Doklady of the National Academy of Sciences of Belarus, 2008, Vol.52, No.3
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Doklady of the National Academy of Sciences of Belarus, 2008, Vol.52, 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
Shlyk V. A.
Vertices of integer partition of polytopes. pp. 510
Email: v.shlyk(at)gmail.com
Summary: The vertices of integer partition of polytopes recently introduced by the author are studied. The main result is a criterion of representability of a given partition as a convex combination of two others. The criterion implies an exact bound (log(n+ 1)) for the number of different parts of partitions that are vertices, as well as a necessary condition for a partition to be a vertex. The vertices of the partition of polytopes correspond to the number multisets similar to Sidon sets. The results analogous to those for the vertices are shown to be true for these multisets. A lifting type method to construct the sets of vertices is proposed.
Matus P. P., Kolodynska A.
One class of difference schemes for a system of the equations of acoustics. pp. 1114
Summary: In the present work two classes of explicit difference schemes for the Cauchy problem for a system of the equations of acoustics are constructed and investigated. The first class is based on using the LaxWendroff approximation and the second one applies ordinary central difference derivatives with respect to space and time. It turns out that if the Courant number is equal to unity, then these schemes are exact even in solving numerically the problems with discontinuous solutions.
Zabreiko P. P.
On M. A. Krasnosel'skii theorem. pp. 1519
Email: zabreiko(at)mail.ru
Summary: The article deals with Krasnosel'skii theorem on addition of winding numbers of continuous vector fields on a single sphere in spaces R^{m} and some related statements. A new simple proof for continuous vector fields at the boundaries of bounded domains in R^{m} is presented; it is shown that this result is not trivial in the cases m = 1, 2, 4, 8 and only in these cases. The general theorem on addition of winding numbers for products of continuous vector fields in these cases is presented.
Gabasov R., Kirillova F. M., Lavrinovich L. I.
Optimal control of a dynamical object through time difference measurements of state variables. pp. 2026
Email: lavrinovich(at)bsu.by
Summary: For a linear constrained problem in the class of discrete control actions the problem of constructing optimal openloop (optimal programs) and positional solutions is under consideration. It is supposed that the components of current values of the control system are measured with different frequency. A method of constructing optimal programs generalizing the previous results obtained by the authors is justified. The fast correction procedure for optimal programs for implementing optimal feedbacks is elaborated.
Nifagin V. A.
Estimation of the intense condition of a hardening elasticplastic space weakened by a spherical cavity. pp. 2732
Email: vladnifagin(at)gmail.com
Summary: Considering the method of solution of spatial boundaryvalue problems for the plasticity law with nonlinear hardening, the general solutions to the basic problems are obtained on the basis of special representations of functions of several complex variables. The method of decomposition into power parameter is used for reduceig a problem to the sequence of connected linear problems. At each stage the RiemannHilbert problem is solved. For illustration of the applied methods considered the boundaryvalue problem on the intensedeformed condition of the space with a spherical cavity is solved. The approximate analytical solution is constructed. The influence of the plastic properties on the balance of material is investigated. Numerical results are presented and compared with the similar data available in literature.
INFORMATICS
Kolyada A. A., Chernyavsky A. F.
Methods of calculating the integrated characteristics of a modular code. pp. 3340
Email: niipfp(at)bsu.by, RAZAN(at)tut.by
Summary: Theoretical fundamentals of the general technology of calculation of integrated characteristics of a modular code at symmetric intervals are developed, the original methodology of optimization of not modular procedures is described. Its basis is the principle of minimally redundant modular coding and also intervalindex characteristics.
PHYSICS
Korshunov F. P., Alexeeva T. A., Zlotski S. V., Lazar A. P., Uglov V. V., Ulyanenkov A. P.
Nondestructive analysis of gradient residual stresses in polycrystalline coatings by the GIXRD method. pp. 4147
Email: lazar_a(at)ifttp.basnet.by
Summary: The investigation of gradient residual stresses in the Ti_{x}Cr_{1x}N polycrystalline coating of thickness 1.2 µm on steel substrate is reported. The coating has been prepared by using cathode arc vapour deposition. The distribution of Ti, Cr and N elements in the coating has been determined by AugerElectron Spectroscopy. The Xray measurements in GIXRD and XRD geometries have been carried out on a D8 Bruker AXS diffractometer on the CuKa characteristic line. Different (HKL) Bragg reflections at fixed Xray incidence angles have been used to evaluate the residual stresses. The classical sin^{2}Y method has been modified for GIXRD geometry to take into account the crystallographic deformations within thin surface layers with a gradient stress distribution.
Pilipovich V. A., Esman A. K., Goncharenko I. A., Kuleshov V. K., Zykov G. L.
Highresolution controlled integrally optical filter on waveguide microresonators. pp. 4851
Summary: A controlled narrowband integrated optical filter based on two optically coupled waveguide ring microresonators separated at 200 nm apart and from straight input and output optical waveguides is proposed and investigated. It is shown that by optimizing the design parameters and the structure of a selective element one can create a simple and economical integrated optical filter with a bandwidth of 0.1 nm and with a frequency separation of 0.2 nm between the neighboring optical carrier waves for the signal/noise ratio of 50 dB. Using such filters makes it possible to increase the quantity of concurrently transmitted optical carrier wavelengths up to 160 and more, thus providing the communication rate up to 1.6 Tbit/sec in one direction by one optical fiber.
Tomilchik L. M.
Minimal acceleration in the modified Newton dynamics as inertial force manifestation. pp. 5256
Email: lmt(at)dragon.basnet.by
Summary: It is shown that the effects of background acceleration defined by cosmological expansion arise naturally in the framework of Lagrange conformallysymmetric dynamics. The connection of the acceleration with the minimal acceleration of the modified Newton dynamics (MOND) is established and an explicit expression for the phenomenological TullyFisher law is obtained.
Ryzhkovskii V. M., Goncharov V. S., Mitsiuk V. I., Glazkov V. P., Somenkov V. A.
Magnetic state of diamagnetically diluted Mn_{1,2}Zn_{0,8}Sb alloy at T>300 K studied by neutron diffraction. pp. 5759
Email: ryzhkov(at)iftttp.basnet.by
Summary: The existence of the hightemperature cluster phase in the Mn_{1,2}Zn_{0,8}Sb alloy composed of ferrimagnetically ordered Mn I and Mn II atoms was shown by the neutron diffraction method. The conclusion on the "magnetic phase lamination" in the diamagnetically diluted Mn_{2}(Zn)Sb alloys with large Zn contents was confirmed.
CHEMISTRY
Andrianov A. M.
Computeraided design of the potential drugs for AIDS therapy based on the analysis of the specific interactions between immunophilins and the HIV1 gpl20 V3 loop. pp. 6065
Email: andrianov(at)iboch.basnet.by
Summary: The model for a structural complex between the FKBP protein belonging to the immunophilins family and the CRK peptide imitating the immunogenic crown of the H1V1 gpl20 V3 loop was built by the computer approach that combined the 3D protein structure modeling with the molecular docking methods. The analysis of specific interactions responsible for the complex stabilization was realized, and the FKBP stretch giving rise to the overwhelming majority of efficacious contacts with a CRK molecule was identified. The most probable 3D structure of this stretch in the free status was predicted, and its collation with the Xray structure of the identical peptide built into the protein chain of the immunophilin was implemented. Based on the obtained results, the amino acid sequence of the molecule, the synthetic copy of which may be utilized as a promising chemical compound in the studies on designing effective and safe drugs for AIDS therapy, was suggested.
Navakouski M. J., Matveyentsev V. D., Vashkevich I. I., Sviridov O. V.
Synthesis and biospecific properties of a biotinthyroxine conjugate. pp. 6671
Email: navakouski(at)iboch.basnet.by
Summary: A conjugate containing the residues of vitamin H (biotin) and thyroid hormone thyroxine has been obtained by Nacylation of N(3aminopropyl)biotinamide with Nacetylthyroxine Nhydroxysuccinimide ester. The conjugate synthesized was able to interact biospecifically with biotinbinding proteins avidin and streptavidin as well as with monoclonal and polyclonal antibodies to thyroxine. The properties of the biotinylated thyroxine as a bifunctional ligand allowed its use in the development of a test system for a lanthanide immunofluorometric assay for free thyroxine in human serum.
BIOLOGY
Sidor L. S., Orlov P. A., Kartel N. A.
Application of the cell and tissue culturing technology in vitro for producing transgenic plants of barley (Hordeum vulgare L.). pp. 7276
Email: l.sidor(at)igc.basnet.by
Summary: The article presents the results of studying the regenerative ability of 14 spring barley cultivars of the Belarusian breeding in the immature embryo culture. Two genotypes with a high regenerative ability were revealed, the possibility of their use in the programs on genetic transformation being shown.
Titok V. V., Kubrak S. V., Raldugina G. N., Abdeev R. M., Piruzian E. S., GoldenkovaPavlova I. V., Khotyleva L. V.
Production of genetically modified plants of fiber flax (Linun usitatissimum L.) based on the bacterial endo1,4bglucanase gene. pp. 7781
Email: v.titok(at)igc.basnet.by
Summary: A morphogenic potential of fiber flax cultivars of Belarusian breeding (Dashkovsky, K65, L41, Rodnik) was investigated under agrobacterial transformation conditions. Conditions of in vitro plant culturing and composition of nutrient media were chosen. A cultivar with the highest regenerative ability under the given culturing conditions was revealed. Genetically modified plants with the heterological gene of bacterial enzyme were produced on its basis. The produced transgenic plants will be used for studying the expression of endo1,4bglucanase in a plant cell and for finding out the role of the above enzyme during cellulose synthesis and in the mechanism of assembly of plant cell wall polysaccharides.
Ignatovets O. S., Leontiev V. N.
Mechanism of prometryne degradation due to bacteria genus Pseudomonas. pp. 8286
Email: leontiev(at)bstu.unibel.by
Summary: In the article the results of research of microbial degradation of striazines pesticide  prometryne are presented. A strain destructor of prometryne actively growing in a medium with herbicide as the only source of carbon is selected. Participation of a monooxygenase fermental system of bacteria in prometryne degradation is shown. Kinetic parameters of degradation was determined. The metabolites produced by the selected strain during degradation of prometryne are identified by the method HPLCMS and the mechanism of degradation of prometryne is offered.
TECHNICAL SCIENCES
Sorokin V. V.
Regularities of the steam and water twophase flow in a pebble bed. pp. 8789
Email: vnvv(at)sorokin.belpak.minsk.by
Summary: The application area of the dependences for calculation of twophase steam and water flows in a pebble bed is proved up to 15.6 MPa of the absolute pressure level. The pressure loss of the main flow characteristics as well as the correlation between the steam quality and the void fraction are considered. A uniform steam distribution over the pebble bed cross section is found to be stable and unstable. There is a set of threephase contact lines of watersteamsolid on the surface of pebbles for the void fraction of more than 0.10.3.
Zhukova Yu. V., Baranova T. A., Isaev S. A., Zhdanov V. L.
Numerical simulation of unsteady crossflow past a circular cylinder at different Reynolds numbers. pp. 9095
Email: svaturb(at)hmti.ac.by, baranova(at)hmti.ac.by
Summary: The article presents the results of numerical simulation of crossflow past a heated circular cylinder at Reynolds numbers Re =3000, 5900, 18900. The temperature difference between the free stream and the heated cylinder was 25 degrees. Calculation was performed using computer codes Fluent and VP2/3. Menter's and SpalartAllmares' models were adopted for modeling turbulence. Comparative analysis of the total drag, the Strouhal number and the Nusselt number was made. Results of numerical simulation were compared with the available experimental data.
EARTH SCIENCES
Aksamentova N. V., Tolkachikova A. A., Trusov A. I.
Metallogeny of ultramafic rocks of the crystalline basement of Belarus. pp. 96102
Email: aksam(at)igig.org.by, tolk(at)igig.org.by
Summary: High Cr, Ni, Co, Pd concentrations and oxidefacies ore and sulfide mineralizations located in the ultramafic rocks of the Argelovshchina complex, as well as its comparison with ore complexes from the other regions permit a conclusion about its possible palladiumsulfidenickel metallogeny.
AGRARIAN SCIENCES
Koronec I. N., Tanana L. A., Taranenko Z. I.
Influence of differentselection bulls on the basic economicuseful signs of daughters. pp. 103107
Email: zoyatar81(at)mail.ru
Summary: Researches are devoted to the study and the allround analysis of economicuseful qualities of the daughters of bulls of the Belarusian, Canadian, German, Danish and Dutch selection. As a result of the conducted researches it is established that at the both farms the daughters of the bulls of the Belarusian, Canadian, German, Danish and Dutch selection have no considerable distinctions in the indicators of the dairy efficiency between the studied groups in the cut of lactations. Cows of the Dutch selection surpassed those of the same age of the Belarusian, Canadian, German and Danish selection in a milk yield by 4.824.4%, is fat  and protein contain by 4.723.8 and 5.123.3% (P < 0.050.001), both on lactations I and II, which speaks about the possibility of a wide use of bulls of the Dutch selection for increasing the efficiency of blackmotley cattle of Belarus.
Sheiko I. P., Khochenkov A. A., Khodosovsky D. N., Sheiko R. I.
Quality of highprotein animalorigin feed components for test control growing of pigs. pp. 108112
Email: belniig(at)tut.by
Summary: The complex investigations of highprotein animalorigin feed components were carried out with the intent to include them in compound feeds for test control growing of pigs. In samples the feeding value and safety indices were studied. The fish meal had the most stable content of crude protein and irreplaceable amino acids and was useful to balance crude protein and lysine levels in compound feeds.
Chizhikov Yu. A., Sokolov G. A.
Use of caustobioliths and products on their basis for reducing the soil losses due to deflation. pp. 113117
Email: agrico(at)yandex.ru
Summary: The results of experiments on the increase of the wind erosion stability of friable sandy soil as a result of application of various kinds of natural organic materials and products on their basis are discussed. It is established that the application of cattle manure, lowtype peat, brown coal and special ameliorant has resulted in a significant (2540%) decrease of soil losses due to deflation in comparison with the control variant without fertilization.
SOCIAL SCIENCES AND HUMANITIES
Gorovets T. V., DovnarZapolsky E. M., Kiris V. V., Kliyachkouskaya A. V., Raikov S. N., Saiko A. P.
Complex laser testing of material, historical and art examination of the easel painting. pp. 118124
Email: raikov(at)imaph.basnet.by
Summary: Complex technological, historical and art examination of the easel painting presumably of famous artist Zigmunt Sidorovich (18461881) has been carried out. The nonauthenticity of the investigated landscape has been established. This painting was written after the death of Zigmunt Sidorovich. The laser spectrometer allowing the detailed investigation of the element composition of any unique solidstate sample in a mode of practically nondestructive control with minimal sampling has been modified. The methodical maintenance of such examination has been fulfilled.
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