Doklady of the National Academy of Sciences of Belarus, 2010, Vol.54, No.4
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Doklady of the National Academy of Sciences of Belarus, 2010, Vol.54, No.4

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
Zabreiko P. P., Korots Yu. V.
Majorated mappings principle for generalized Hammerstein integral equation. pp. 512
Email: zabreiko@mail.ru; korots@gmail.com
Summary: The article deals with the mixed Hammerstein integral equations with Lipschitzian nonlinearities. It is stated that for studying such equations a modification of the wellknown Kantorovich principle of majorable mappings is convenient. The equations in the space С and L_{p} (1£p£µ) are considered in details.
Akopian D. V., Gorokhovik V. V.
On a generalization of the Szpilrajn theorem. pp. 1320
Email: gorokh@im.basnet.by
Summary: For a given partial order and an equivalency relation both defined on the same set we present a necessary and sufficient condition for existence of a total preorder such that its asymmetric part contains the asymmetric part of the given partial order and its symmetric part coincides with the given equivalency relation. This result generalizes the classical Szpilrajn theorem on extension of a partial order to a perfect (linear) order.
Gabasov R., Dmitruk N. M., Kirillova F. M.
Optimal control of a dynamical system in a rendezvous problem with a moving target. pp. 2127
Email: kirill@nsys.by; dmitruk@im.basnet.by
Summary: This article deals with rendezvous problems for a dynamical object with a moving target under uncertainties. Different types of information about the system behavior are considered. The following problems are studied: a determined optimal rendezvous problem; an optimal rendezvous problem for a moving target with unknown maneuvering actions; an optimal rendezvous problem under uncertainty with noise measurements of the outputs of the object and the target. Optimal feedback control realizations in real time are described.
Yadchenko A. A., Zayats P. I.
Factorization of certain irreducible linear groups. pp. 2835
Email: yadchenko_56@mail.ru; de2000@tut.by
Summary: In this work the signs of factorization of the irreducible complex linear group of 2degrees were obtained.
Likhoded N. A., Tolstikov A. A.
Parallel sequences of grain computations. pp. 3641
Email: likhoded@im.basnet.by
Summary: A mathematical tool for construction of sequences of grain computations is designed. The conditions for parallel implementation of the sequences are obtained.
Knyazhishche L. B.
Nonmonotonic functionals for stabilization and disturbances parry to delay systems. pp. 4246
Email: klb@im.basnet.by
Summary: Positivedefinite on a part of phase space Lyapunov functionals based asymptotic stability tests are stated to delay systems. A new notion and a new class of small disturbances which don't destroy the delay system stabilization are described.
INFORMATICS
Gordon V. S. †, Dolgui А. В., Strusevich V. A.
Schedules with precedence restriction and positiondependent servicing durability. pp. 4752
Email: itekan@newman.basnet by
Summary: We demonstrate that several single machine scheduling problems with positionally dependent processing times can be solved in polynomial time, provided that the graph that defines precedence constraints admit modular decomposition into factors of a bounded width.
PHYSICS
Korzhik M. V., Borisevich A. Y., Dormenev V. L., Mechinskii V. A., Misevich O. V., Fedorov A. A.
Radiation stability of optical properties of scintillation crystals due to highenergy protons. pp. 5357
Email: korzhik@inp.minsk.by
Summary: It is stated for the first time that when highenergy protons (24 GeV) interact with scintillator substance of lead tungsten up to the flux of 10^{13} particles/cm^{2} corresponding to the 10year cycle of operation of a Collaboration CMS detector, in it nonrecoverable defects are not formed, which deteriorate essentially the scintillation properties of material. The results obtained allowed us to estimate in a new manner a possible time of use of detectors based on lead tungsten crystals in experiments at the large hadron collider in CERN as well as to transfer it to the elevated luminosity regime
Korshunov F. P., Bogatyrev Yu. V., Gurin P. M., Gurinovich V. A.
Effects of fast electron irradiation of silicon epitaxial n^{+}pstructures. pp. 5863
Email: korshun@ifttp.basnet.by
Summary: The influence of electron irradiation with 6 MeV energy on the parameters of epitaxial silicon n^{+}pstructures has been investigated. A dose dependence of change of n^{+}pstructure parameters has been established. The constant of radiation change of the lifetime of minority charge carriers (K_{t}=1×10^{13} см^{2}/эл×s) has been determined. Parameters of the basic radiation defects in epitaxial silicon n^{+}pstructures (divacancy, complexes carbon of introduction  oxygen of introduction, and boron of introduction  oxygen of introduction) have been determined.
Kisel V. V., Ovsiyuk E. M., Red'kov V. M.
Solutions of the DuffinKemmer equation for a particle with spin 1 in the homogeneous magnetic field. pp. 6471
Email: redkov@dragon.basnet.by
Summary: With the use of the matrix 10dimensional DuffinKemmer formalism in cylindrical coordinates and tetrad the exact solutions of the quantummechanical equation for a particle with spin 1 in the presence of an external homogeneous magnetic field are constructed. Three linearly independent types of solutions are separated; in every case the formula for energy levels has been found.
CHEMISTRY
Krivoguz Yu. M., Pesetskii S. S., Agabekov V. E.
Specific features of polyethylene functionalization in melt. pp. 7277
Email: otdel5mpri@tut.by
Summary: Details of grafting transethylene dicarboxylic acid (TEDA) onto metallocene linear lowdensity polyethylene (LLDPE) and lowdensity polyethylene (LDPE) in the course of reactive extrusion have been investigated. It was found that the graft effectiveness (a) of TEDA rises with an increase in the peroxide initiator content irrespective of the polyethylene (PE) type. The avalues for LDPE were found to exceed those for LLDPE. The rheological properties of LLDPE, compared to LDPE, undergo more appreciable changes owing mostly to side reactions of macromolecular crosslinking that occur during grafting. It was established that in the grafted product, some portion of carboxylic groups got transformed into anhydride ones. It was found that TEDA grafting caused a decrease in the concentration of end double bonds along with a growth in intramolecular unsaturation in the two PE types.
Halavach T. N., Cherviakovsky E. M., Kurchenko V. P.
Proteolysis and antigenic properties of native and heated Plactoglobulin. pp. 7883
Email: kurchenko@tut.by
Summary: The influence of Plactoglobulin (blg) and whey protein concentrate (WPC) heat treatment on the degree of their alkalase proteolysis and antigenic properties was investigated. By the method of fluorescent spectroscopy the temperature factor impact on the conformational stability of blg was established. According to the SDSPAGE analysis and HPLC, the increasing of blg alkalaze proteolysis as a result of preliminary heat treatment at 60100 ^{0}C was established, whereas in composition of WPC  at 70100 ^{0}C. By the doubleimmunodiffusion method and ELISA immunoreactivity the conservation for heated (blg and WPC was shown. However the heat treatment of protein substrates at (³ 80 ^{0}C caused a high degree of (blg, (alactalbumin, bovine serum albumin proteolysis and the decrease of the antigenic properties by 6575 % for enzymatic hydrolysates.
Anishchenko I. V., Andrianov A. M.
Conformational analysis of the HIV1 variable V3 loops: modeling of 3D structures and determination of the patterns in their spatial organization. pp. 8491
Email: anishchenko.ivan@gmail.com; andrianov@iboch.basnet.by
Summary: Static and dynamic models for the 3D structures of the variable V3 loops of the HIV1 subtypes В, С, and D were generated by computer modeling tools as well as the comparative analysis aimed at specifying the regularities in their spatial organization, the knowledge of which is of great importance to implement successfully the V3based antiHIVl drug design projects, was carried out. As a result, the HIVl V3 segments 37,1520, and 2832 were shown to form the structurally rigid sites recognizable by the receptors of sensitive cells. The patterns in the spatial organization of the HIV1 V3 loop, whereby the biologically crucial residues of the identified conservative stretches reside in (bturns of the V3 polypeptide chain were found. It is suggested that these elements of the secondary structure may be used by the virus to come in the specific and efficacious interactions with the receptors of macrophages and Tlymphocytes making for its strong fixation on the cell membrane surface.
BIOLOGY
Guzenko E. V., Lemesh V. A., Sidorenko E. V., Khotyleva L. V.
Identification of simple hybrids and determination of uniformity of maize inbred lines based on microsatellite DNA polymorphysm. pp. 9296
Email: E.Guzenko@igc.basnet.by
Summary: The article presents the results of SSRanalysis of moleculargenetic polymorphism in parental lines and their corresponding maize simple hybrids. The character of inheriting amplicons obtained by SSRPCR was studied. The detected codominant microsatellite markers located on different chromosomes allowed the identification and differentiation of inbred lines and hybrids. Homogeneity of the material was also investigated by microsatellite markers and the relationship was established by comparing microsatellite profiles of maternal and paternal forms and corresponding hybrids. The results obtained point to a high resolving power of the SSRtechnique and the scope of its application for estimating true percent of hybridity in purchased seed batches of maize. A similar analysis for electrophoretic protein (zein) spectra cannot be assurance of obtaining true data as the genes encoding zeins are only a slight part of genome.
Blotskaya Zh. V., Vabishchevich V. V., Domash V. I., Azizbekian S. G., Zavadskaya M. I., Khripach V. A.
Inhibition of cucumber green mottle mosaics virus by the treatment of seeds with plant growth regulators. pp. 97100
Email: deprik@yandex.ru
Summary: The inhibition of cucumber green mottle mosaics virus (CGMMV) by the treatment of seeds with plant growth regulators was examined. It is shown that soaking the cucumber seeds in the 1 % solution of Tubelak during 8 h or in the 0.05 % solution of Epin during 2 h leads to the suppression of the virus development and limits disease symptoms.
Palash A. L.
Diel change adundance of zooplankton at different densities of scirpus limnatis (Schoenoplectus lacustris). pp. 101104
Email: apalash@mail.ru
Summary: The diel horizontal migration of zooplankton in macrophyte bad and open water in the littoral zone of eutrophic lake has been studied. Cladoceras are divided into two groups: planktobenthic and planktonic species. The daytime abundance of Cladocera (planktobenthic and planktonic) was greater in the open littoral, while during the night time the abundance was the highest in the center of the macrophyte beds. The coefficient variation in the center of the macrophyte beds and open water was greater than the edge of the beds, which was associated with the horizontal migration of zooplankton.
MEDICINE
Manak N. A., Prystrom A. M., Gaishun E. I.
Relation between the parameters of arterial vessel elasticity and vessel wall stiffness. pp. 105108
Email: gaishunl@tut.by
Summary: A new series of arterial vessel elasticity parameters, which consider the vessel wall stiffness and the nonlinear relation of distensibility coefficient to pressure, is offered. A procedure of choosing parameters is mentioned, which is based on the analysis of diametertopressure curves, namely, the parameters for the following three groups of arterial vessels are built: high elasticity vessels, medium hardness vessels and vessels with significant signs of atherosclerosis.
Mankouskaya S. V., Demidchik Yu. E.
Moleculargenetic diagnostics of thyroid papillary carcinoma at the preoperative stage. pp. 109113
Email: info@belmapo.by
Summary: Preoperative cytological and molecular investigations in primary verification of thyroid papillary carcinoma were carried out. The sensitivity and specificity of the cytological analysis were equal to 69.5 and 78.6 %, respectively. The sensitivity of the molecular test was varied from 18.6 to 94.9 % at the specificity of 92.9100 %. When combined the both methods of diagnostics allowed revealing papillary carcinoma in 100 % of the investigated cases. On the basis of the obtained results the advanced diagnostic algorithm of revealing the giventype thyroid cancer was offered.
EARTH SCIENCES
Aizberg R. Ye., Beskopylny V. N., Gribik Ja. G.
Synrift structure of the Pripyat trough. pp. 114118
Email: chistaya@nature.basnet.by
Summary: A hierarchic system of the synrift structural division of the Pripyat Trough was elaborated. This system was used to distinguish new tectonic features in the surface structure of the basement and oilpromising complexes of the platform cover. The system suggested may serve as the basis for assessment of the structural position of hydrocarbon occurrences, as well as of the regional subdivision into oilgeological areas.
TECHNICAL SCIENCES
Leshchinskaja I. K., Shutova A. L., Prokopchuk N. R.
Combined acid hardening catalyst for epoxycontaining melaminealkyd enamel body paint. pp. 119124
Email: ikaurenius@mail.ru
Summary: In preparing epoxycontaining melaminealkyd enamel body paint a composition of a combined acid catalyst, which allows obtaining at a lowered drying temperature a coating with high hardness and shock durability, excellent adhesion and elasticity, is developed. The «lifetime» of the paint with a combined acid catalyst is 12 hours.
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