# Доклады Национальной академии наук Беларуси, 2005, Том 49, No.3

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2005, Том 49, No.3

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Ismailov Z. I.*
**Discreteness of the spectrum of the normal differential operators of second order.** pp. 5--7

*Summary:* In this work, in the Hilbert space of vector-functions on a finite interval all normal extensions of the minimal operator generated by the differential-operator expression of second order are described in terms of abstract boundary conditions. Furthermore, the discreteness of a spectrum of these extensions is studied.

*Benediktovich V. I.*

**Noncrossing subgraphs in topological graph ***K*_{3,3}. pp. 8--13

*Summary:* It is proved that in arbitrary simple topological graph *K*_{3,3} there exists a noncrossing Hamiltonian path if the number of all crossings in the graph is not equal to 9 and there always exists a noncrossing spanning tree.

*Voroshilov A. A., Kibas A. A.*

**Cauchy-type problem for the diffusion equation of fractional order.** pp. 14--18

*Summary:* The Cauchy-type problem for the linear differential equation with the Riemann--Liouville partial fractional derivative of positive order with respect to time is investigated. The equation under consideration generalizes the heat equation and the wave equation. Using direct and inverse Laplace and Fourier transforms, a closed solution of the above problem is found in terms of a sum of the convolutions of the special Wright functions and of the given functions from the initial conditions.

*Kurdina M. A.*

**Properties of the solutions of nonlinear parametrical optimal control problems in the neighborhood of a regular point.** pp. 19--23

*Summary:* Properties of the solutions of nonlinear parametrical optimal control problems with minimal energy in the neighborhood of a regular point are investigated. It is proved that in this case changing the initial condition does not change the structure, and determining elements are determined by solving a system of nonlinear equations.

*Pesetskaya T. I.*

**Study of the problem of a priori estimation of posteriori distributions for control systems with disturbances.** pp. 24--29

*Summary:* A problem of a priori estimation of posteriori distributions for control systems with disturbances (a pre-posteriori analysis problem) that is a new theoretical element in the area of output control under uncertainty conditions is studied. A notion of a positional solution of the problem under consideration is introduced. An approach for solving the problem of the pre-posteriori analysis and the algorithm for constructing realizations of its positional solutions in real time are developed.

*Yanovich L. A.*

**Hermite--Birkhoff interpolation formulas for functions of matrix variable.** pp. 30--33

*Summary:* The interpolation formula of special kind for functions of matrix variable is constructed, when the knots are scalar matrixes. The class of matrix multinomials, for which this formula is invariant, is indicated. Representation and estimation interpolation are obtained.

*Velichko M. V.*

**Jordan block structure of root elements in irreducible representations of simple algebraic groups.** pp. 34--37

*Summary:* The Jordan block structure of images of root elements in irreducible *p*-restricted representations of algebraic groups of type *A*_{2} in characteristic *p* is described. As a rule, almost all a priori possible dimensions of Jordan blocks occur; all exceptions are indicated explicitly. This description enables one to solve the same problem for a wide class of representations of simple algebraic groups.

*Matysik O. V.*

**Regularization of the operator equations in the Hilbert space.** pp. 38--43

*Summary:* A new implicit method for solution of the operator equations in the Hilbert space is proposed. Convergence of a method is proved in the case of an *apriori* choice of a number of iterations, error estimations are obtained. The case of nonuniquencss of the solution of the equation is investigated. For the proposed method the opportunity of the application of the residual stop rule and the rule of neighboring approximations is proved.

**ФИЗИКА**

*Shwed O. L.*
**Theory of elastoplastic materials with finite elastic strains and rotations.** pp. 44--48

*Summary:* The classical geometrically nonlinear model of an ordinary elastic medium is generalized to the elastoplastic one. The state equation is taken in the form of the generalized Mumagan law. The criterial deviator is defined, the hyperelastic medium in the active process becomes hyper-plastic. This condition is introduced using the objective O-derivative. The spin of the rotation tensor that accompanies the elastic deformation in the active process is obtained. The deviator section of the finite surface is found. A new method for considering the Baushinger effect is obtained. Determining velocity equations for tensors, scalar functions and theory parameters are postulated. Elastic deformation distortion tensors are determined. Plastic deformations and rotations (turns) are found from the Krener-Lee expansion. The dual description of the process in terms of actual and unloading configurations is obtained that eliminates the rotation (turn) effect. Strengthening parameters of the R. Shmidt type are introduced. Both aspects of the strengthening phenomenon are described. The Savar effect is described.

*Makarenko L. F., Korshunov F. P., Lastovski S. B., Gurinovich V. A., Zamjatin N. I.*

**Determination of defect occupancy levels in semiconductors from DLTS data.** pp. 49--51

*Summary:* A method to determine the occupation function and ionization enthalpy for defects in semiconductors from the data of DLTS-mcasurements is proposed. The range of charge carrier concentration over which it is possible to observe the temperature dependence of DLTS-peak amplitude S_{max}(T) for metastable defects is calculated. Experimental test of the proposed method is carried out for divacancies in silicon crystals with the resistivity of 4 kW cm and 2 kW cm. It is assumed that the proposed method can be used for identification of defects with negative correlation energy.

*Kudryashov V. V., Tomilchik L. M.*

**Model with a hyperbolic space metric for single-electron states in a quantum dot.** pp. 52--55

*Summary:* In order to describe single-electron states in a semiconductor quantum dot, the new model is proposed which is based on using a generalized quadratic in momenta kinetic energy induced by introduction of a two-dimensional space hyperbolic metric. The exact wavefunctions are obtained. The corresponding energy spectrum contains a finite number of terms.

**ХИМИЯ**

*Dostanko A. P., Kaidau A. L., Vasflevich V. P., Stepanenko V. N., Khitko V. I., Vinogradov L. M., Akulich A. V., Vasilevich A. V., Hlushko E. V.*
**Energy-saving technology of producing polysilicon from secondary raw materials of processing of apatites at the Gomel Chemical Factory.** pp. 56--60

*Summary:* The new production technology of solar-grade silicon from silicon is presented. Research results of the major technological processes are described. The efficiency of application at the final stage of a fluidized bed reactor is shown

*Kisselev P. A., Schwartz D., Kisseleva S. N., Bovdey N. A., Roots I.*

**High-selective hydroperoxide-dependent metabolism of 17b-estradiol and estrone to their procancerogenic hydroxiderivatives by human cytochrome P-450A1.** pp. 61--64

*Summary:* Oxidation of 17b-estradiol (E2) and estrone (E1) was studied in the enzymatic system consisting of human recombinant cytochrome P-4501 A1 and cumene hydroperoxide. As reaction products only procancerogenic 2-OH- and 4-OH- metabolites of both E1 and E2 were formed. The functional role of this reaction was discussed.

**БИОЛОГИЯ**

*Mikheyeva T. M., Genkal S. I.*
**Changes in the species composition of plaktonic centrophyceae diatom algae in Naroch ecosystem lakes during evolution of their trophic state.** pp. 65--69

*Summary:* The Naroch lakes (Naroch, Myastro, Batorino) have passed different periods of evolution of their trophic state: 1) the period with insignificant antropogenic load, 2) the period of antropogenic eutrophication and 3) the period of deeutrophication that was accompanied by structural changes and unstable state of phytoplankton communities. The invasion of some new and disappearence of aboriginal species of centric diatom algae was discovered in the lakes. In the period of deeutrophication the invasion of *Cyclotella comensis* Grun. that was mentioned for the Belarus territory only as a fossil representative was revealed in three lakes. The data on seasonal dynamics and interyear abundance fluctuations of this species during 12 years period (1992--2003) are presented. In the Naroch lake the new for sciense species *Cyclotella narochanica* (Genkal et Mikheeva sp. nov.) and in the Naroch and Myastro lakes the new for algae flora of Belarus species *Stephanodiscus heterostylus* (Hakansson et Meyer) were discovered.

*Titok M. A., Prokulevich V. A., Janniere L.*

**Influence of replication factors during the process of maintenance of plasmid ***Bacillus subtilis* pBS72. pp. 70--75

*Summary:* Replication of a low copy number, *Bacillus sublilis* plasmid, pBS72 requires two elements, the initiator protein RepA and the iteron-containing origin. It also requires host-encoded primosomal proteins DnaB, DnaC, DnaD, DnaG and Dnal, DNA polymerases DnaE and PolC, polymerases DnaN and DnaX, but not the two primosomal initiators DnaA and PriaA or helicasc PcrA and DNA polymerase I. From this, it is inferred that the plasmid replication function is of theta type and is carried out by a replication fork indistinguishable from that of the chromosome. Initiation of plasmid replication likely involves the hostencoded minor DnaD pathway of primosome loading since it is independent of DnaA and PriA that activate the two major primosomal systems. The RepA protein is proposed to strongly stimulate this pathway for acting at the plasmid origin. Stability studies strongly suggest that the partition of low copy number Gram-positive plasmids can be ensured by replication functions. Replication proteins DnaB and Dnal were identified as key elements in this process. By analogy, it is proposed that replication factors are pivotal components of the chromosome partition apparatus in *Bacillus subtilis*.

*Koroleva N. Yu., Gordei I. A., Peneva T. I.*

**Spare proteins of seeds -- genetic markers of secalotriticum genome expression.** pp. 76--79

*Summary:* A new type of rye-wheat amphidiploids secalotriticum rye Novosibirskaij x Triticale L246 (S246) and its parent forms (rye Novosibirskaij and triticale L246) is investigated by the method of proteins markers. It is shown by the comparative analysis of expression of the proteins complex in secalotiticum with its parent forms that in a considered sample of secalotriticum the expression of rye genome IRS chromosomes is legible. Secalotriticum S246 can be used in the selection of rye-wheat amphidiploids with the well defined expression of rye genome.

**МЕДИЦИНА**

*Demidchik Y. E., Demidchik E. P., Gedrevich Z. E., Reiners C., Kondratovich V. A., Biko J., Saenko V. A., Mine M., Yamashita S., Mankouskaya S. V.*
**Childhood thyroid carcinoma: prognostic factor.** pp. 80--85

*Summary:* The study was aimed with evaluating the results of surgical treatment and follow-up in a large group of operated thyroid cancer patients under 15 years old to identify risk factors for recurrences. The group included 737 pediatric patients with papillary and follicular carcinomas. The mean follow-up period was 96.6 months (1.5--220.2 months range). Recurrences were detected in 200 (27.1%) cases, including 73 (9.9%) local relapses, 89 (12.1%) distant failures, and a combination of local and distant failures in 38 (5.1%) patients. The multivariate logistic regression revealed the following independent parameters significantly associated with the risk of lymph nodes involvement: young age at diagnosis, multifocal carcinomas, N1 status and non-fulfilled ipsilateral or bilateral neck dissection. For lung metastases, the significant risk factors were females, infants at diagnosis and the presence of symptoms.

**НАУКИ О ЗЕМЛЕ**

*Konischev V. S.*
**Cornices in Famennian salt uplifts of the Prypyat trough.** pp. 86--89

*Summary:* Cornices described in Famennian salt massifs of the Pripyat Trough include both the injection ones and those enveloped by overlying deposits.

*Makhnach A. A., Peryt T. M., Halas S.*

**On the isotope composition of sulphur and oxygen of sea water sulphate in the middle and late Devonian.** pp. 90--94

*Summary:* On the basis of the investigation of the sulphur and oxygen composition of sulphate minerals from the Middle and Late Devonian deposits of Belarus and the Ukraine, the most probable d^{34}S and d^{18}O values of marine sulphate in the Eifelian, Frasnian and Famennian are determined.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Timoshpolsky V. I., Pavlyukevich N. V., Mikhalev S. B., German M. L.*
**Calculation of radiative and convective heating of steel blanks in annular furnaces.** pp. 95--97

*Summary:* On the basis of the comparison of the results of solution of the nonlinear problem on steel blank heating in annular furnaces by the numerical method and the method of equivalent sources in a one-dimensional approximation, a possibility has been shown to use the latter for fast estimation of the heating time of a blank to the temperature of the heating medium.

*Antonjuk W. E., Berestnev O. W.*

**Basic principles of dynamic stabilization of the geometrical shape of details.** pp. 98--102

*Summary:* The basic requirements to a choice of the process of dynamic stabilization are formulated. The basic settlement formulas on purpose of a mode of dynamic stabilization are given. The results of research of dynamic stabilization are obtained.

*Kovalevskii A. A., Dolbik A. V., Lazarouk S. K., Labunov V. A.*

**Thermodynamic estimation of product accumulation due to electrochemical reactions in a porous silicon layer.** pp. 103--106

*Summary:* Calculstions of thermodynamic parameters, mainly, the izobaric-isothermal potential (Gibbs energy) for possible reactions at the porous silicon formation have been made in order to predict the product accumulation in a porous space. The most probable reactions are the hydrogen formation and the silicon hydride formation.

**СОЦИАЛЬНО-ГУМАНИТАРНЫЕ НАУКИ**

*Nikitenko P. G., Platonova L. A.*
**Problem of the enterprise choice for construction of a competitiveness management model.** pp. 107--109

*Summary:* The problem of the enterprise choice is solved for competitiveness management model construction. The choice's criterion is represented by the concrete enterprise competitiveness factor deviation from the average one for all analyzed enterprises.

*Fiodorova J. A.*

**Problem of the creative work in the labor activity of employees.** pp. 110--112

*Summary:* The problem of the creative activity is investigated from the positions of the civil law in jurisprudence. In the labour law the creative activity is considered basically as the feature of cerebration of the employees.
In the article it is proposed to investigate the creative activity in two aspects: as a kind of activity and as a feature of man's cerebration. The author made the conclusion that the professional creative activity of employees is a kind of the labour activity and its result is a creation of new material and spiritual values.
The author also investigated the features of material and spiritual values created by employees, the differences between the results of the creative activity and results of the brainwork which are not creative.

*Bychkova G. M.*

**National system of higher education in a context of modern social-economic processes.** pp. 113--118

*Summary:* The transition of the society to new social-economic managing conditions directly affects the system of higher education. Among the factors directly influencing the progress of the society, of special importance is the preparation of the highly skilled experts for all spheres of activity. The scientific staff of maximum qualification determines the development of economy and culture, the principles of functioning of the state and society. All spheres of the human activity are based on the modern science-consuming processes, and filling a national product, and also an index of the development of the human potential depends on their active realization. The education becomes a strategic field that provides the national security. The competitiveness of the country is judged through the level of the education preparation of the rising generation.

**АГРАРНЫЕ НАУКИ**

*Gusakov V. G.*
**Food safety and independence: urgency of fundamental researches and main tasks of their realization.** pp. 119--122

*Summary:* In the article the concept of the problem of food safety is given, its theoretical-methodological essence is defined. The definition of the categories of food safety and food independence is made, demonstrating their different nature and trend. The necessity of creating the special program of the basic researches "Food safety" is justified, in the context of which the purpose and tasks of the offered program are defined.

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Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: *12 ноября 2006 г.*

Создана при участии Игнатия И. Корсака

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