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Doklady of the National Academy of Sciences of Belarus, 2011, Vol.55, No.5

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Doklady of the National Academy of Sciences of Belarus, 2011, Vol.55, No.5

(Doklady Natsionalnoi Akademii Nauk Belarusi)

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

Volume 55, Number 5; September-October, 2011

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Prokhorovich M. A., Radyna Ya. M.
Convergence rate of Steklov means for functions from Sobolev classes on the space of p-adic numbers. pp. 5-8.

Summary: A convergence rate of Steklov means for functions from Sobolev classes on the space of p-adic numbers is investigated.

Korzyuk V. I., Kozlovskaya I. S.
Solving the Caudiy problem of the hyperbolic equation for a homogeneous differential operator in the case of two independent variables. pp. 9-13.

Summary: In the article, the solution of the Cauchy problem for the m-order hyperbolic equation with constant coefficients, where m is a positive integer and the operator of the equation is a composition of the first-order differential operators in the case of two independent variables, was found in the analytical form.

Shlyk V. A.
Vertices of the master Gomory polyhedron. pp. 14-17.

Summary: We proved that there exists a subset of vertices of the master Gomory polyhedron, from which all other vertices can be built with the use of two combinatorial operations. Moreover, these operations transform vertices to adjacent ones and leave them on the same nontrivial facets . We also establish interrelations between the coefficients of inequalities which define nontrivial facets containing a given vertex.

Budarina N. V., Dickins N. D., Bernik V. I.
Real and complex roots of integer polynomials in the neighborhood of their small values. pp. 18-21.
E-mail: bernik|

Summary: Conditions are found for the value of an integer polynomial, its first and second derivatives, for which the closest root to argument belongs to the field of real or complex numbers. Estimations from below for the number of polynomials of the bounded degree and height, which have close complex-conjugate roots, are proved.

Zabreiko P. P., Korots Y. V.
Modification of Minty-Browder theorem. pp. 22-27.

Summary: In the article it is shown that if hemi-continuous operator A satisfies the one-sided variable Lipshits condition on a certain ball of Hilbert space, then all the necessary conditions of the Minty-Browder principle are fulfilled. In addition, operator A fixed point uniqueness zone is defined more exactly than in the Minty-Browder principle. Due to the fact that this modification is applied to the Hammershtain equation with positively defined kernel, new solvability conditions for Hammershtain equation are found.

Prokopchuk A. V., Tikhonov S. V., Yanchevskii V. I.
Special properties of homogeneous skew fields of noncommutative rational functions. pp. 28-34.

Summary: Let A be a skew field, j1,…,jn be its automorphisms. Necessary and sufficient conditions on A and j1,…,jn are obtained for the existence of homogeneous twisted polynomial rings over A in n variables with respect to j1,…,jn. Furthermore, the structure of quotient skew fields of such rings (homogeneous skew fields of noncommutative rational functions) is described in the case where the group generated by j1,…,jn is finite and has no nontrivial inner automorphisms. Besides, exponents of generic abelian crossed products are computed in terms of appropriate constant algebras.

Demenchuk A. K.
Control of the asynchronous spectrum of a linear system with some constant elements of the matrix of coefficients. pp. 35-39.

Summary: We consider a linear control periodic system with reverse communication. It is supposed that the average matrix coefficient is block triangular in the critical case and some elements of the matrix of the coefficient are constant. The control problem of asynchronous spectrum is solved.



Sergeenko M. N.
Hadron masses and Regge trajectories for the funnel type potential. pp. 40-43.

Summary: The potential approach in hadron physics to solve the relativistic two body problem is used. Interaction of particles in the system is described by the relativistic quasi-potential equation of Bethe-Salpeter type with the scalar potential. Eigenvalues of the system - squared hadron masses - are defined by the quasi-classical method. Mass spectra, Regge trajectories, aR(t), of hadrons and the pomeron, aP(t), in the whole region of the invariant variable t are obtained in apparent form.

Tolkachev E. A.
Galileo invariant electrodynamics with sources and the relativity principle. pp. 44-48.

Summary: It is shown that in the presence of external electric-type sources there is only one non-relativistic limit of Maxwell's equations satisfying the principle of Galilean relativity. This limit does not coincide with the field equations of Ampere-Weber electrodynamics which were formulated by Maxwell in 1855. Dual invariance and the principle of relativity allow the introduction of only a magnetic charge density into the non-relativistic equations of electrodynamics. Non-relativistic vacuum equations of electrodynamics in the macroscopic form are not dually invariant.

Goncharenko А. М.
Rotary solitons. pp. 49-51.

Summary: Some properties of optical rotary solitons are considered.



Potkin V. I., Bumagin N. A., Zelenkovskii V. M., Petkevich S. K., Zubenko Yu. S., Livantsov M. V., Belov D. S.
Synthesis and structure of palladium(II) complexes with of the oxime 5-(n-tolyl)isoxasol-3-carbaldehyde and 4,5-dichloroisothiazol-3-carboxylate fragment. pp. 52-57.

Summary: The corresponding Pd(II) complexes were synthesized through the interaction of oxime 5-(n-tolyl)isoxazol-3-carbaldehyde and sodium 4,5-dichloroisothiazol-3-carboxylate with sodium tetrachlorpalladate. The structure of complexes was determined on the basis of IR spectra data and quantum chemistry calculations by DFT method. The calculated and experimental frequencies were in satisfactory agreement.

Kulak T. I., Oleynikova I. A., Tkachenko O. V., Kalinichenko E. N., Kolbanova E. V., Krasinskaya T. A., Kukharchyk N. V.
Synthesis and properties of 2’,5’-oligoadenylate analogs containing ribavirin and 9-(2,3-anhydro-b-D-ribofuranosyl)adenine. pp. 58-62.

Summary: 2’,5’-oligoadenylate analogs containing ribavirin fragment
E-mail: s in 5’-terminal or/and middle position of oligonucleotide chain and 9-(2,3-anhydro-b-D-ribofuranosyl)adenine residue in 2’-terminal position of oligomer have been prepared. The compounds prepared are much more stable to the action of snake venom phosphodiesterase in comparison with the native 2’,5’-trimer of adenylic acid. It has been found that the introduction of ribavirin residue in 5’-terminal position of oligonucleotide molecule leads to the enhanced stability of the corresponding compounds to the hydrolysis with phosphodiesterase 2’,5’-oligoadenylate derivatives may be used instead of phytotoxic ribavirin for the elimination of pathogenic raspberry ringspot virus during in vitro microclonal propagation of black currant and sour cherry.

Pashkovsky F. S., Adamovich Yu. A., Shinkovich M. A., Lakhvich F. A.
Synthesis of 4,8-interphenylene heteroprostanoid and their precursors on the basis of 3-aryltetronic acids. pp. 63-67.

Summary: A simple and general approach to synthesizing 4,8-interphenylene 10-oxa-13-aza-, 11-oxa-13-azaprostanoids as well as key butenolide and nitromethyl precursors of 11-deoxy-10-oxa-analogs of prostaglandins on the basis of readily available 3-aryltetronic acids has been proposed.



Buseva Zh. F.
Evaluation of the impact of environmental factors on the Cladocera non-predatory specific mortality in different-type shallow lakes. pp. 68-71.

Summary: The impact of water temperature, TDS, pH, dissolved oxygen as possible causes of the Cladocera mortality in littoral and pelagic zones of sallow lakes was investigated. The non-predatory specific zooplankton mortality was measured using the method described by Seepersad & Crippen, 1978 to identify dead and alive individuals. A high positive correlation between water temperature, TDS and non-predatory mortality was found.

Vezhnovetz V. V., Semenchenko V. P.
Impact of warming on a vertical distribution of zooplankton in a mesotrophic stratified lake. pp. 72-75.

Summary: The vertical distribution of zooplankton abundance in the deep mesotrophic lake Sita was studied during summer of 2008 and 2010 characterized by different temperature in the epilimnion layer (22.0 and 26.2 0C respectively). The high temperature led to a decrease in dissolved oxygen in metalimnion. In spite of the high temperature, zooplankton abundance was shifted to the water upper layer. This caused changes in the zooplankton structure and the cold water species in epilimnion were replaced by eurythermic species.

Makarevich А. М., Reshetnikov V. N.
Antioxidant activity of the berries of Vaccinium corymbosum L . and Vaccinium uliginosum L. pp. 76-81.

Summary: According to the available literature data, phenol substances, in particular anthocyanidins and their glycosides are one of the most perspective natural antioxidants. Berries of Vaccinium corymbosum L. and Vaccinium uliginosum L. accumulate a wide range of biologically active substances. As a result of our research, the levels of the high content of anthocyanins in the berries of 20 cultivars of Vaccinium corymbosum L. and in Vaccinium uliginosum L. were defined. The highest level of anthocyanins (more than 600 mg%) was found in berries of Patriot, Carolina Blue, Stanley, Herbert, Northland. In the studied cultivars, the portion of anthocyanin pigments as a part of phenol substances makes up 20 to 60 %. The high antioxidant activity in cultivars of Vaccinium corymbosum L. Patriot, Northland, Carolina Blue, Nelson and in the berries of Vaccinium uliginosum L. in the system with cation-radicals ABTS+× was established. A positive correlation between the antioxidant activity, the content of phenol compounds and anthocyanyns pigments, which can be used for estimating the biological activity of the berries of blueberry and phytopreparations on their basis was shown.



Konischev V. S.
Tremlian phase of the tectonic and magmatic activity in the Pripyat trough. pp. 81-85.

Summary: The tremlian phase of the tectonic and magmatic activity was determined first t
E-mail: ime in the Pripyat trough. During this phase, the territory was uplifted and lower salt deposits were washed at upper parts of some tectonic steps. As a result, salt rock was deposited at lower parts of steps Acid volcanism takes place during this phase at the south part of the Pripyat trough.

Aizberg R. Ye., Beskopylny V. N., Gribik Ja. G.
Structural regions distinguished within the intersalt complexes of the Pripyat oil- and gas-bearing basin. pp. 86-90.

Summary: A cartographic model of structural regions distinguished within the intersalt complex of the Pripyat oil- and gas-b
E-mail: earing basin has been compiled Structural features of the same name revealed both in the intersalt, and subsalt complexes differ in their morphology, divisibility into blocks and show intersalt deposit washouts and not exactly matching boundaries.



Vityaz P. A., Komarov V. I., Komarova V. I., Shipko A. A., Senyut V. T.
Creation of nanostructured composite modifiers for aluminium alloys. pp. 91-96.

Summary: Presented fundamentally new physical and chemical aspects of the creation of nanostructured composite ceramic fillers of various systems based on micro-and ultrafine powders of oxides and nitrides. The initial charge serves as donor formers of nanoscale fillers due to chemical reactions which take place in it, as well as media extenders in the melt and a uniform distribution in them. It was established that the developed dispersing fillers have a significant impact on the structure of the alloy, leading to a decrease in grain size in 5-30 times. The friction coefficient of developed cast composites in boundary friction is reduced by 3-8 times, wear resistance increases to 55 times the carrying capacity increases 2 times compared with the original alloy.

Rusetsky A. M., Novikova Z. A., Gorodkin G. R., Korobko E. V.
Development of magnetostructured fluids with controlled rheology for high-precision finishing processing of optical products. pp. 97-104.

Summary: In the article the data on the investigation of physical-chemical characteristics and peculiarities of rheological behavior of magnetosensitive fluids in magnetic fields are presented . Also, we report on their application at high-quality finishing polishing of optical details.

Stepanenko D. A., Minchenya V. T.
Development and study of a novel type of non-contact ultrasonic motors based on the principle of structural asymmetry. pp. 105-111.

Summary: The article presents results of theoretical and experimental studies of an ultrasonic motor with a ring-shaped stator and a rotor actuated by acoustic radiation forces resulting from its interaction with acoustic stator field. Values of acoustic radiation forces and their torque exerted on the rotor are determined by finite element method. Dynamics of the rotor is studied using qualitative theory of nonlinear differential equations Dependence of rotor dynamics on initial conditions is investigated. Experimental relations between the angular rotor speed and vibration amplitude of the stator are given.



Zharko V. I., Pinevich D. L., Serduchenko N. S., Samokhodkina S. V.
Medical economics and innovation management. pp. 112-117.

Summary: Problems of medical economics and medical innovations are the major making part of new organizational forms of the public health services system and are directed to creating high-tech and effective medicine in Belarus. It allows one to considerably increase the level of medical aid rendering to the population of the country and will also promote the performance of the demographic safety program.

Levko O. N., Sedov S. G., Golobokov S. V.
Archaeological study of constructions of the Castle of Shklov with the use of a method of resistance. pp. 118-122.

Summary: The article is informed of the archaeological research of stone constructions of the castle of Shklov that are dated to the 16th - 18th centuries. They are represented by the parts of the bases of defensive towers, passable gate and elements of houses dwellings (floor, the basis of the pise-walled stove). Opportunities of use of a geophysical method of resistance in revealing the abnormal zones containing the rests of stone constructions are shown. Geophysical researches with instrument «Elektrozond» are experimental in character.

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