. A broadspectrum hydroxamate inhibitor of matrix metalloproteinase GM6001, specific inhibitor of matrix metalloproteinase 8 (MMP8) or specific inhibitor of matrix metalloproteinase 9 (MMP9) substantially reduced the generation of sCXCR2 by activated PMN. Our data point to the involvement of metalloproteinases MMP9, and mainly MMP8 in the regulation of CXCR2 expression on human neutrophils via its proteolytic conversion to the soluble form.
Lemesh V. A., Mozgova G. V., Grushetskaya Z. E., Piluk J. E., Bakanovskaya A. V., Khotyleva L. V.
Identification of the mutant fad2 and fad3c alleles in the Belarusian varieties of Brassica napus L. pp. 8891.
Email: G.Mozgova@igc.basnet.by
Summary: The identification of mutant fad2 and fad3c alleles of genes controlling fatty acids synthesis in rape seeds in the cultivar accession, line variety and 11 cultivars of Belarusian summer rape has revealed a wide range variation in fad2 gene mutation frequency, and the absence of mutant allele of the fad3c gene in the cultivars and line variety. It is established that summer rape cultivar accession gr. 73704 individual plants are double mutant on fad2 and fad3c genes. The presented results will be perspective for a markerassisted selection of the fad2 and fad3c alleles in parental genotypes in the development of rape hybrids based on the collection of cultivars differing in fatty acids levels and summer rape cultivar accession gr. 73704, the individual plants of which are characterized by the high levels of oleic and the lowered levels of linolenic acids.
Polyukhovich Y. V., Savchuk A. V., Voronkova E. V., Yermishin A. P.
Hybridization efficiency between Solanum verrucosum Schltdl and 1EBN wild diploid potato species with the use of rescue pollination by S. phureja IvP 35. pp. 9296.
Summary: The high efficienc
Email: yermishin@igc.basnet.byy of using as a bridgespecies of Solanum verrucosum in combination with rescuepollination by S. phureja IvP 35 for introgression into breeding of valuable germplasm of 1EBN wild diploid potato species, which are practically not crossable with cultivated potato, is demonstrated.
Voronova N. V., Buga S. V., Kurchenko V. P.
Cryptic subspecies detection in the evolutionally young groups of aphids (Rhynchota: Homoptera: Aphididae) by COI partial sequences. pp. 97102.
Summary: The high mo
Email: voronoff@list.rurphological variability of aphids requires the development of special methods for detection of cryptic species or subspecies. Analysis of partial sequences of the COI gene results in a reproducible phylogenetic signal on the level of species and subspecies. Where the usual morphological methods fail the COI partial sequence analysis allows the differentiation between morphologically indistinguishable subspecies within a cryptic species complex. In particular, we establish the existence of three genetically different Myzus cerasi and two Brachycaudus helichrysi subspecies. At the same time, we show through COI partial sequence analysis of the Aphis fabae complex that there is a lack of gene differences sufficient for subspecies differentiation.
MEDICINE
Eremin V. F., Gasich E. L., Sasinovich S. V.
New unique HIV1 recombinant form revealed in Belarus. pp. 103109.
Email: veremin@mail.ru
Summary: On the basis of sequencing the structural gag, pol, env genes regions and the subsequent phylogenetic analysis of the DNA fragments obtained, a new unique recombinant form of HIV1 having the following structure B^{gag} A^{pol} A^{env} is revealed and described for the first time in the world. The recombinant nature of the new HIV1 isolate has been confirmed by means of SimPlot software. As it has appeared, the new HIV1 isolate has a more difficult mosaic structure, which has been shown by the example of studying the sequences of gene pol 1450 bp in length. The analyzed gene pol DNA region consists of alternating HIV1 sequences of subtypes A and B. Sequences of the new unique recombinant form of a HIV1 on genes gag, pol and env are registered in the international database EMBL/Genbank/DDBJ at numbers FR775442.1, FN995656.1, FR775443.1.
EARTH SCIENCES
Korshunov F. P., Medvedeva I. F., Murin L. I., Litvinko A. G., Markevich V. P.
Effect of impurity content and irradiation temperature on the efficiency of defect generation in ntype silicon. pp. 110114.
Email: korshunov@ifttp.basnet.by
Summary: The generation rates of the secondary defects in Czochralskigrown and floatzone nSi crystals with different doping level irradiated at different temperatures with 4 MeV electrons and ^{60}Co grays have been studied by means of electrical measurements. It is found that at initial fluencies of irradiation practically all nonannihilated vacancies and selfinterstitial atoms take part in the formation of electrically active complexes with impurities. The production efficiency of these defects (A, Ecenters, and carbonrelated complexes) upon irradiation with ^{60}Co grays is affected mainly by the separation probability of the close vacancyself interstitial pairs and depends substantially on the Fermi level position in irradiated crystals.
SOCIAL AND HUMANITIES SCIENCES
Artyukhin M. I., Pushkevich S. A.
External migration potential of the population of Belarus: a sociological analysis. pp. 115118.
Email: art47@mail.ru; pushkevich@gmail.com
Summary: The external migration potential of the population of Belarus is examined in the article and its low rate is determined. The motivation of potential migrants is revealed and their social portraits are formed on the basis of sociological research. Conclusion is made that the migration must not be considered as a simple mechanical movement of the people but as a complicated social process affecting a lot of socioeconomic life aspects.
Beryozkina N. Yu.
Radziwills' book collections: from the history of catalogue creation. pp. 119122.
Email: natalyb@kolas.basnet.by
Summary: In the article the creation of printing catalogues, inventories, and registers, which introduce the contents of Radziwills' Book Collection, is considered. Special attention is given to the library at Nesvizh. Presently, the Central Science Library of the National Academy of Sciences of Belarus stores more than 3.5 thousand books from Antoniy Radzivill's library. The scientific description of editions and the preparation of printing catalogues are carried out.
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