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Doklady of the National Academy of Sciences of Belarus, 2010, Vol.54, No.3

Homepage / Publications / Scientific Journals

Doklady of the National Academy of Sciences of Belarus, 2010, Vol.54, No.3

(Doklady Natsionalnoi Akademii Nauk Belarusi)

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

Volume 54, Number 3; May-June, 2010

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Yanchevskii V. I.
Conjugation problem of groups of rational points for outer forms of anisotropic groups of type Аn. pp. 5--7

Summary: A solution of the conjugation problem of groups of rational points for outer forms of anisotropic groups of type An is given.

Barkova E. A., Zabreiko P. P.
Nonlocal theorems on the Cauchy problem for differential equations of fractional order. pp. 8--13

Summary: In this article we prove existence theorems of solutions to nonlocal Cauchy problems for differential equations of fractional order in Banach spaces with Caputo's derivatives. We have also obtained sufficient conditions for uniqueness of solutions of these equations.

Gulo I. N., Yanovich L. A.
Quadrature formulas for stochastic integrals of nonrandom periodic functions. pp. 14--19

Summary: Quadrature formulas of an utmost degree of trigonometric accuracy with determined nodes for stochastic integrals of nonrandom 2p-periodic functions are constructed. Error estimates for constructed quadrature formulas under different approximations of integrable function by trigonometric polynomials are obtained.

Mikulich Y. H.
Asymptotics of approximations of |x| using rational interpolation process. pp. 20--25
E-mail: у

Summary: The rational interpolation process for |x| on [-1, 1] and the behavior of their uniform approximations are investigated. Previously in 1989, in the papers by Rovba E. A. similar approximation formulas were already investigated. Later on, in the joint work by Rovba E. A. and Mikulich Y. H. the constants in the asymptotical formula were found in the case of approximation using interpolation functions of odd degree with a fixed number of poles. In the present article we have found exact constants in the approximation formulas in the case of arbitrary degree of interpolation functions and a fixed number of poles. In order to find exact constants in the asymptotical behavior of uniform approximations Laplace's method was used.

Balashchenko V. V., Samsonov A. S.
Canonical f--structures on naturally reductive Ф-spaces of order 6. pp. 26--31

Summary: In the article the canonical f-structures on arbitrary homogeneous Ф-spaces of order 6 (in other terminology, homogeneous 6-symmetric spaces) are considered in the case of naturally reductive metric. We indicate necessary and sufficient conditions under which these structures belong to the classes in the generalized Hermitian geometry such as nearly Kahler f-structures (NKf) and Hermitian f-structures (Hf). Types of invariant distributions generated by the canonical structures on homogeneous Ф-spaces of order 6 are also characterized.

Shlyk V. A.
Number of approximate partitions of natural numbers into a sum of algebraic numbers. pp. 32--35
E-mail: v.

Summary: We give a bound on the number of times a sum of algebraic numbers occurs in a given neighbourhood of a fixed natural number.



Buganov O. V., Tikhomirov S. A., Shulenkov A. S., Stankevich V. V., Ermolenko M. V., Gaponenko S. V.
Ultrafast all-optical modulator for 1.5 mm driven by a Ti:Al203 laser. pp. 36--40

Summary: The concept of an ultrafast light modulator for a wavelength of ~ 1.5 mm controlled by the fundamental harmonic of a Ti:Al203 laser has been demonstrated. The possibility of realization of this concept was experimentally confirmed. We have demonstrated a strong spectrally wide nonlinear response in multilayer heterostructures based on GaAs/(AlGa)xOy with the relaxation time of 1-3 ps in the spectral range where both materials have negligible absorption. These short times correspond to the e-h plasma relaxation time.

Zhestkov S. V., Novashinskaya V. S.
Existence of soliton solutions of the systems of Schrodinger's connected (2+l)--dimensional equations with Kerr's nonlinearity and any nonlinearity power laws. pp. 41--46

Summary: For the systems of any order of Schrodinger's connected (2+l)--dimensional equations with any power laws the method of constructing soliton-like solutions is developed. The necessary and sufficient conditions of existence of solitons are obtained

Ovsiyuk E. M., Kisel V. V., Red'kov V. M.
Solutions of the Dirac equation in the homogeneous magnetic field on the background of the Lobachevsky space. pp. 47--54

Summary: Exact solutions of the quantum-mechanical Dirac equation for a spin S = 1/2 particle in the Riemannian space of constant negative curvature, the hyperbolic Lobachevsky space, in the presence of an external magnetic field, being the analogue of the homogeneous magnetic field in the Minkowski space, are constructed. A generalized formula for energy levels describing the quantization of the particle motion in magnetic field on the background of the Lobachevsky space geometry has been obtained.

Hursky L. I., Grushevskaya H. V., Kalanda N. A.
Nonadiabatic paramagnetic model of a pseudogap state in high--temperature cuprate superconductors. pp. 55--62

Summary: Pseudogap anomalies for the state of cuprate high-Tc superconductors have been examined within the framework of a nonadiabatic paramagnetic model. A peculiarity of this model is the presence of dynamic supersymmetry. A Schrodinger equation was used to describe the movement of paired electrons. An equation was established which allows finding a gap energy of offered cuprate pair. It was shown that the nonadiabatic paramagnetic model of pseudogap conforms completely to the experimental data.



Eryomin A. N., Zhavnerko G. K., Yashin К. D., Osipovich V. S., Agabekov V. E.
Fluorescence of CdSe/ZnS nanoparticles and their complexes with bovine serum albumin in reverse micelles. pp. 63--70

Summary: Fluorescence of CdSe/ZnS nanoparticles (NP) in reverse micelles of aerosol ОТ (АОТ) is studied depending on the relation of H20/AOT concentration and the presence of bovine serum albumin (BSA). It is proved that the NP included in AOT reverse micelles in isooctane. In that case and also in the presence of BSA in micelles, besides fluorescence in the range of 548-556 nanometers, intensive emission of light with maxima at 331, 379, 435-437, 481-490 and 535-537 nm with a Stokes shift of 6-7 nm in relation to the wavelength of exciting light is observed. The character of the spectra remains after transfer of NP from AOT reverse micelles in isooctane to a water solution of sodium chloride, which confirms the fact of the formation of complexes between NP and BSA. It is assumed that the combination of the mechanisms of both light dispersion on the complexes of NP with AOT and BSA and resonant energy transfer from NP on AOT molecules and BSA with its subsequent illumination can be the reason for non-fluorescent emission of light.

Opanasenko O. N., Zhigalova O. L., Krut'ko N. P., Ostrovskaya E. F.
Regulation of colloid-chemical properties of mixes of cathionic surfactants in the presence of low-molecular spirits. pp. 71--76

Summary: The joint behaviour of mixes of cathionic surfactants on the basis of di- and polyamines with quarternary ammonium bases salts is investigated. It is established that in the presence of low-molecular spirits the mixes of cathionic surfactants have higher micellizating and solubilizating ability. The revealed laws in the behaviour of the mixes of cathionic surfactants in the presence of low-molecular spirits allow one to adjust their colloid--chemical properties and to increase the efficiency of emulsifying and dispersive actions of the mixes of cathionic surfactants at the oil/water interface.

Sinelyov V. A., Babenko A. S., Gilep I. L., Usanov S. A.
Polymorphism of BDKRB2, NOS3, AGT, ACE and AGTR1 genes and human physical performance. pp. 77--83

Summary: The present work is aimed at defining associations of +9/-9 polymorphism of BDKRB2 gene, a/b and G894T polymorphisms of NOS3 gene, M235T polymorphism of AGT gene, I/D polymorphism of ACE gene and A1166C polymorphism of AGTR1 gene with human physical performance. 139 qualified swimmers and 164 control subjects were genotyped. Athletes had higher frequencies of the following genotypes: -9/-9 (+9/-9 polymorphism of BDKRB2 gene), GG (G894T polymorphism of NOS3 gene) and AA (A1166C polymorphism of AGTR1 gene) compared to the control group. TT and aa genotypes of NOS3 genes, as well as CC genotype of AGTR1 gene were not identified in the group of swimmers. We demonstrate a difference in the genotype of athletes specialized in different disciplines of swimming. On the basis of the genotypes of swimmers and the control group we identified the optimal genotype for enhanced indexes of physical performance.

Khlebnikova T. S., Piven Yu. A., Lakhvich F. A.
4'-Fluoro-containing isoflavonoids: synthesis and spectroscopic investigations. pp. 84--87

Summary: A new approach to the synthesis of 4'-fluoro-containing isoflavonoids has been developed. The synthesis of 7-hydroxy--4'--fiuoroisofiavone and its chemical transformations are described. The structures of synthesized compounds are verified by spectroscopic data.



Galkovskaya G. A., Kalinovska K., Molotkov D. V., Trifonov O. V.
Influence of stratification on the vertical distribution of microzooplankton in oligotrophic lake. pp. 88--91

Summary: The vertical distribution of microzooplankton (Ciliata, Rotifera) was investigated in the oligotrophic stratified lake. On the border of meta- and hypolimnion the crowds of ciliates and rotifers were revealed. This means that on this border there take place small bacterial--detritus particles -- the basic feeding sources for microzooplankton. The quantity of ciliates falls abruptly with increasing the depth of hypolimnion. Rotifers keep a high quantity on the lower horizons of hypolimnion. This can be a result of competition of force out. The revealed processes promote the lake self-cleaning.

Galinousky D. V., Leontiev V. N., Nikitinskaya T. V., Raiski A. P., Khotyleva L. V., Titok V. V.
Identification of CesA-genes expressed in the stems of fiber flax plants (Linum usitatissimum L.). pp. 92--97

Summary: We have identified the cellulose synthase genes that are involved in the fiber formation in fiber flax stems. We have compared the HVRII fragments amplified on cDNA matrix that was synthesized on total RNA extracted from fiber flax stems, with the CesA--genes from Arabidopsis thaliana. We have found three cellulose synthase genes -- LusCesA4, LusCesA7 and LusCesA9. We have revealed the existence of the expression of cellulose synthase genes of the CesA4, CesA7 and CesA9 classes in fiber flax stems at the rapid growth phase.

Davidovskii A. I., Veresov V. G.
Structural determinants of the antitumor action of drug compound TW-37. pp. 98--100

Summary: The computational docking approach was employed to establish the structural determinants of inhibition of antiapoptotic proteins by anticancer agent TW-37. The results obtained suggest that the inhibition of antiapoptotic proteins of the Bcl-2 family by TW-37 is caused by binding this compound to the hydrophobic grooves of antiapoptotic proteins Bcl-2, Bcl-xL and Mcl-1, thus preventing their possible interaction with proapoptotic proteins. It is shown that unlike gossypol, the main contribution to high binding free energy is provided by hydrophobic interactions due to high complementarity of TW-37 to the hydrophobic groove caused by enhanced flexibility of this compound because of extra hinge bonds between phenol rings as compared to gossypol. Unexpectedly, it was found that the signature region NWGR of these proteins does not participate in binding, unlike the binding of gossypol and ABT737.



Konoplia E. F. †, Litvinchuk A. V., Zaiceva O. A., Stashkevich D. G.
Analysis of the apoptosis of brain and liver cells induced by ionizing radiation. pp. 101-104

Summary: The PCR--analysis of the expression of two oncogenes (bax/bcl-2) in the liver and brain tissues of the animals after being exposed to gamma-rays at doses of 1.0 and 4.0 Gy at remote terms after the action of (30, 60, 90 days) was made. The proofs of start-up of the genetic program of apoptosis of brain and liver cells were obtained. This can be a reason for functional dysfunction of a particular organ and the whole organism.

Bogdan V. G., Zafranskaya M. M., Gain Yu. M., Demidchik Yu. E.
Comparative description of composite biomatrices with a three-dimensional gelatinous matrix and adipose derived mesenchymal stem cells (adMSC). pp. 105-109

Summary: In the conditions of experiment in vitro, comparative study was for the first time made of the efficiency of co--culturing with adipose derived mesenchymal stem cells (adMSC) rats in a three--dimensional gelatinous matrix on different variants of the surgical meshes "Prolene", "Vypro", "Ultrapro", "Vicryl" and "Proceed". It is proved that the three-dimensional gelatinous matrix realistically raises the composition ability of biomatrises to provide adhesion and growth of adipose derived mesenchymal stem cells (adMSC). It is established that the gelatinous covering levels the importance of the composition of the surgical meshes for adhesion of adipose derived mesenchymal stem cells (adMSC) amongst samples containing nodestruction monothread: "Prolene", "Vypro" and "Ultrapro". Herewith, a realistically greater amount of the hutches on surgical mesh "Vicryl" without polypropylene is saved.



Tyutyuma V. D.
Mechanism of the separating effect in the Ranque vortex tube. pp. 110-114

Summary: The model for flow in the Ranque vortex tube based not on thermal interaction but on mechanical interaction between cold and hot streams is proposed. It is demonstrated that for the description of the Ranque-Hilsch effect it is necessary to take into account, in addition to radial flow, the mass sampling or addition and also to ensure a more smooth conjugation of forced and peripheral vortexes, requiring the continuity of not only a tangential velocity component but also that of its first derivative with respect to radius. By using the developed approach the flow in the vortex tube is considered as a system of interacting sinks and sources of vortexes.



Vitsiaz S. P.
Ancient Prussians: areas of settlement (to a problem of the Jatvings origin). pp. 115-124

Summary: In the article the ancient Prussians settlement is estimated on the basis of a correlation of the positions of the Polish and Russian scientific schools. The facts of local dynamics of the Western Baits settlement are allocated (moves between the areas of the Sambia Peninsula, the adjacent coast of the Baltic Sea and Masury Lakeland) during 1 half of Ith. AC under the influence of external immigrants, which had the economic bases (amber trade). A conceptual position is proposed that the mass disappearance of the Western Baits monuments in Masury Lakeland (during VII-XI cc.) was the consequence of the next external influence on the region in 3/4 of Ith AC, as a result of which the carriers of the Sudovian culture moved to the Sambia Peninsula. A conclusion is drawn that there is no direct succession between the antique "Sudines" and the medieval "Sudovians/Jatvings" and, accordingly, the latter are formed directly on the basis of the Prussian culture. It is offered to correlate the return move of the Prussians (to Masury Lakeland and further to Upper Nemanland, in the Early Middle Ages (IX-XI cc.)) with the influence of the next wave of external immigrants (foundation of the trading center of Caire, the subsequent organization of a Trading way from Caire upstream of the Neman river). It is expedient to define the Jatvings as one of the late Prussian branches and to correlate the areas of their settlement with the medieval confederation of the Prussian tribes

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