Doklady of the National Academy of Sciences of Belarus, 2010, Vol.54, No.1
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Doklady of the National Academy of Sciences of Belarus, 2010, Vol.54, No.1

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
Lemeshevsky S. V., Makarov E. K., Matus P. P.
Bihari lemma and its application to the analysis of the stability of nonlinear difference schemes. pp. 59
Email: svl(at)im.basnet.by; makarov(at)im.basnet.by; matus(at)im.basnet.by
Summary: The difference analogue of the Bihari lemma allowing one to obtain a priori estimates of the stability with respect to the initial data and the righthand for solutions of difference schemes for nonlinear equations of mathematical physics is proved. The proven lemma assists to determine the point of time after which the singularity of the solution can arise.
Chuiko M. M.
Stability and convergence of difference schemes for equations of polytropic gas. pp. 1014
Email: chuiko(at)im.basnet.by
Summary: A priori estimates of the stability in the sense of the initial data of the difference scheme approximating polytropic gas equations in the Riemann invariants are obtained. The results of computational experiment confirming the theoretical conclusions are given.
Monastyrnyi P. I., Stelmakh S. N.
Convergence of the bilateral multiple shooting method for systems of nonlinear ordinary differential equations of second order. pp. 1520
Email: stelmakhs(at)mail.ru
Summary: The algorithm of the multiple bilateral shooting for systems of nonlinear ordinary differential equations of second order is prposed, its convergence for the boundaryvalue problems with the Weissisolated solution is proved, direct, multiple and bilateral multiple shootings are compared.
Tsegel'nik V. V.
Analytical properties of a nonlinear system of two secondorder differential equations. pp. 2125
Email: tsegvv(at)bsuir.by
Summary: An autonomous system of two secondorder nonlinear differential equations is considered. It is shown that this system is a Painlevetype system. In particular, it is demonstrated that its solution is expressed in terms of solutions of the equation for the simplest polynomial Hamiltonian associated with the second Painleve equation. Other properties of the solutions of this system are considered.
Likhoded N. A.
Characterization of the locality of parallel implementations of imperfectly nested loops. pp. 2632
Email: likhoded(at)im.basnet.by
Summary: Quantities for characterization of the locality of imperfectly nested loops are introduced and studied. Conditions for localization of input and intermediate data in virtual processors are obtained.
Dmitruk N. M.
Some problems of state estimation in optimal output feedback synthesis for linear dynamical systems. pp. 3338
Email: dmitruk(at)im.basnet.by
Summary: This article deals with two state estimation problems that arise in connection with optimal output feedback synthesis problems for linear timevarying deterministic systems subject to bounded disturbances on incomplete measurements. Algorithms for solving problems under consideration are presented.
Niparko N. S.
Stability of Lyapunov's indices in one problem on their control. pp. 3943
Email: nadden(at)mail.ru
Summary: A sufficient condition for the stability of Lyapunov's indices of the linear differential system, whose Cauchy matrix at the neighboring points of some arithmetic progression is an upper triangle matrix, is obtained.
Lyakhov D. A., Lomovtsev F. E.
Weak solutions of the Cauchy problem for the secondorder hyperbolic differentialoperator equation with a variable domain . pp. 4443
Email: spiritptd(at)yahoo.com; lomovcev(at)bsu.by
Summary: New theorems of existence, uniqueness and continuous dependence of weak solutions of the Cauchy problem for the secondorder hyperbolic differentialoperator equation with a variable domain of a smooth unbounded operator coefficient are proved. A new method to prove the uniqueness of weak solutions of hyperbolic differentialoperator equations is suggested. Correct solvability in the weak sense of the mixed problem for the wave equation with the timedependent boundary condition is established.
PHYSICS
Rychkov Yu. M., Akimov A. L, Vasilevich A. E., Zaerko D. V., Zaikova S. A.
Propagation of electromagnetic waves of microwave frequency in controlled twodimentional periodic structures. pp. 4449
Email: rychkov(at)grsu.by
Summary: In the present work the experimental research of regularities of propagation and localization of electromagnetic waves of microwave frequency in the twodimensional periodic structure with adjustable parameters is made. The experimental results can be directed to meet the challenges of creating new microwave electroniccontrolled devices.
Vlasov R. A., Lemeza A. M.
Moving optical solitons in dense resonant periodic media. pp. 5053
Email: r.vlasov(at)dragon.basnet.by; azemel(at)gmail.com
Summary: Solitonlike solutions are obtained for the twowave system of MaxwellBloch equations that govern the coherent nonlinear interactions of light pulses with a onedimensional periodic passive resonant medium where the refraction index is spatially modulated and thin layers of resonant particles influenced by the local field are localized at the maxima of the refraction index. It is shown that the phase of the stationary pulse is nonlinearly dependent on the pulse amplitude, which is a consequence of dipoledipole interactions between closely spaced atoms. It is established that the velocity of the soliton is an ambiguous function of its duration (bistability of second kind).
Kudryashov V. V., Baran A. V.
Rashba spinorbit interaction in the quantum ring in the presence of a magnetic field. pp. 5459
Email: kudryash(at)dragon.basnet.by
Summary: The exact wave functions and energy levels are obtained for an electron in a twodimensional quantum ring with a confining potential of finite depth in the presence of an external magnetic field and the Rashba spinorbit interaction.
CHEMISTRY
Vorobiov P. D., Cherednichenko D. V., Vorobieva E. V., Krutko N. P., Regino A. V.
Effect of surfactants on the flocculation of aqueous and saline kaolin dispersions by cationic poly electrolytes. pp. 6064
Email: evorobieva(at)igic.basnet.by
Summary: Colloidal properties, adsorption and flocculation ability of cationic polyelectrolytes (acrylamide copolymers) with different charged groups content were studied in the presence of surfactants. Results showed that the flocculation effectiveness increases when using lowcharged cationic flocculants compared to highlycharged ones, the flocculation effectiveness of such polymers does not depend on the presence of surfactants and low molecular salts. These questions are important for practical applications of polymers, e. g., waste water treatment.
Potkin V. L, Malshakova M. V., Belykh D. V., Petkevich S. K, Kutchin A. V.
Synthesis of chlorine E_{6} halogen derivatives. pp. 6570
Email: potkin(at)ifoch.basnet.by
Summary: The series of chlorine E_{6} derivatives and polychloro(bromo)carboxylic acid were synthesized. The compounds obtained are of interest for the study of the antitumor activity.
Gerlovsky D. O., Litvinko N. M., Skorostetskaya L. A., Kuchuro S. V., Kalinichenko E. N., Farina A. V.
Phosphodiesters of Acyclovir  new inhibitors of pancreatic phospholipase A_{2} pp. 7582
Email: nata(at)presidium.basnet.by
Summary: A new type of competitive inhibitors of pancreatic phospholipase A_{2}  di and threephosphoesters of Acyclovir – has been found. It is shown that a necessary condition for the inhibiting action of this compound is the presence of the aromatic fragment in the effector molecule. 2(4(Nitrophenyl)ethylphosphate Acyclovir is perspective for a further study as an antipancreatitis remedy of nucleic nature with a softened mode of action.
Halauko Yu. S., Serebryanskaya T. V., Matulis V. E., Gaponik P. N., Ivashkevich O. A.
Experimental and theoretical study of the cytotoxic activity of new tetrazolecontaining cisplatin analogues and their transisomers. pp. 8389
Email: hys(at)tut.by
Summary: Quantum chemical calculations within the framework of DFT were carried out for a set of platinum (II) complexes with nitrogencontaining heterocycles. A physically interpretable QSAR model was developed and a correlation between the biological activity and structural properties was obtained by means of the multiple linear regression method. The range of new tetrazolecontaining platinum (II) complexes was synthesized, and their cytotoxic activity was experimentally determined and compared with the values predicted by the QSAR model. Crucial properties of compounds and their relationship with the mode of action were discussed.
BIOLOGY
Golubev A. P., Bodilovskaya O. A., Slesareva L. E.
Impact of prolonged selffertilization on the growth and reproduction in Lymnaea stagnalis (Gastropoda, Pulmonata)  intermediate host of causative agents of helminthismes. pp. 9093
Email: algiv(at)rambler.ru
Summary: The parameters of growth and reproduction in families of pond snail Lymnaea stagnalis from selffertilization (SF) and crossfertilization (CF) in the second and seventh successive generations at grouping and individual rearing have been estimated in laboratory experiments. At the same time a prolonged reproduction by CF led to shortening of the beginning of reproduction by 1555 days, a decrease of the body mass and total fecundity per lifespan were seen. The average values of the intrinsic population growth of L. stagnalis at both modes of reproduction differed insignificantly and retained at the high level. A minimal period of a twofold increase of L. stagnalis population abundance at SF and CF amounts to 1215 and 1156 days, respectively. Therefore the measures of control of natural nidi of helminth diseases based on the decrease of abundance of L. stagnalis populations seem to be ineffective. A few residuary mollusks reproduced by SF are able to restore the initial abundance of population for a short period of time.
Gorbunova N. В., Ulashchik V. S., Batai L. E., Vodchits A. I., Orlovich V. A.
Laser radiation influence of the spectral 2 mm region on the level and activity of a_{2}macroglobulin and a_{1}antitripsin in rat tissues. pp. 9497
Email: l.batay(at)ifanbel.basnet.by; nbgorbunova(at)mail.ru
Summary: The changes in the content and activity of protease inhibitors (a_{2}macroglobulin and a_{1}antitripsin) in the blood serum and the liver tissue of newborn rat males after the local thermal influence of highintensive laser radiation at a wavelength of ~ 2 mm (power density of 45 and 70 W/cm^{2}) were demonstrated.
MEDICINE
Beletzky A. V., Nikolaev V. I., Ermakov S. F.
Medicobiological aspects of regulating the tribological properties of blood serum as a potential liquidcrystalline synovial medium for treating osteoarthrosis. pp. 98103
Email: erms(at)yandex.ru
Summary: Proceeding from the experimental studies with a cartilageoncartilage friction pair using pendulum tribometry a difference has been established in the influence of medicinal preparations based on hyaluronates and chondroitin sulfate upon blood serum lubricity. It is proved that during the cartilageoncartilage friction interaction the best tribiological characteristics in the complex of blood serum, which practically coincide with those of natural synovial fluid, provide medicinal preparations based on chondroitin sulfate.
SOCIAL AND HUMANITIES SCIENCES
Nikitenko P. G., Platonova L. A.
Competitiveness and selforganization in the international economy: the conceptual approach. pp. 104108
Email: platonova.larisa(at)mail.ru
Summary: A new concept of scientific assessment and analysis of the competitiveness of the international economy on the basis of selforganization is offered. The approach is practically tested for the Republic of Belarus and 94 countries of the world community. Conclusions are made.
Shaton E. V.
Formation of methodological approaches to an estimation of efficiency of purchasing activity for the state needs. pp. 109113
Email: ekshaton(at)tut.by
Summary: This article proposes a method of estimation of the effectiveness of procurement activities and an integrated indicator, developed on the basis of fundamental principles of international public procurement. The author developed a method of ranking the organizations according to the results of the effectiveness of procurement process. There are calculations of the integrated indicator of the effectiveness of procurement and the rate of agencies according to the results of the effectiveness of procurement process in 2008.
AGRARIAN SCIENCES
Gusakov V. G.
System of principles of providing food safety. pp. 114116
Summary: In the article, the system of principles is determined for the first time. The upholding of these principles in complex allows attaining stable food safety and balanced food supply of the country.
Tsyganov A. R., Vildflush I. R., Batyrshaev E. M.
Influence of complex usage of mineral fertilizers and plant protection means on the intensity of productive processes, yield and quality of grain winter wheat. pp. 117122
Email: kancel(at)baa.by
Summary: In the article the information about the influence of separate and complex usage of mineral fertilizers and plant protection means on the intensity of productive processes, yield and quality of grain by cultivation of winter wheat is presented.
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