Doklady of the National Academy of Sciences of Belarus, 2010, Vol.54, No.3
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Doklady of the National Academy of Sciences of Belarus, 2010, Vol.54, 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
Yanchevskii V. I.
Conjugation problem of groups of rational points for outer forms of anisotropic groups of type А_{n}. pp. 57
Email: yanch@im.basnet.by
Summary: A solution of the conjugation problem of groups of rational points for outer forms of anisotropic groups of type A_{n} is given.
Barkova E. A., Zabreiko P. P.
Nonlocal theorems on the Cauchy problem for differential equations of fractional order. pp. 813
Email: elenab@tut.by; zabreiko@mail.ru
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. 1419
Email: yanovich@im.basnet.by
Summary: Quadrature formulas of an utmost degree of trigonometric accuracy with determined nodes for stochastic integrals of nonrandom 2pperiodic 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. 2025
Email: у.mikulich@gmail.com
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 fstructures on naturally reductive Фspaces of order 6. pp. 2631
Email: Andrey.S.Samsonov@gmail.com; Balashchenko@bsu.by
Summary: In the article the canonical fstructures on arbitrary homogeneous Фspaces of order 6 (in other terminology, homogeneous 6symmetric 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 fstructures (NKf) and Hermitian fstructures (Hf). Types of invariant distributions generated by the canonical structures on homogeneous Фspaces of order 6 are also characterized.
Shlyk V. A.
Number of approximate partitions of natural numbers into a sum of algebraic numbers. pp. 3235
Email: v. shlyk@gmail.com
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.
PHYSICS
Buganov O. V., Tikhomirov S. A., Shulenkov A. S., Stankevich V. V., Ermolenko M. V., Gaponenko S. V.
Ultrafast alloptical modulator for 1.5 mm driven by a Ti:Al_{2}0_{3} laser. pp. 3640
Email: ermolenko@imaph.basnet.by
Summary: The concept of an ultrafast light modulator for a wavelength of ~ 1.5 mm controlled by the fundamental harmonic of a Ti:Al_{2}0_{3} 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)_{x}O_{y} with the relaxation time of 13 ps in the spectral range where both materials have negligible absorption. These short times correspond to the eh 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. 4146
Email: zhestkov_s@rambler.ru
Summary: For the systems of any order of Schrodinger's connected (2+l)dimensional equations with any power laws the method of constructing solitonlike 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. 4754
Email: redkov@dragon.basnet.by
Summary: Exact solutions of the quantummechanical 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 hightemperature cuprate superconductors. pp. 5562
Email: grushevskaja@bsu.by; lhur@bsuir.by
Summary: Pseudogap anomalies for the state of cuprate highTc 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.
CHEMISTRY
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. 6370
Email: yan47@mail.ru
Summary: Fluorescence of CdSe/ZnS nanoparticles (NP) in reverse micelles of aerosol ОТ (АОТ) is studied depending on the relation of H_{2}0/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 548556 nanometers, intensive emission of light with maxima at 331, 379, 435437, 481490 and 535537 nm with a Stokes shift of 67 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 nonfluorescent emission of light.
Opanasenko O. N., Zhigalova O. L., Krut'ko N. P., Ostrovskaya E. F.
Regulation of colloidchemical properties of mixes of cathionic surfactants in the presence of lowmolecular spirits. pp. 7176
Email: zhigalova.o@mail.ru
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 lowmolecular 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 lowmolecular spirits allow one to adjust their colloidchemical 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. 7783
Email: sinelyov@iboch.basnet.by
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'Fluorocontaining isoflavonoids: synthesis and spectroscopic investigations. pp. 8487
Email: khlebnicova@iboch.basnet.by
Summary: A new approach to the synthesis of 4'fluorocontaining isoflavonoids has been developed. The synthesis of 7hydroxy4'fiuoroisofiavone and its chemical transformations are described. The structures of synthesized compounds are verified by spectroscopic data.
BIOLOGY
Galkovskaya G. A., Kalinovska K., Molotkov D. V., Trifonov O. V.
Influence of stratification on the vertical distribution of microzooplankton in oligotrophic lake. pp. 8891
Email: gal@biobel.basnet.by
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 bacterialdetritus 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 selfcleaning.
Galinousky D. V., Leontiev V. N., Nikitinskaya T. V., Raiski A. P., Khotyleva L. V., Titok V. V.
Identification of CesAgenes expressed in the stems of fiber flax plants (Linum usitatissimum L.). pp. 9297
Email: dimgal200@rambler.ru
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 CesAgenes 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 TW37. pp. 98100
Email: veresov@ibp.org.by
Summary: The computational docking approach was employed to establish the structural determinants of inhibition of antiapoptotic proteins by anticancer agent TW37. The results obtained suggest that the inhibition of antiapoptotic proteins of the Bcl2 family by TW37 is caused by binding this compound to the hydrophobic grooves of antiapoptotic proteins Bcl2, BclxL and Mcl1, 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 TW37 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.
MEDICINE
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. 101104
Email: stashkevichl@gmail.com
Summary: The PCRanalysis of the expression of two oncogenes (bax/bcl2) in the liver and brain tissues of the animals after being exposed to gammarays 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 startup 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 threedimensional gelatinous matrix and adipose derived mesenchymal stem cells (adMSC). pp. 105109
Email: bogdan_5@mail.ru
Summary: In the conditions of experiment in vitro, comparative study was for the first time made of the efficiency of coculturing with adipose derived mesenchymal stem cells (adMSC) rats in a threedimensional gelatinous matrix on different variants of the surgical meshes "Prolene", "Vypro", "Ultrapro", "Vicryl" and "Proceed". It is proved that the threedimensional 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.
TECHNICAL SCIENCES
Tyutyuma V. D.
Mechanism of the separating effect in the Ranque vortex tube. pp. 110114
Email: tvd@hmti.ac.by
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 RanqueHilsch 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.
SOCIAL AND HUMANITIES SCIENCES
Vitsiaz S. P.
Ancient Prussians: areas of settlement (to a problem of the Jatvings origin). pp. 115124
Email: vit@history.minsk.by
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 VIIXI 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 (IXXI 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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