# Доклады Национальной академии наук Беларуси, 2004, Том 48, No.1

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2004, Том 48, No.1

## СОДЕРЖАНИЕ

**To the Readers of the Journal "Doklady NAN of Belarus".** p. 5

**МАТЕМАТИКА**

*Osinovskaya A. A.*
**Restrictions of irreducible representations of algebraic groups of types E**_{n} and F_{4}, to naturally embedded A_{1} -subgroups and the Jordan block structure of unipotent elements. pp. 6--9

*Summary:* The irreducible *p*-restricted representations of algebraic groups of types E_{n} and F_{4} in characteristic p > 0 are studied. Composition factors of the restrictions of such representations to naturally embedded A_{1} -subgroups are found. Jordan block sizes of root unipotent elements of such groups in representations with locally small highest weights with respect to p are determined.

*Chernyavsky A. F., Evdokimov A. A., Kolyada V. V., Revinsky V. V.*

**Recursive minimally redundant interval-modular numerical systems.** pp. 10--14

*Summary:* New class interval-modular numerical systems for precision calculations are offered. In comparison with known analogues, the given systems provide essential simplification of non-modular operations, reduction in base sets of tables and types of functional sites, reduction of number of typical parts of algorithms of arithmetics, and substantial increase in flexibility of regulation of calculation accuracy.

*Gabasov R., Kirillova F. M. *

**Principles of optimal control.** pp. 15--18

*Summary:* Three principles of optimal control are analyzed for linear optimal control problems (open-loop control, closed-loop control and on-line control). The optimal on-line control principle is applied to the on-line stabilization of dynamical systerns by bounded controls.

*Yanovich L. A., Gulo I. N.*

**Asymptotic estimates for a class of Wiener integrals in space of functions of two variables.** pp. 19--23

*Summary:* Asymptotic formulas for special functional integral with large parameter with respect to Wiener measure in space of functions of two variables are obtained.

*Kavaleuskaya E. I.*

**Diophantine approximation with respect to different valuations.** pp. 24--27

*Summary:* We prove an analogue of the convergence part of Khinchine's theorem for simultaneous approximation of zero in **R** x **C** x **Q**_{p} by values of polynomials P_{n}(y) Î Z[y].

*Suprunenko I. D.*

**The minimal polynomials of unipotent elements in irreducible representations of the symplectic group over a field of characteristic two.** pp. 28--31

*Summary:* The minimal polynomials of the images of unipotent elements in rational irreducible representations of the symplectic group over a field of characteristic 2 are found. If the image of a representation does not coincide with the standard realization of the group considered, the degrees of these polynomials are almost always equal to the orders of the relevant elements. All exceptions are connected with some elements of order £ 16 and are indicated explicitly. The solution of a similar problem for the classical algebraic groups in odd characteristic and for the special linear group in characteristic 2 has been announced by the author in this journal [2001. Vol. 45, N 3. P. 41-44] and [2003. Vol. 47, N 5. P. 9-13].

*Gaishun I. V.*

**Invariant subspaces and invariability to perturbations of two-parameter discrete systems.** pp. 32--34

*Summary:* Let å be a two-dimensional discrete system. An invariable subspace for å is defined. Some conditions of independ ence of output for the system å from perturbations are obtained.

*Zabreiko P. P., Shevelevich K. V.*

**The Hicks and Le Chatelier -- Samuelson theorems for linear integral equations.** pp. 35--39

*Summary:* This paper deals with analogues of the Hicks and Le Chatelier -- Samuelson theorems for linear integral equations. It is proved that analogues of these theorems hold for nonnegative integral operators if corresponding economic system is productive. In particular, the criterion of productivity in *L*_{p} and *C* is given.

*Kharin Yn. S.*

**Markov chains with ***r*-partial relations and their statistical estimation. pp. 40--44

*Summary:* A new general small-parametric model MC (*s, r*) called Markov chain of the order s with *r*-partial relations is proposed. Statistical estimators of the parameters of MC (*s, r*) are constructed and their probabilistic properties are analyzed.

*Rybak I. V.*

**Monotone and conservative difference schemes for equations with mixed derivatives.** pp. 45--48

*Summary:* In the paper, for multidimensional elliptic and parabolic equations with mixed derivatives, conservative difference schemes of the second order of approximation are developed. The proposed schemes satisfy the grid maximum principle both for constant-sign and alternating-sign coefficients at mixed derivatives. For the developed algorithms, the a priori estimations of stability and convergence in the grid norm *C* are obtained.

*Gorbuzov V. N., Pronevich A. F.*

**Integrals of ****R**-linear systems in exact differentials. pp. 49--52

*Summary:* A spectral method of construction of the first integrals basis for **R** - linear systems in exact differentials is elaborated.

**ФИЗИКА**

*Korshunov F. P., Kurilovich N. F., Prokhorenko T. A., Shesholko V. K., Bumai Yu. A.*
**Influence of treatment in hydrogen plasma and gamma irradiation on spectrum of defects in unalloyed ***n*-GaAs monocrystals. pp. 53--56

*Summary:* Influence of treatment in hydrogen plasma and y-quanta irradiation on energetic spectrum of defects in unalloyed n-GaAs monocrystals has been investigated with DLTS method. The hydrogenation of the investigated crystals leads to disappearance of EX1, EX2 and EX3 bands that are the macroscopic defects in the surface regions of crystals, to increasing in EL2 traps concentration and to reconstruction of EL5 defect into EL6 and EL14 ones. After irradiation of the investigated crystals, the bands E1(E2) appeared in DLTS spectra, that are the radiation defects. These traps concentrations (both in hydrogenated and unhydrogenated crystals), EL6 and E3 traps concentrations (in hydrogenated crystals) increase when irradiation dose increases. The concentrations of EX1, EX2 and EX3 defects in irradiated unhydrogenated crystals decrease when irradiation dose increases. Concentration of defect EL2 decreases when irradiation dose increases at small irradiation doses and is invariable at further irradiation.

*Tomilchik L. M., Tolkachev E. A., Kisel V. V., Tereshenkov V. I.*

**Particle motion in magnetic-type field on the curved D = (1+2) space-time background.** pp. 57--59

*Summary:* Problem of motion of a charged probe particle and a particle with isospin in D = (l+2)-dimensional space-time in rota-tionally symmetric gravitating magnetic (chromomagnetic) field is considered. The generally covariant Hamilton-Jacobi equation is solved in quadratures. It is shown that the particle motion is finite.

**ХИМИЯ**

*Kostyuk N. N., Dick T. A., Trebnikov A. G.*
**Synthesis and physicochemical analysis of Sm (II, III) acety-lacetone chelate complexes.** pp. 60--64

*Summary:* Sm (II, III) acetylacetone chelate complexes were synthesized by electrochemical method. It was shown that anode dissolution of the metal samarium over acetylacetone leads to formation of the Sm (II, III) chelate complexes: xSm(acac)_{2} • ySm(acac)_{3} • zHacac. Factors *x*, y and *z* depend on quantity of the electricity, which flew through the electrolysis cell.
The compositions of the obtained substances were confirmed by the physicochemical analysis (ultimate analysis, IR-, mass spectroscopy and thermal analysis (thermogravimetric, isothermal warming-up and differential scanning colorimetry).

*Kuchuro S. V., Rakhuba G. N., Rubinov D. B., Zheldakova T. A., Babitskaya S. V., Litvinko N. M.*

**3,5-disubstituted thiotetronic acid derivatives -- new inhibitors of secretor phospholipases A**_{2}. pp. 65--68

*Summary:* Inhibitory effects of synthesized *de novo* thiotetronic acid derivatives on the activity of secretor phospholipases A_{2} with different specifity (*Naja naja oxiana* snake venom PLA_{2}) and pancreatic PLA_{2} have been studied.

**БИОЛОГИЯ**

*Yakushev B. I., Efremov A. L., Matusov G. D., Sak M. M.*
**Methods of soil sample selection during radio-ecological monitoring in natural phytocenosis.** pp. 69--71

*Summary:* It is elaborated a method for study of radioactive contamination of the soil (Ci/km^{2}). It is recommended to take soil samples at a point with middle value of gamma radiation exposure dose on the surface of the soil for a plot.

*Shimko V. E., Kulminskaya I. V., Kalitukho L. N., Gordei I. A., Kabanova S. N.*

**Structural and functional distinctions of photosynthetic apparatus in inbred lines of winter rye (Secale cereale, L.) in view of productivity.** pp. 72--76

*Summary:* High- and short-stalked inbred lines of winter rye were revealed to differ in the content and dynamics of photosynthetic pigment accumulation, in parameters of photosynthetic activity and relationship between these traits and elements of productivity and morphostructure at various developmental stages of plants. The lines with clear genotypic differences in structural and functional characteristics of photosynthetic apparatus were selected.

*Kirillov V. A., Stebenyaeva E. E., Paplevka A. A., Demidchik E. P.*

**Morphometric changes in the population of lymphoid cells of cervical lymph nodes with papillary cancer metastases.** pp. 77--80

*Summary:* With the help of morphometry, it has been shown that with regional metastases of thyroid papillary cancer, a change in the ratio of small and large lymphocytes in cervical lymph nodes tissue occurs. Cellular mechanism of morphometric changes in the population of the lymphoid series cells in the focus of metastases localization is discussed. It is proposed to use the revealed regularities for diagnosis of papillary cancer regional metastases by noninformative cytological preparations.

*Savchenko G. E., Klucharcva E. A., Kabashnikova L. F.*

**Protochlorophyllide accumulation and photoreduction system in coleoptiles of etiolated cereal seedlings.** pp. 81--83

*Summary:* It was shown that protochlorophyllide (Pchlde) forms with maxima at 630 and 655 nm in fluorescence spectra (-196 °C) were present in coleoptiles of etiolated seedlings of different cereals. Their relative contents were changed along the organ. Under irradiation in vivo (20 °C), the Pchlde 655 was transformed into chlorophyllide with maximum at 693 nm. The results indicate the presence of photodependent Pchlde-oxidoreductase in coleoptiles.

*Prokhorov A. V.*

**Xenotransplantation in treatment of insulin-dependent diabetes mellitus (immunological and morphological assessment).** pp. 84--87

*Summary:* This paper presents the results of the morphological investigations of macroincapsulated islet cells of the pancreas of rabbit fetuses transplanted into the abdominal area of the aorta of 12 dogs with alloxanin-induced diabetes mellitus. The investigations showed that xengenic islet cells in the blood stream were not rejected and preserved all morphological signs of vitality. Parallel investigations of the immunological status of 11 patients with insulin-dependent diabetes mellitus demonstrated that after xenotransplantion of b-cells in the blood stream, there were no significant changes in activation of lymphocytes and in accumulation of cytotoxic immune complexes. Post-operative follow-up during the period over 2 years showed that xenotransplantation was a rather effective method of surgical treatment of diabetes, and immunoisolation of cells and their transplantation into the blood stream allowed to overcome the immunological barrier of the recepient without the immunosuppressive therapy.

**НАУКИ О ЗЕМЛЕ**

*Aizberg R. Ye., Garetsky R. G., Kudriavcts I. D., Starchik T. A.*
**On tectonics of the Orsha Depression and its correlation with basement structures.** pp. 88--92

*Summary:* New data obtained from regional seismic profiling with CDP method and some other geological and geophysical evidences available were used to justify that the Orsha Depression is bounded in the north by a high-amplitude fault and the basement surface sinks to the north-west of the Valdai Graben. Numerous concordant and disconcordant slip faults (their vertical amplitude ranges from tens to 560 metres) have been revealed in the bottom part of the platform cover. A mechanism of inheritance of some features of the old structure of the crystalline basement was proved to be of considerable importance in the Orsha Depression evolution.

*Abravets S. M., Veres S. A.*

**Valavsk deltas complex in the Devonian deposits in the South Pripyat Polcorift.** pp. 93--99

*Summary:* The Valavsk fan deltas found within the Pripyat Trough are described by thick (up to 600 m) deposits formed, in the Early Famennian time. Similar complexes form rather thick sequences near the boundaries of highlands, where a delta is developed at the margins of piedmont alluvial fans. Fan deltas found within the territory of the southern part of the Pripyat Trough in intersalt deposits have some features and structural peculiarities in common with similar formations distinguished and studied in other regions. The alluvial fan models could be most likely applied properly to regions that are paleorift structures like the Pripyat Trough.

*Tsiumentsau V. L.*

**Clay container rocks in oversaline Devonian deposits in the North Pripyat Trough.** pp. 100--102

*Summary:* Based on core samples and data of industrial geophysics and results of fluid intrusion tests, unconventional clay interstitial high-capacity bazhenite-like container rocks revealed in oversaline Devonian deposits in the North Pripyat Trough, which increases potential oil-bearing capacity of these deposits.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Sheleg V. K., Pyatov V. V., Kovchur A. S.*
**Calculation of temperature fields in elements of screw press.** pp. 103--109

*Summary:* Study of temperature fields in elements of screw press at formation of powder materials are conducted. The axis-symmetric task of the theory of heat conductivity is solved by a method of the final integrated transformations suggested by G. A. Grinberg in 1946. Temperature fields are found as expansion in series by own functions of corresponding homogeneous task of Storm -- Liouville.
Results of calculations can be used for development of new process technologies and screw equipment in powder metallurgy, especially sensitive to temperature influences.

*Spiglazov A. V., Stavrov V. P., Sviridyonok A. I.*

**Friction influence on viscous flow of high-filled thermoplastic compositions compressed between two parallel-sided plates.** pp. 110--113

*Summary:* The laws of viscous squeeze flow of a disk and sliding at the border are investigated at compression of a high-filled thermoplastic compositions between two parallel plates. The adequacy to model of power-law non-Newtonian fluid with friction on a contact surfaces is experimentally proved.

**СОЦИАЛЬНО-ГУМАНИТАРНЫЕ НАУКИ**

*Nikitenko P. G.*
**Noospheric thinking formation as a claim of the XXI century.** pp. 114--119

*Summary:* There have been considered the problems and ways of the Belarusian model of the innovational sustained development in the context of the planetary civilizational process, globalization and noospherization.

*Palchikov N. N., Sayanova I. G.*

**Analysis of building of profit on completed construction and assembling work.** pp. 120--124

*Summary:* It is necessary to intensify the analysis of financial results, because they are the main instant of forming financial stability of a company and one of the basic principles of improving well-being of the workers.
In modern publications on financial result analysis, oversimplified method of analysis is used. This method does not consider influence of all factors on financial results forming. The basis volume for financial result analyses is total receipts (netto) reflected in Income Statement. Total receipts (netto) is derivative receipts index reflected in the account "Sales" and many factors connected with VAT and other payments from receipts (brutto) influence on receipts forming.
Thus, the detailed analysis of financial results forming beginning with receipts (brutto) with learning tax and tax-free payments, which influence indirectly upon receipts forming (netto) will allow building company to evaluate the value of financial results forming more really and objectively influence on financial stability of building company.

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

Создана при участии Игнатия И. Корсака

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