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Doklady of the National Academy of Sciences of Belarus, 2009, Vol.53, No.3

Homepage / Publications / Scientific Journals

Doklady of the National Academy of Sciences of Belarus, 2009, Vol.53, No.3

(Doklady Natsionalnoi Akademii Nauk Belarusi)

Published by The Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus

Volume 53, Number 3; May-June, 2009

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Matus P. P., Kolodynska A.
Stability of difference schemes for equations of polytropic gas in Euler variables. pp. 5--9
E-mail: matus(at); akolodynska(at)

Summary: A priori estimates of the stability with respect to the initial data of linearized difference schemes approximating the equations of polytropic gas in Euler variables are obtained. The results of computational experiments confirming the theoretical conclusions are given.

Kilbas A. A., Skoromnik O. V.
Solution of first-kind integral equations with the Gauss hypergeometric function in the kernels in the weight space of summable functions. pp. 10--15
E-mail: anatolyKilbas(at)

Summary: Two integral first-kind equations on the positive half-axis involving the Gauss hypergeometric function in the kernels are studied. Using the representations of the integral operators in the left-hand sides of the considered equations as compositions of fractional integral operators with power weights, the conditions for their boundedness from one weight spaces of summable functions into another are proved. These results are applied to derive explicit solutions of the studied integral equations in the considered spaces.

Orlovich Yu. L., Gordon V. S., Werner F., Dolgui A. B., Finke G.
Complexity of dissociation set problems in some hereditary classes of graphs. pp. 16--20
E-mail: orlovich(at); gordon(at)

Summary: A subset of vertices in a graph is called a dissociation set if it induces a subgraph with vertex degree at most 1. A dissociation set is maximal if no other dissociation set contains this set. We show that the problem of finding a maximal dissociation set of minimum size in a given graph is NP-hard in the general case, and some polynomially solvable cases for this problem are derived. Moreover, we show that the maximum dissociation set problem is NP-hard for planar line graphs of planar bipartite graphs.

Usnich A. V.
Discrete dynamical system on the pair of matrices. pp. 21--24
E-mail: ausnich(at)

Summary: We introduce a discrete dynamical system on the pair of matrices given by some rational transformations. We prove that this dynamical system is birationally equivalent to the fiber bundle of an algebraic torus and the action on the fiber is given by a multiplication in the torus.

Guo W., Lucenko Ju. V., Skiba A. N.
Structure of finite non-nilpotent groups in which every two 3-maximal subgroups are permutable. pp. 25--28
E-mail: lucenko_av(at); skiba(at)

Summary: The cerficle is devoted to the description of the structure of finite non-nilpotent groups in which every two 3-maximal subgroups are permutable. In particular, finite non-nilpotent groups with all normal 2-maximal subgroups or with all normal 3-maximal subgroups are described.



Chernyavsky A. F., Kolyada A. A.
Method and algorithm of scaling in a minimally redundant modular number system. pp. 29--37
E-mail: razan(at)

Summary: The problem of synthesis is studied in the context of minimally redundant modular coding of scaling procedures that are oriented to the scales of a special kind. The basis of the offered approach is made by the technology of parameterization of error of the integer approximation of fractions. On the basis of the created technology a new algorithm of scaling, providing a (2.5-3)-multiple decrease of the number of working tables is developed.

Boriskevich A. A., Tsviatkou V. Yu.
Method of scalable embedded image coding based on the hierarchical wavelet structure clustering. pp. 38--48
E-mail: anbor(at); vtsvet(at)

Summary: A new method of fast scalable embedded wavelet structure coding based on an adaptive hierarchical clustering for progressive image compression with and without loss and forming a hierarchical embedded code structure with scalability on spatial and frequency resolutions and quality is proposed. The adaptive hierarchical clustering is to select a clustering level quantity, a cluster size and detecting zero and nonzero cluster trees. The method allows us to decode progressively the versions of the image with various resolution and quality from the same code for adapting to limited communication channel throughput, monitor resolution, and hardware computational platform productivity of user terminal. The notations of scalability on spatial and frequency resolutions and quality are presented. Modeling results have shown that the method provides high compression speed, flexible embedded code scalability in resolution and quality, and compression ratio up to the known SPIHT, SPECK and JPEG 2000 algorithms.



Akimov A. I., Vasilevich A. E., Zaerko D. V., Zajkova S. A., Rychkov Ju. M., Sedenevsky Ju. S.
Features of distribution of electromagnetic waves of the microwave range in periodic structures. pp. 49--52
E-mail: rychkov(at)

Summary: In the work the experimental research of distribution and localization of electromagnetic waves of the microwave range in periodic structured dielectric environments is executed. The influence of geometrical and electrophysical parameters of periodic environments on the passage and reflection of electromagnetic waves is defined.

Tolkachev E. A.
Born--Infeld constitutive relations in schrodinger form: the symmetry approach. pp. 53--59
E-mail: tea(at)

Summary: A new most compact and consistent algebraic representation of the Born--Infeld constitutive relations is derived using the biquaternionic formalism. To this end, these equations are only the one non-trivial case according to the Lorentz and dual symmetries of the constitutive relations dependent on the unique "material" parameter. It is demonstrated that the Lagrangian form-invariance under the continuous dual transformations is not a necessary condition of the corresponding Euler--Lagrange equations of dual invariance.

Ulashchyk V. S., Zalesskaya G. A.
Spectral manifestations of photoprocesses initiated by the different wavelength light action on blood in vivo. pp. 60--63
E-mail: zalesskaya(at)

Summary: The intravenous blood irradiation using light sources is considered as a therapeutic method inducing the light oxidative stress without manifestation of toxicity at right dosage.



Lapotko D. O., Hleb E. Y.
Laser-induced heating of a medium around light-absorbing nanoparticles. pp. 64--67
E-mail: iclab(at)

Summary: Pulsed photothermal bulk heating of the suspension of gold nanoparticles (spheres, rods, and shells) was found to have two different patterns: quasi-homogenous heating at low laser fluence when no bubbles emerge and "no bulk heating" effect at higher fluence when the vapor bubbles are generated around gold nanoparticles. Time-resolved imaging and thermal lens methods yielded no detectible bulk heating outside the bubbles despite an increased release of thermal energy by the nanoparticles, which is different from the thermal behaviour of homogenous absorbing fluids.



Matrunchik Ju. V., Vorobiova E. V., Krutko N. P., Basalyga I. I.
Features of swelling of polymeric hydrogel based on polyacrylic acid in the presence of ethanol. pp. 68--72
E-mail: secretar(at)

Summary: It has been shown that the degree of swelling of hydrogel based on polyacrylic acid and polyvinyl alcohol in the binary water-ethanol mixture increases with increasing ethanol up to 60%. It has been stated that the viscosity and plasticity of the swollen hydrogel increases in the presence of ethanol in composition of an absorbed solution. The results of the present work have shown an opportunity of use of the materials obtained as a base of disinfectant, clearing and protective composition for hand skin treatment.

Gilep I. L., Usanov S. A.
Polymorphism of ACTN3 and ACE genes and human muscular performance. pp. 73--78
E-mail: agilep(at); usanov(at)

Summary: The capacity to physical performance of individuals is determined by a set of genetic factors. The study of a correlation of sport achievements with the structure and expression of certain genes is a perspective approach in sports practice. To understand such associations, the genetic markers hypothetically capable to cause direct or indirect impact on the work of cardiovascular and muscular system have been chosen: I/D polymorphism of gene ACE and R577X polymorphism of gene ACTN3. The data obtained in the present work indicate that the presence of II genotype of ACE gene will offer advantages in performance of the aerobic work the success of which depends on oxygen transport functions of cardiovascular system. The presence of DD genotype of ACE gene will assume the ability of heart muscle to perform intensive, short-term work, while the presence of RR genotype of ACTN3 gene gives a predisposition to the development of sprint and power qualities. The presence of XX genotype of ACTN3 gene limits the growth of sports results, especially in sprint and power kinds of sports. The obtained data confirm the presence of association between the development of certain physical qualities and various polymorphic variants of genes ACE and ACTN3 and can be used as criteria for a diagnostic complex for selection and correction of sports specialization of young athletes.

Anishchenko I. V., Andrianov A. M.
Comparative modeling for structure predictions of the HIV-1 V3 variable loops: application to the virus subtype A. pp. 79--86
E-mail: anishchenko.ivan(at); andrianov(at)

Summary: Using the methods of comparative modeling, the ensemble of the low-energy structures was generated for the consensus amino acid sequence of the HIV-1 subtype A V3 loop and its most probable conformation was defined based on the general criteria commonly used as a measure of the quality of protein structures in terms of their 3D folds and local geometry. To reveal common structural motifs in the HIV-1 V3 loops regardless of their sequence variability and medium inconstancy, the simulated structures and their individual stretches were collated with each other as well as with those of V3 deciphered previously by NMR spectroscopy and X-ray studies for diverse virus isolates in different environments. As a result, three V3 segments containing the highly conserved and biologically meaningful residues of gpl20 were shown to retain their 3D main chain shapes in all of the cases of interest presenting the forward-looking targets for AIDS drug researches.

Trostyanko I. V., Dolgopalets V. I., Kisel M. A., Lakhvich F. A.
New approach to 5-avinolevulinic acid lipophilic esters synthesis. pp. 87--89
E-mail: trostyanko(at)

Summary: A new approach to the synthesis of 5-aminolevulinic lipophilic acid esters is proposed. It is the preparation of 5-nitro-levulinic acid esters starting from succinic anhydride and their following catalytic reduction by ammonium formate in the presence of zinc or Reney nickel.



Bazhanov D. P., Yatsevich K. K., Bazhanova A. A.
Identification of chlorinated s-triazines degrading bacterium Herbaspirillum huttiense B601 by analyzing the 16S rRNA gene sequence and Rep-PCR genotyping. pp. 90--94
E-mail: d.bazhanov(at)

Summary: A chlorinated s-triazine degrading bacterium B601 was identified as Herbaspirillum huttiense by analyzing the 16S rRNA gene sequence and Rep-PCR genotyping. While the definition of the genus was possible after the BLAST search, the attainment to the species required the genotyping by ERIC and BOX PCR followed the phylogenetic analysis involving 16S rRNA gene sequences of type and exactly identified reference strains.

Ryzeuski V. K., Pljuta M. V., Leshchenko A. V., Yermalayeva I. A., Novik I. V.
New fish species in the fauna of Belarus. pp. 95--97
E-mail: barbus(at)

Summary: Data on a finding of five earlier not described fish species in waterbodies/streams of Belarus are given.

Ostapenya A. P., Zhukova T. V.
Change of the ecological situation in Lake Bolshie Shvakshty and its cause. pp. 98--101
E-mail: ostap(at)

Summary: The consequences of the installation of herbivorous fish Ctenopharingodon idella in the lake with high parameters of water quality and high recreational potential are considered. As a result of 6 years regular installation of the herbivorous fish into the lake, it has become a hypertrophy waterbody. The transparency of water has decreased from 3 m up to 0.45 m. The chlorophyll contents has increased by the order and achieved 50 µg/l.The mechanism of changes in structural and functional organization of the ecosystem of Lake Bolshie Shvakshti is considered from the positions of the concept of alternative stable state functioning of the lake ecosystem in the submersed aquatic vegetation presence and under its suppression.



Novikova L. N., Archakova L. I.
Ultrastructure blood-brain barrier of the rabbit brain lateral ventricles choroid plexus for acute ischemia. pp. 102--106
E-mail: mail_me07(at)

Summary: The ultrastructure of structural components of the blood-brain barrier (BBB) in adult rabbit brain lateral ventricle choroids plexus for acute experimental ischemia is studied. The extensive analysis of the ultrastructure revealed that acute ischemia in adult rabbit, induced by 30 min and 3 hour of bilateral carotid occlusion, caused the morphological destruction in the BBB of lateral ventricle choroids plexus. The ultrastructural damage of the BBB in choroids plexus was more evidence for 3 hour acute ischemia. It is concluded that the revealed ultrastructural damage in more cases are reversible.



Sheiko I. P., Fedorenkova L. A., Sheiko R. I.
Peculiarities of adaptation of pigs of highly valuable meat genotypes for the conditions of industrial technology. pp. 107--111
E-mail: belniig(at)

Summary: The peculiarities of adaptation of pigs of highly valuable meat genotypes for the conditions of industrial technology are studied. It was determined that the most important factor for successful work with genetic material of the global level was the balanced nutrition and infrastructure development, which corresponds to the modern demands.



Nikitenko P. G., Platonova L. A.
Appraisal and analysis of competitiveness level of world countries. pp. 112--117

Summary: The analysis of the competitiveness level of the countries offered for 2002, 2003, 2005 years according to the new competitiveness theory of the authors is based on the systematic approach and synergetrics.

Zaborovskiy A M.
Methodology of structural and technological effects of the GDP energy intensity dynamics assessment. pp. 118--123

Summary: The methodology for quantitative assessment of structural (via changes in GDP structure) and technological (via changes in energy efficiency of technologies) effects of GDP energy intensity dynamics has been elaborated. The main idea is in the GDP energy intensity decomposition by structural and technological components. This makes possible to calculate the corresponding values of effects, assessing their contribution to the energy efficiency of the economy growth (decrease). The calculations made showed that fuel and energy resource saving in 2006 as compared with 1995 has been achieved by 8.6% due to the structural changes in the economy and by 85.5% due to the energy efficiency of technologies increase. The energy-saving policy structural component insufficiency has been revealed. To achieve the energy efficiency level of the developed countries the Republic of Belarus needs to ensure the macroeconomic programming of the GDP energy intensity decreasing in coordination with the strategy of structural economic reforms.

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Created with assistance of Dr. Ignatii I. Korsak
Copyright © 2009 The National Academy of Sciences of Belarus
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