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# Doklady of the National Academy of Sciences of Belarus, 2008, Vol.52, No.3

/ Publications / Scientific Journals

Doklady of the National Academy of Sciences of Belarus, 2008, Vol.52, No.3

## CONTENTS

### MATHEMATICS

Shlyk V. A.
Vertices of integer partition of polytopes. pp. 5--10
E-mail: 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. 11--14

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 Lax-Wendroff 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. 15--19
E-mail: 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 Rm and some related statements. A new simple proof for continuous vector fields at the boundaries of bounded domains in Rm 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. 20--26
E-mail: lavrinovich(at)bsu.by

Summary: For a linear constrained problem in the class of discrete control actions the problem of constructing optimal open-loop (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 elastic-plastic space weakened by a spherical cavity. pp. 27--32

Summary: Considering the method of solution of spatial boundary--value 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 Riemann--Hilbert problem is solved. For illustration of the applied methods considered the boundary-value problem on the intense-deformed 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. 33--40
E-mail: 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 interval-index characteristics.

### PHYSICS

Korshunov F. P., Alexeeva T. A., Zlotski S. V., Lazar A. P., Uglov V. V., Ulyanenkov A. P.
Non-destructive analysis of gradient residual stresses in polycrystalline coatings by the GIXRD method. pp. 41--47
E-mail: lazar_a(at)ifttp.bas-net.by

Summary: The investigation of gradient residual stresses in the TixCr1-xN 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 Auger-Electron Spectroscopy. The X-ray 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 X-ray incidence angles have been used to evaluate the residual stresses. The classical sin2Y 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.
High-resolution controlled integrally optical filter on waveguide microresonators. pp. 48--51

Summary: A controlled narrow-band 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. 52--56
E-mail: lmt(at)dragon.bas-net.by

Summary: It is shown that the effects of background acceleration defined by cosmological expansion arise naturally in the framework of Lagrange conformally-symmetric 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 Tully--Fisher law is obtained.

Ryzhkovskii V. M., Goncharov V. S., Mitsiuk V. I., Glazkov V. P., Somenkov V. A.
Magnetic state of diamagnetically diluted Mn1,2Zn0,8Sb alloy at T>300 K studied by neutron diffraction. pp. 57--59
E-mail: ryzhkov(at)iftttp.bas-net.by

Summary: The existence of the high-temperature cluster phase in the Mn1,2Zn0,8Sb 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 Mn2(Zn)Sb alloys with large Zn contents was confirmed.

### CHEMISTRY

Andrianov A. M.
Computer-aided design of the potential drugs for AIDS therapy based on the analysis of the specific interactions between immunophilins and the HIV-1 gpl20 V3 loop. pp. 60--65
E-mail: andrianov(at)iboch.bas-net.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 H1V-1 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 X-ray 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 biotin-thyroxine conjugate. pp. 66--71
E-mail: navakouski(at)iboch.bas-net.by

Summary: A conjugate containing the residues of vitamin H (biotin) and thyroid hormone thyroxine has been obtained by N-acylation of N-(3-aminopropyl)biotinamide with N-acetylthyroxine N-hydroxysuccinimide ester. The conjugate synthesized was able to interact biospecifically with biotin-binding 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. 72--76
E-mail: l.sidor(at)igc.bas-net.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., Goldenkova-Pavlova I. V., Khotyleva L. V.
Production of genetically modified plants of fiber flax (Linun usitatissimum L.) based on the bacterial endo-1,4-b-glucanase gene. pp. 77--81
E-mail: v.titok(at)igc.bas-net.by

Summary: A morphogenic potential of fiber flax cultivars of Belarusian breeding (Dashkovsky, K-65, L-41, 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 endo-1,4-b-glucanase 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. 82--86
E-mail: leontiev(at)bstu.unibel.by

Summary: In the article the results of research of microbial degradation of s-triazines 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 HPLC-MS and the mechanism of degradation of prometryne is offered.

### TECHNICAL SCIENCES

Sorokin V. V.
Regularities of the steam and water two-phase flow in a pebble bed. pp. 87--89
E-mail: vnvv(at)sorokin.belpak.minsk.by

Summary: The application area of the dependences for calculation of two-phase 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 three-phase contact lines of water-steam-solid on the surface of pebbles for the void fraction of more than 0.1--0.3.

Zhukova Yu. V., Baranova T. A., Isaev S. A., Zhdanov V. L.
Numerical simulation of unsteady cross-flow past a circular cylinder at different Reynolds numbers. pp. 90--95
E-mail: svaturb(at)hmti.ac.by, baranova(at)hmti.ac.by

Summary: The article presents the results of numerical simulation of cross-flow 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 Spalart-Allmares' 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. 96--102
E-mail: aksam(at)igig.org.by, tolk(at)igig.org.by

Summary: High Cr, Ni, Co, Pd concentrations and oxide-facies 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 palladium-sulfide-nickel metallogeny.

### AGRARIAN SCIENCES

Koronec I. N., Tanana L. A., Taranenko Z. I.
Influence of different-selection bulls on the basic economic-useful signs of daughters. pp. 103--107
E-mail: zoyatar81(at)mail.ru

Summary: Researches are devoted to the study and the all-round analysis of economic-useful 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 4.8-24.4%, is fat -- and protein contain by 4.7--23.8 and 5.1-23.3% (P < 0.05--0.001), 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 black-motley cattle of Belarus.

Sheiko I. P., Khochenkov A. A., Khodosovsky D. N., Sheiko R. I.
Quality of high-protein animal-origin feed components for test control growing of pigs. pp. 108--112
E-mail: belniig(at)tut.by

Summary: The complex investigations of high-protein animal-origin 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. 113--117
E-mail: 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, low-type peat, brown coal and special ameliorant has resulted in a significant (25--40%) decrease of soil losses due to deflation in comparison with the control variant without fertilization.

### SOCIAL SCIENCES AND HUMANITIES

Gorovets T. V., Dovnar-Zapolsky 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. 118--124
E-mail: raikov(at)imaph.bas-net.by

Summary: Complex technological, historical and art examination of the easel painting presumably of famous artist Zigmunt Sidorovich (1846--1881) has been carried out. The non-authenticity 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 solid-state sample in a mode of practically nondestructive control with minimal sampling has been modified. The methodical maintenance of such examination has been fulfilled.