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Doklady of the National Academy of Sciences of Belarus, 2009, Vol.53, No.5

Homepage / Publications / Scientific Journals

Doklady of the National Academy of Sciences of Belarus, 2009, Vol.53, No.5

(Doklady Natsionalnoi Akademii Nauk Belarusi)

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

Volume 53, Number 5; September-October, 2009

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Kasabutsky A. F.
Regular linear differential systems, whose irregularity sets are intervals. pp. 5--9
E-mail: Kasabutski(at)

Summary: A set of irregularity (regularity, respectively) of the linear differential system х- = A(t)x which is proper according to Lyapunov, is called the set of all those values of the real parameter µ, at which the system х- = µ A(t)x is irregular (regular, respectively). Examples of regular systems, whose irregularity set is the interval or open ray, as well as examples of proper systems, whose irregularity set is the section or closed ray, are made.

Rasolko G. A., Alsevich L. A.
Decomposition of the singular integral with logarithmic singularity and Cauchy's kernel of Chebyshev's polynomials. pp. 10--14
E-mail: rasolka(at)


Yanovich L. A., Ignatenko M. V.
Interpolation operator Hermite-Birkhoff polynomials in the space of smooth functions. pp. 15--21
E-mail: yanovich(at); ignatenkomv(at)

Summary: A new class of algebraic interpolation Hermite--Birkhoff arbitrary fixed degree polynomials for scalar functions is constructed. Based on this the interpolation operator Hermite-Birkhoff difference structure formulas and some their generalizations in the space of smooth functions are obtained. The type of operator polynomials, for which these formulas are invariant, is indicated.

Volkov V. M., Tsiunchyk H. S.
Split-step method with the use of infinite impulse response filters for solving nonlinear Schrodinger equations. pp. 22--25
E-mail: v.volkov(at)

Summary: For numerical solving of nonlinear Schrodinger equations, a modified fourth- order split-step method with extra group delay compensated IIR filters is proposed and investigated. Advantages of the proposed scheme over the split-step Fourier method are shown.

Minchenko L. I., Stakhovski S. M.
Constraint qualifications in mathematical programming problems. pp. 26--31
E-mail: kanc(at)

Summary: Constraint qualification of constant rank is studied and generalized. It is proved that the generalized constant rank constraint qualification implies the metric regularity condition.

Kalugina M. A., Bernik V. I.
Lower bounds for a number of rational points near plane curves. pp. 32--35
E-mail: marina_kalugina(at); bernik(at)

Summary: In this article a lower bound for a number of rational points in a narrow strip near a plane curve is obtained. This curve can be defined by some continuously differentiable function.

Korzyuk V. I., Erofeenko V. T., Pulko Ju. V.
Classical solution of the initially boundary-value problem for the wave equation with the integral boundary condition with respect to time. pp. 36--41
E-mail: korzyuk(at); erofeenko(at); pulko(at)

Summary: The unique existence of the solution of the initially boundary-value problem for the wave equation with a special integral boundary condition is proved in the article. A classical solution of the problem is also obtained in analytical form. Such problems appear in modeling electromagnetic fields with the arbitrary time dependence when the interaction between the field and solids is modeled by impedance boundary conditions.



Mazhul V. M. †, Sukhodola A. A.
Spectral-kinetic characteristics of eye lens tissue phosphorescence in norm and at cataract. pp. 42--45
E-mail: sukhodola(at)

Summary: Room temperature phosphorescence (RTP) in the microsecond range for cortex and core of human eye lens in the normal state and at cataract under excitation of the ultraviolet nanosecond laser pulse is investigated. Based on RTP transient spectra measuring for time delays of 250 and 1350 µs it is shown that the phosphorescence spectrum of eye lens in the normal state coincides with that of tryptophan. The long-wave component associated with the phosphorescence of tryptophan oxidation products and lipid peroxidation appears during the cataract evolution. Spectral and kinetic characteristics of RTP of tryptophan and tryptophan oxidation products and lipid peroxidation are determined.

Borisevich N. A., Povedailo V. A., Tselesh E. E., Yakovlev D. L.
Structure of carbazole complexes with indole derivatives cooled in the supersonic jet. pp. 46--51
E-mail: poved(at)

Summary: Fluorescence excitation spectra of jet-cooled complexes of carbazole with one molecule of indole derivatives (indole, 1-methylindole, 3-methylindole) are studied. The consideration of the forms of the rotational contours of bands of pure electronic and electronic-vibrational transitions in complexes yields that they belong to different spatial isomers. A complex of carbazole with 3-methylindole makes only a single form of isomer, whereas with 1-methylindole -- three isomers. For the carbazole-indole complex the distribution of the band intensities in the fluorescence excitation spectra as well as the spectral shift in the complex relative to the bare carbazole specifies the presence of several spatial structures, which is proved by quantum-chemical calculations.

Bogush A. A.†, Krylov G. G., Ovsiyuk E. M., Red'kov V. M.
Maxwell electrodynamics in complex form, solutions with the cylindrical symmetry in the Riemann space S3. pp. 52--58
E-mail: redkov(at); krylov(at)

Summary: The complex formalism of Riemarm--Silberstein--Majorana--Oppenheimer in Maxwell electrodynamics is extended to the case of the arbitrary pseudo-Riemann space - time in accordance with the tetrad recipe of Tetrode--Weyl--Fock--Ivanenko. In this approach, the Maxwell equations are solved exactly on the background of the static cosmological Einstein model parameterized by special cylindrical coordinates and realized as a Riemann space of constant positive curvature S3. A discrete frequency spectrum w for electromagnetic modes depending on the curvature radius of space and three parameters is found. In the case of the elliptical model some part of the constructed solutions should be rejected by continuity considerations.



Matrunchik Ju. V., Vorobiova E. V., Krutko N. P., Basalyha I. I.
Swelling of the hydroheat-sink polymeric complex based on polyacrylic acid in solutions of salts. pp. 59--62
E-mail: secretar(at)

Summary: The swelling of a hydroheat-sink polymeric complex (HPC) based on polyacrylic acid in solutions of low-molecular salts (K+, Cu2+, Zn2+, Fe2+, Fe3+) is investigated. It has been stated that the degree and speed of HPC swelling decrease with increasing the salt concentration and also with growing the cation charge. It has been shown that the dispersion of a pre-swollen hydroheat-sink polymeric material promotes the uniform absorption of the salt solution and prevents the liquid phase isolation from HPC.

Pashkovsky F. S., Shchukina E. M., Lakhvich F. A., Kuzmitsky B. B., Golubeva M. B., Lyubin G. S.
Synthesis and immunobiological properties of 7-aza-9-oxa-10-methyl-l l-oxoprost-8(12)-ene acid methyl ester. pp. 63--66
E-mail: prostan(at)

Summary: 7-Aza-9-oxa-10-methyl-ll-oxoprost-8(12)-ene acid methyl ester has been synthesized in four steps on the basis of the 5-methyltetronic acid. The investigation of its biological activity has revealed that the compound possesses a high immune-response modulating potential of activating action and is practically nontoxic. It can be referred to a potential chemical-pharmaceutical product perspective for medicine and pharmacy.

Sivets G. G.
Synthesis derivatives of L-ribofuranose and 2-deoxy-L-ribofuranose from L-arabinose. pp. 67--72
E-mail: sivets(at)

Summary: Synthesis of methyl 2-O-acetyl-3,5-di-O-pivaloyl-a-L-ribofuranoside and 1,2-di-O-acetyl-3,5-di-O-pivaloyl-a, b-L-ribofuranoside has been performed starting from L-arabinose. An effective approach to methyl-2-deoxy-L-ribofuranoside was investigated via 2-O-mesyl derivatives of methyl-a-L-arabinofuranoside.



Titok V. V., Leontiev V. N., Nikitinskaya T. V., Lugin V. G., Khotyleva L. V.
Analysis of the fiber quality in common flax (Linum usistatissimum L.) subspecies. pp. 73--79
E-mail: V.Titok(at)

Summary: The application of scanning electron microscopy, thermogravimetric and IR spectrometric methods, allowing the detection of fine differences in the structure and chemical composition of cell walls, has been shown to be promising for estimating the fiber quality in common flax subspecies. The analysis of electron microscopic images has revealed significant differences in the diameter of elementary fiber, the quantity of incrusting components and ultrastructural characteristics of elementary fibers in flax subspecies. The study of the IR spectra of flax subspecies has revealed the bands of stretching vibrations typical for bast fiber and also the variation in the content of major components of cell walls. The thermogravimetric analysis has found the variability between flax subspecies that consists in destruction temperature shifts, the form and the height of the primary and secondary peaks, thus pointing to fine differences in the fiber composition.

Rizevsky S. V., Akimova L. N., Kurchenko V. P.
Taxonomic status determination of cercaria of the Trichobil-harzia ocellata species group and the revealing of genetic polymorphism between individuals of populations of different reservoirs. pp. 80--84
E-mail: rizevsky(at)

Summary: The whole ITS-region, ITS-1 and ITS-2 of 2 individual cercaria of the Trichobilharzia ocellata species group from the intermediate host L. stagnalis were amplified in PCR. The comparative analysis of the PCR product length was carried out. Nucleotide sequences of ITS-2 were obtained from the individuals of two reservoirs and were compared with the European ones. Due to these data the investigated cercaria from L. stagnalis belong to one species -- Trichobilharzia szidati. ITS-2 sequences of T. szidati from two reservoirs of Belarus differ in 1 nucleotide in position 313. The genetic polymorphism between the individuals from populations of two reservoirs revealed with RAPD-PCR was studied.



Novikova L. N.
Ultrastructural bases of innervation of the rabbit cerebral lateral ventricles choroid plexus. pp. 85--89
E-mail: mail_me07(at)

Summary: Electron microscopic studies of the lateral ventricles choroid plexus in the rabbit brain have revealed a well developed innervation system in them. The innervation system of the choroid plexus is composed of myelinated and nonmyelinated nerve fibers and free nerve terminals. This review describes the innervation of capillaries. The choroid capillaries have been shown to be innervated by afferent and efferent nerve terminals. Nerve fibers can be adjacent to the basal membrane of the endothelium as well as can end on the other structural components of capillary walls.



Aksamentova N. V., Trusov A. I., Zhmodik S. M., Agafonov L. V.
First find of the platinum mineral in the crystalline basement of Belarus. pp. 90--94
E-mail: aksam(at)

Summary: The platinum mineral -- platinum diarsenide (sperrylite) was discovered in the olivine-hornblende pyroxenites of the Early--Proterozoic Argelovschina complex in Belarus as an inclusion in nickel cobaltite. The presence of the proper mineral phase of platinum in rocks and the increased Pt and Pd content, as well as the intercumulus shape of metallic mineral segregations point to the possibility of formation of higher concentrations of the PMG in some parts of the intrusive massif favourable for their localization.

Selivanova E. V.
Petrography of gabbroids of the ore-bearing massif of Novoselki (Belarus). pp. 95--99
E-mail: helen_selivanova(at)

Summary: The article considers the petrography of gabbroids of the massif of Novoselki. By the ratio of the main rock-forming minerals a number of rocks from unaltered gabbro to metagabbroids are found.



Sorokin V. V.
Modeling of the process of keeping a thick rotating particle layer in the vortex chamber. pp. 100--103
E-mail: vnvv(at)

Summary: A two-phase dynamical system of a rotating layer of solid particles infiltrated with fluid is considered. The layer is kept inside a short hyperbolic vortex chamber. The chamber walls support a thick rotating layer. The particle motion on the permanent cycle orbit is maintained by the resultant of forces of flow drag and the support reaction (of walls and other particles). The moment balance between wall friction and momentum transferred from fluid to particles sets up a layer rotation velocity. The quasi-fluid state of the layer is due to particle oscillations. The particles, which are pressed and follow the relief of the guiding apparatus placed at the side wall of the vortex chamber, are the source of oscillations.

Pleskachevsky Yu. M., Selkin V. P.
Radiation-induced destruction of polytetrafluoroethylene at violated electron equilibrium in the macroheterogeneous polymer-metal system. pp. 104--107
E-mail: pleskym(at), selkin_v(at)

Summary: The peculiarities of radiation-induced destruction of polytetrafluoroethylene have been studied in the macroheterogeneous polytetrafluoroethylene -- metal system. It has been established experimentally that the destruction of polytetrafluoroethylene under the effect of g-radiation on the interface at a few tens micrometers distances surpasses the values corresponding to more distant from metal substrate (copper, lead) layers. This effect is attributed to a higher concentration of secondary electrons near the metal surface in the polymer material. These secondary electrons are formed as a result of the gamma-quanta influence and the corresponding large amount of absorbed in this region of the polymer radiation energy.

Vinidiktova N. S., Pinchuk L. S., Goldade V. A., Novikov V. P.
Use of polymer crazing for creation of antimicrobial polyester fibers. pp. 108--112
E-mail: mpri(at)

Summary: Experimental data are presented on the crazing of polyethylene terephthalate fibers in antimicrobial surfactant liquids Althosan, katamine, triclozan and colloidal solution of silver. The zones of the fibers subjected to extension have been determined in which adsorption of technological fluids proceeds more intensively. On this basis, new methods of producing antimicrobial chemical fibers are proposed. Information is given on the adoption of the methods developed in the industry of chemical fibers.



Sheiko I. P., Tanana L. A.,Yepishka T. I., Mostovoi D. I., Piashko V. V.
Relationship between the polymorphism of the kappa-casein gene and the dairy efficiency of cows of various breeds. pp. 113--118
E-mail: belniig(at)

Summary: Cows of the red Belarusian pedigree group and the Belarusian black-motley breed in the private agricultural unitary enterprise "Novu Dvor -- Agro" in the Svisloch area and also highly productive cows of the Belarusian black-motley breed in the agricultural production cooperative "Obuhovo" in the Grodno area have revealed the polymorphism of the gene of kappa-casein (CSN3). Genotypes CSN3AA, CSN3AB and CSN3BB are revealed. The dairy efficiency (milk yield, content of fat and fiber in milk, quantity of dairy fat and dairy fiber) of animals with various genotypes of kappa-casein is studied. The economic benefits when manufacturing cheese from milk of cows with various genotypes of kappa-casein are calculated.

Khodosovsky D. N.
Principles of technological adaptation of continuously functioning pig breeding enterprises. pp. 119--122
E-mail: belniig(at)

Summary: The basic principles of technological adaptation of continuously functioning pig breeding enterprises are: increasing the heat-proof effectiveness of fences, sealing the sections for animal management, supplying outside air into tambours or galleries for its partial heating by biological warmth, increasing the air capacity and the floor area per 1 animal. These measures will let us increase the safety of suckling piglets by 8.9--16.3%, and the safety of piglets at growing by 3.8--20.5%.

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