# Доклады Национальной академии наук Беларуси, 2004, Том 48, No.4

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2004, Том 48, No.4

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Kostyukova O. I.*
**Behavior of optimal control problem solutions in neighborhood of weakly degenerate point.** pp. 5--9

*Summary:* For parametric linear-quadratic optimal control systems with delay, properties of solutions are investigated in a neighborhood of a weakly degenerate point. Asymptotic expansion of the solutions with respect to a parameter is presented.

*Radyna Y. M.*

**Adelic mnemofunctions and Fourier transform.** pp. 10--14

*Summary:* New algebra of mnemofunctions (non-linear generalized functions) with convolution on global space of adeles is presented with archimedean and non-archimedean places treated separately. Linear space of adelic Schwartz--Bruhat distributions is embedded into this algebra, so that all distributions (to be exact, corresponding mnemofunctions) can be multiplied. Examples of distribution embedding and multiplication are given.

*Gorbuzov V. N., Korolko I. V., Tyshchenko V. Yu.*

**Trajectories of differential systems on Bendixon's sphere.** pp. 15--19

*Summary:* Topological and analytical features of autonomous polynomial differential systems of the second order are investigated at Bendixon's transformations. An approach to construction of indefinitely critical point on Bendixon's sphere in terms of (final) circular sequence of adjacent elliptic, hyperbolic and parabolic sectors on the basis of indefinitely critical points located on equator of Puancare's sphere is developed. All set of holomorphic (dynamic systems) on Bendixon's sphere is found, and the topological atlas of behavior of their trajectories is constructed.

*Osinovskaya A. A.*

**Restrictions of representations of type D**_{n} algebraic groups to naturally embedded A_{2} subgroups. pp. 20--23

*Summary:* Restrictions of modular irreducible *p*-restricted representations of algebraic groups of type *D*_{n} to naturally embedded subgroups of type *A*_{2} are studied. Let *n* > 3 and со be the highest weight of a representation considered. The composition factors of such restrictions are determined in cases of locally small weights со with respect to *p*. Here the class of locally small weights is determined in terms of their values on four simple roots linked at the Dynkin diagram of a group.

*Minchenko L. I., Tarakanov A. N.*

**On differentiability of maximum function on G-regular multifunctions.** pp. 24--28

*Summary:* Calculation of various types of derivatives of maximum functions defined on values of multifunctions is an important problem for quasidifferential calculus, sensitivity analysis of parametric extremum problems, necessary extremum conditions theory and other parts of theory of optimization. In particular, it is interesting to choose a class of multifunctions, which have directionally differenti-able maximum function.
One of the major results in this field was achieved in the works of V. F. Demyanov and A. M. Rubinov, where a class of multifunctions allowing first-order approximations was selected. Also, other classes of so-called weakly uniformly differentiable multi-functions and strongly differentiable multifunctions are kown to have the described property.
In this pfper, a larger class of multifunctions is introduced, which has the required property and contains all of the classes mentioned above.

*Skums P. V., Suzdal S. V., Tyshkevich R. I.*

**On polynomial solvability threshold for recognition problem of edge intersection graphs of linear 3-uniform hypergraphs.** pp. 29--33

*Vasilyeva T. I., Prokopenko A. I.*

**Projectors and lattices of normal subgroups of finite groups.** pp. 34--37

*Summary:* Connections between lattices of normal subgroups of finite group and its projectors are studied.

**ИНФОРМАТИКА**

*Rylov A. S.*
**On speaker recognition by VQ-space of speech parameters.** pp. 38--41

*Summary:* A function analogy of same procedures in two well known methods of speaker recognition are shown. In the first method, HMM-parameter eigenspaces are compared and in the second method, VQ-parameter spaces are compared. It is shown that the first method is insignificantly reliable then the second method. But the second method has many advantages. Therefore, it is concluded to use the VQ-parameter spaces for speaker recognition.

**ФИЗИКА**

*Lukashevich M. G., Popok V. N., Odzaev V. B., Lukashevich S. M., Khaibulin R. I., Bazarov V. V.*
**Electron-transport properties and Anderson transition in polyimide films implanted by cobalt ions.** pp. 42--47

*Summary:* Temperature dependence of resistance is studied for polyimide (PI) samples implanted by Co^{+} ions with fluences of 2.5 x 10^{16} -- 1.25 x 10^{17} cm^{-2} at ion current densities of 4.8 and 12 µA / cm^{-2}. It is found that electron transport in the implanted samples originates from radiation-induced changes of the PI and Co nanoparticle formation and it depends dramatically on ion current density. A variable range hopping mechanism dominates for all fluences at a low ion current density of 4 µA / cm^{-2} while a transition to a semimetallic type of conductance is observed with an increase in ion current density due to agglomeration of the Co nanoparticles forming a percolation way for the charge carriers. It is shown that both quantum effects of weak localisation and electron-electron interaction give a significant contribution to the transport mechanism.

**ХИМИЯ**

*Kolnenkov V. P., Samodurov V. P., Klimza S. V.*
**Tritium sorption in clays at water--clay interactions.** pp. 48--51

*Summary:* It is shown that different degrees of absorption are involved in interactions of clay rock -- tritiated (322 ± 3) KBk/1 hydrocarbonate -- calcium water. Tritium sorption runs by isotope exchange mechanism and the partition coefficient shows less than one value in all experiments. Clays are in the following sequence: palygorskite > bentonite > kalinite by their absorption capacities. Practically, acid (HCl) and alkaline (NH_{4}OH) medium does not change this sequence. The analogous result observed in Ca-, Na- and NH_{4}-forms of the same alumosilicates.

*Ulyanova T. M., Krut'ko N. N., Titova L. V., Medichenko S. V.*

**Structure and properties of implant material for bone tissue regeneration.** pp. 52--56

*Summary:* The processes of implant grafting material preparation and its physical-chemical properties were investigated. A conformity of composition, crystal and porous structures of synthesized material and mineral matrix of human bone was established. Based on this investigation, a new bone-replacing material (porous calcium phosphate, shape-stable ceramics with the structure of hydroxyapatite) has been developed. This ceramics is biologically compatible with soft and bone tissues, not toxic, it does not have heavy metals and poisonous impurities bad for the body. Medical tests in the clinics in the Republic of Belarus showed good results and supported a feasible use of a porous calcium phosphate material "KAFAM" for surgical grafting.

**БИОЛОГИЯ**

*Astapovich N. I., Golovneva N. A., Shchetko V. A., Kondratieva L. V., Grel M. V.*

**On mechanism of antimicrobic activity of Bifidobacteria.** pp. 57--61

*Summary:* It was shown that antimicrobic activity of Bifidobacterium adolescentis MC-42 and Bifidobacterium bifidum 791 againts some gram-negative and gram-positive bacteria was determined by several different factors. In addition to synthesis of organic acids, growing bifidobacterium produced antagonistically active compounds of protein-peptide nature -- bacteriocin-like agents, showing activity mainly with respect to closely related species. Inhibiting agents are thermostable, glucanaseresistant, showing sensitivity to trypsin. Maximum production was observed at the end of logariphmic phase of Bifidobacteria growth.

*Tsvirko L. S.*

**Peculiarities of rabies pathogen circulation on reserve and adjacent territories in Polesie.** pp. 62--66

*Summary:* This paper presents materials of retrospective and current analyses of the situation concerning rabies on specially guarded territories in the Gomel Region and measures for prophylaxis of the infection.

*Soltanov V. V., Komarovskaya L. M.*

**Changes in efferent firing of the splenic nerve induced by application of lipopolysaccharide E. coli into the stomach of rats before and after vagotomy.** pp. 67--70

*Summary:* In acute experiments on rats (thiopental sodium anesthesia, 70 mg/kg, intraperitoneally), it was found that application of 10 µg lipopolysaccharide E. coli (LPS) in isotonic solution of NaCl into the stomach was accompanied by inhibition (for 1.5 h and more) of the efferent firing of the splenic nerve. The effect persisted after vagotomy even when the agent in a dose 1 µg, being ineffective before, was used. The existence of a mechanism of interoceptive influences on the immunocompetent function of the spleen is suggested.

*Titovich O. I., Eroshevskaya L. A., Kvach S. V., Barai V. N., Zinchenko A. I.*

**Biotechnological approach to preparation of double-stranded polynucleotide complexes containing modified nitrogen bases.** pp. 71--74

*Summary:* A new approach to preparation of double-stranded polynucleotide complexes containing modified nitrogen bases is suggested. It consists in a consecutive transformation of modified bases into homoribopolynucleotides that are able to form double-stranded helices in water solutions, using cells and enzymes of Escherichia coli, Erwinia herbicola, Saccharomyces cere-visiae and Enterobacter amnigenus as biocatalysts.

*Chernyakova Yu. M., Kadolich Zh. V., Pinchuk L. S., Nikolaev V. L, Tsvetkova E. A., Beloenko E. D.*

**Tribiological properties synovia as criterion of functional deficiency of joint lubrication.** pp. 75--79

*Summary:* The results of tribological investigations aimed at estimation of functional disorders of the joint synovial fluid are described. The friction coefficients of movable metal-polymer joints simulating endoprosthetic friction joints have been determined at lubrication by human synovia with different pathological degrees. The dynamics of the friction coefficient variation have been studied at the lubricating layer exposure to the electromagnetic field simulating the biofield of a natural joint. It was the first time when the spectra of thermostimulated currents of the healthy and pathologic synovia were obtained and interpreted.

*Liakhnovich G. V., Kabachevskaya E. M., Volotovsky I. D.*

**Role of phospholipases С and D in phytochrome signal transduction in plant cell.** pp. 80--82

*Summary:* The phospholipase C (PLC) inhibitors lithium ions (Li^{+}) and neomycin were shown to decrease the effect of red light illumination on the oat phospholipase D (PLD) activity. Using the experimental results and literature data the regulation of PLD activity by light was suggested to occur according to the following scheme: light ® tphytochrome ® PLC ® ¯-PIP_{2} ® ¯PLD.

**НАУКИ О ЗЕМЛЕ**

*Karataev G. I., Belov Yu. V.*
**Gravity monitoring in Belarus: new data and interpretation.** pp. 83--86

*Summary:* Gravity monitoring has been conducted for many years on the territory of Belarus. Abnormal changes of the field in time are revealed. Interpretation of these anomalies is given: they are conditioned with deep density heterogeneities of the Earth's crust corresponding to layers of high electric conductivity.

*Rylova T. B., Savchenko I. E.*

**Reconstruction of paleotemperatures of the Belaya Vezha and Mogilev interglacial periods in Belarus.** pp. 87--91

*Summary:* Data of the palynological analysis served as the base for the reconstruction of paleotemperature indexes for each of 8 regional pollen zones revealed in the sediments of the Byelovezhian Interglacial of the Belarus Pleistocene. Proposed pa-leotemperatures for the Mogilevian Interglacial are reconstructed only for the time of climatic optimum. Reconstructions were carried out with the application of the method of plant "climatic areas" combination plants -- components of the studied floras.

*Tsiumentsav V. L.*

**Submeridian lithologic zonality of the Sargaevo and Semiluki deposits in the Savichi and adjacent areas subject to directions of oil exploration.** pp. 92--94

*Summary:* Submeridian lithologic zonality controlled by pre-platform tectonics has been revealed in the Sargaevo and Semiluki deposits in the Savichi and other areas. We suggest conducting a purposeful research on nature and degree of influence of pre-platform faults on lithology and dislocation of subsalt region of sedimentary cover in Pripyat Trough on the whole.

*Ovsiannikova S. V., Smith J. T., Kudelsky A. V., Madruga M. J., Pashkevich V. I., Yankov A. I.*

**Behaviour of radioactive cesium in bottom sediments of stagnant lake.** pp. 95--101

*Summary:* Behaviour of ^{137}Cs in bottom sediments of undrained lake located within Belarusian Chernobyl zone has been studied. The reserves of radionuclide exchangeable form, the cationic exchange capacity of selective ^{137}Cs sites ([FES], [HAS]) in the undrained lake, the rate parameters of ^{137}Cs vertical migration and the radionuclide distribution coefficients between the solid phase and the pore water of the bottom sediments have been established. The obtained data on the coefficients of selectivity (K_{c}NH_{4}/K)) show that ammonium influence on mobility of ^{137}Cs in the studied lake is higher than that of potassium, especially in winter period.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Mikulik N. A., Reyzina G. N.*
**Development of factor models and applications for solution of problems of vibration loading of vehicle cushioning systems.** pp. 102--106

*Summary:* Idea and the concept of analysis of vibration loading of cushioning systems are stated on the basis of mathematical tool and oscillations of complex dynamic systems. Application modules for vibration loading analyses are developed.

*Gordienko A. I., Kozhuro L. M., Kheifetz M. L., Koukhta S. V.*

**Use of analogy parameters for development of combined physical-chemical material processing methods.** pp. 107--110

*Summary:* Criteria describing domination of controllable parameters of technological system are presented. Development of plasma-mechanical, electromagnetic and electron-beam superficial methods of processing of constructional materials is considered.

*Vereschyagin M. N., Goransky G. G., Tseluev M. Yu., Kiriluk S. I., Tselueva S. N.*

**Influence of production conditions on physical and mechanical properties and structure of amorphous Fe-Ni-Co-Cr-Mo-B-Si alloy.** pp. 111--114

*Summary:* We show the results of study of structure and physical and mechanical properties of amorphous Fe-Ni-Co-Cr-Mo-B-Si alloy after rapid quenching and its structural peculiarities during the annealing at crystallization temperature. Direct connections between physical and mechanical properties and structure of amorphous alloy and its production conditions are confirmed.

**СОЦИАЛЬНО-ГУМАНИТАРНЫЕ НАУКИ**

*Sadovskaya T. V.*
**National information goods and services market grouping.** pp. 115--118

*Summary:* Current state and problems of functioning of the market of information products and services in the Republic of Belarus are analyzed. Main trends and scientific recommendation to form and regulate the development of the national market are offered.

*Burakov V. S., Dovnar-Zapolsky A. S., Kiris V. V., Kolymago N. V., Naumenkov P. A., Plavinsky N. A., Raikov S. N., Skripchenko T. S.*

**Laser spectral microanalysis of glass bracelets of XI--XIII centuries within the Minsk Fortress.** pp. 119--124

*Summary:* Spectrometer for laser microanalysis of solid-state samples, in particular archeological findings from museum funds is developed and approved. The quantitative analysis of chemical composition of fragments of the glass bracelets found at excavation within the Minsk Fortress and dated XI--XIII centuries is carried out. Specific features of element composition of glass matrixes and impurities of the researched samples characteristic only for the given series of samples are revealed.

/ Издания академии / Научные журналы / К началу страницы

Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: *15 ноября 2006 г.*

Создана при участии Игнатия И. Корсака

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