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Doklady of the National Academy of Sciences of Belarus, 2011, Vol.55, No.4

Homepage / Publications / Scientific Journals

Doklady of the National Academy of Sciences of Belarus, 2011, Vol.55, No.4

(Doklady Natsionalnoi Akademii Nauk Belarusi)

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

Volume 55, Number 4; July-August, 2011

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Korzyuk V. I., Cheb E. S., Thu Le Thi.
Solution of the first mixed problem for the non-rigorous bivawe equation. pp. 5-13.

Summary:Using the method of characteristics the analytical solution of the mixed problem for the four-order equation is under construction. Conditions of coordination of initial and boundary conditions are derived.

Radyna A. Ya.
P-adic counterpart of Mikusinski's operational calculus and its applications to the Fourier and the Mahler expansions of locally constant functions. pp. 14-18.

Summary:The p-adic counterpart of Mikusinski's operational calculus based on C(Zp; Qp) and the discrete Laplace convolution are considered. Some elements of Mikusinski's field are presented. A notion of a p-adic exponent is generalized. Applications to the Fourier and the Mahler expansions of locally constant functions and the convolution of two ball indicators are demonstrated. Two ways of applying the calculus lead to the Fourier expansion for the fractional part of a p-adic number.

Palchik E. M.
Generations by pairs of conjugate elements in finite groups. pp. 19-20.


Suprunenko I. D.
Unipotent elements of nonprime order in representations of the classical groups: two big Jordan blocks. pp. 21-26.

Summary:For irreducible rational representations of the classical algebraic groups in characteristic p > 0 which are not equivalent to a composition of a group morphism and the standard representation, it is proved that the images of unipotent elements of nonprime order almost always have at least two Jordan blocks of size greater than ps; all exceptions are indicated explicitly. This permits one to classify irreducible rational representations of these groups whose images contain unipotent elements with only one Jordan block of size greater than 1.

Wenbin Guo, Kovalyova V. A., Skiba A. N.
S-embedded and m-supplemented subgroups of finite groups. pp. 27-30.


Prokopchuk A. V., Yanchevskii V. I.
Invariant subalgebras of quaternion division algebras with involutions. pp. 31-34.

Summary:Let K be a field of characteristic different from 2 and Q a quaternion division K-algebra with an involution t. In the article the problem of description of t-invariant subalgebras of Q is settled.

Korots Yu. V.
Integral equations with diagonally representable operators.. pp. 35-41.

Summary:This article considers a modification of Kantorovich's fixed point principle with exact (unimprovable) estimates of the internal and external radii of the domain of existence of a unique fixed point of the operator under consideration and new apriori and a posteriori error estimates for successive approximations to the corresponding fixed point. Two applications of the new fixed point principle to nonlinear integral operators of different types are given as well. The applications reflect the fact that different results about existence and uniqueness of a fixed point of the the operator A can be strengthened by a deeper analysis of Lipshitz's condition . Considered examples can be easily generalized to a nonlinear equation with an unknown function that is defined on a measurable space with d-finite measure with values in the space with finite measure.

Bulhakau I. V.
Integral polynomials with close roots in Archimedean and non-Archimedean metrics. pp. 42-44.

Summary:In this article the existence of a big number of integral polynomials with close complex and p-adic roots is proved.



Speransky D. S., Borzdov A. V., Borzdov V. M., Komarov F. F.
Impact ionization effective threshold energy in deep submicron MOSFET with the 50 nm channel length. pp. 45-48.

Summary: In the frame of Keldysh's model the calculation of impact ionization effective threshold energy in the deep submicron MOSFET with the 50 nm channel length by means of Monte-Carlo electron transport simulation is offered. The possibility of the impact ionization rate description by Keldysh's one-parameter model in the considered transistor operating mode is shown.

Andrusevich P. P., Pletyukhov V. A., Strazhev V. I.
Dirac-Kahler equation in space-time 2 + 1 and its application in the theory of graphene. pp. 49-53.

Summary: Internal symmetries of the Dirac-Kahler equation and the system of two Dirac equations in space-times 2+1 dimensions are investigated. It is shown that symmetry groups of the both-type equations are equivalent. This result means that the Dirac quasiparticles in graphene in the low-energy limit can be described by antisymmetric tensor fields.



Eryomin A. N., Zhavnerko G. K., Agabekov V. E.
Synthesis of associates of folic acid with (Zn)ZnS and (Cd) CdS composite nanoparticles. pp. 54-59.

Summary: The technique of the synthesis of composites of folic acid (FA) with (Zn)ZnS and (Cd)CdS nanoparticles (NPs) is optimized. It is proved that FA itself is an effective stabilizing additive in the process of formation of CdS and (Cd)CdS NPs. The composites of FA with CdS or (Cd)CdS NPs demonstrate the high intensity of fluorescence and stability at a storage in comparison with same NPs obtained in the presence of thioglycolic acid FA also forms the composites with zinc-containing NPs However, the efficiency of the FA influence on the fluorescence of Zn-containing NPs is essentially less than in the case of Cd-containing ones.

Nichick M. N., Voitekhovich S. V., Lesnikovich A. I., Ivashkevich O. A.
5-Mercaptotetrazoles as stabilizing agents in synthesis of palladium and platinum nanoparticles. pp. 60-65.

Summary: Palladium and platinum particles were synthesized by two-phase water-toluene protocol based on a reduction of metal complex salts using sodium borohydride as a reducing agent. Synthesized colloidal solutions of Pd and Pt particles are stable in the organic phase for a long period of time (up to 8 months) and average size of Pd particles are in the range of 2.7-3.3 nm with a narrow size distribution. The diameter of Pt nanoparticles was varied from 2 to 5 nm. Thermal treatment at 300 0С in nitrogen atmosphere could be used for modifying the surface of Pd nanoparticles, particularly, for enriching the particles surface with sulfur atoms.



Semenchenko V. P., Suschenya L. M., Vezhnovetz V. V.
Relationship between species richness of littoral zooplankton and hydromorphology for different-type lakes. pp. 66-67.

Summary: The correlation analysis between species richness of littoral zooplankton (Cladocera, Copepoda) and lake hydromorphology are conducted for 21 different-type lakes. The number of species is not correlated with the lake depth, and maximal coefficients of correlation are pointed out for the surface/depth ratio. The main reasons of the differences in relationships between species richness and hydromorphology for pelagic and littoral zooplankton are discussed.

Genkal S. I., Mikheyeva T. M., Stanovaya Y. L.
The evalution of species composition of centric diatom algae (Centrophyceae) changes and their contribution in total biomass of diatoms and phytoplankton as a whole in the lakes of the reservation "Sinsha" (Belarus). pp. 68-75.

Summary: The results of study in the light and scanning electron microscopes of centric diatom algae species composition and their quantitative development in lakes phytoplankton of the reservation with the aim of evaluation of possible changes during 30 years from the beginning of its studying are presented. The short diagnosis and original microphotographs of the reveled species are given. Despite of a few number of Centrophyceae (14 species vs. 56 representatives of Pennatophyceae) the contribution of centric diatoms in the total diatom biomass in the investigated lakes is high and composes from 40 to 80 %. For the past 30 years their species composition practically has not changed, that means that the lakes retained their natural trophy state.



Vismont A. F., Vismont F. I.
Antipyretic effect of L-valine in rats and rabits in endotoxin fever conditions. pp. 76-78.

Summary: A decrease of the blood serum amino acid L-valine content on bacterial endotoxin E. coli (50 mg/kg) effect on an organism in the experiments on rats and rabbits was established It was demonstrated that the fever reaction on bacterial endotoxin in rats was completely eliminated by preliminarily intraperitoneal introduction of amino acid L-valine in a dose of 100 mg/kg which had an antipyretic effect in rabbit after administration in blood flow on the endotoxin reaction peak.

Sidorovich R. R.
Reconstructive surgery for muscular and tendomuscular trasposition in the rehabilitation of patients with brachial plexus injury. pp. 79-88.

Summary: The objective of the study was to assess the efficiency of muscle and tendon transposition techniques in BP injuries . The analyzed results included ones of restoration of the active flexion function of the forearm by muscle transposition techniques (72 cases), wrist and finger extension by tendomuscular transposition (12 cases) and Brachial plexus surgeries to re-innervate musculocutaneous (69 cases) and musculospiral (81 cases) nerves. The total efficacy of latissimus dorsi, pectoralis major, and triceps transpositions was 100 %, which allowed the restoration of the most important movement of the upper limb - forearm flexion in all the operated patients. The efficacy of triceps transposition is 37 5 %, which makes it feasible to do it only if no other suitably innervated muscles are available for transplant. Tendomuscular transplants aimed at wrist and finger extension restoration had an efficacy of 100 %. Combining muscle and tendomuscular transplants helps ensure the functional usefulness of the proximal and distal upper limb sections in traumatic Brachial plexus injuries. Muscle and tendomuscular transplants deliver better results in forearm flexion and wrist and finger extension restoration than BP surgery.



Konischev V. S.
Geodinamic regime of halogenes in the Pripyat trough. pp. 89-94.

Summary: It is shown that the thickness and composition of salt formations of the Pripyat trough depends on the geodynamic regime. The salt formations of large thickness of rift stage were deposited in conditions of active subsidence (38-1293 m/min. year). Salt formations of small thickness were deposited at stages of early and late syneclise in conditions of weak subsidence (5-54 m/min. year).

Aizberg R. Ye., Garetsky R. G., Karabanov A. K., Sviatogorov A. A., Shkabara V. V.
Block division of the Earth's crust of Belarus. pp. 95-99.

Summary: The Earth's crust of Belarus was determined to
E-mail: be a subdivision from the bottom upwards into version-type blocks which are evident in the basement and the platform cover. The differentiation of block-forming faults in their structure - morphological, historical-geological, genetic and other evidences suggests some systems of block subdivision that could be distinguished. The article deals with two of the above systems: passive (static) and active (dynamic at the Late Oligocene-Quaternary stage).



Kheifetz M. L.
Evolution principles of the physical-chemical analysis for the non-equilibrium processes of synthesis and materials use. pp. 100-105.

Summary: To study the non-equilibrium processes of synthesis and nanostructured materials use, it has been proposed to complement the fundamentals of the physical-chemical analysis, as that will enable to detect the transient structures and processes which could be described by non-integer values for emerging phases and degrees of freedom of the system.

Pesetskii S. S., Dubrovski V. V., Koval V. N.
Cold crystallization of polyethyleneterephtalate mixed with polybutyleneterephtalate reinforced with glass fiber. pp. 106-112.

Summary: Changes of characteristics determining the processes of crystallization and relaxation transitions in polyethyleneterephta-late (PET) and its mixtures with 3-50 wt.% polybutyleneterephtalate (PBT) reinforced with 25 wt.% short glass fiber are analyzed. It is shown that PBT additives result in decreasing cold crystallization temperature values. The mutual solubility of PET and PBT amorphous phases of glass fiber reinforced composites which are characterized by a single (decreased as compared to the initial PET) glass transition temperature is revealed. It is also stated that the examined systems are characterized by a single b-process of relaxation in the range from -70.5 up to -79 0C (depending on the composition) indicative of the compatibility of components in the amorphous phase at the level of elementary units of the miscible polyesters macromolecules.

Kuharchik P. D., Semenchik V. G., Pahomov V. A.
Microwave image reconstruction with the synchronous two-antenna aperture synthesis. pp. 113-117.

Summary: The impact of illuminating and receiving antenna spatial displacement on the microwave images quality is investigated Image reconstruction is performed using the two-antenna aperture synthesis. A method of image reconstruction, which reduces image distortions caused by the antenna displacement, is proposed. Theoretical and experimental investigations performed have shown the method efficiency.



Rahimau A. N.
Social demographic characteristics of Caucasus folk ethnic groups living in the Republic of Belarus in the connection with the census. pp. 118-124.

Summary: On the basis of official statistics and ethnological researches the analysis of social demographic characteristics of the Caucasus folk representatives migration to the Republic of Belarus was made, a number of the questions about causes and the character of migration, the choice of places of living, the naturalization and the adaptation to new circumstances, the processes of interaction with the local population both in individual and in group spheres, which shows the specification of the development of the relationships between ethnic groups in the modern Belarusian society were researched.

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