# Доклады Национальной академии наук Беларуси, 2005, Том 49, No.1

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2005, Том 49, No.1

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Sobolevsky S. L.*
**Movable singularities of the binomial ordinary differential equations of the third order.** pp. 5--9

*Summary:* The necessary and sufficient conditions of freedom from the movable critical singularities for the binomial irrational ordinary differential equations of the third order are presented. The principal scheme of the proof is given.

*Demchuk A. K., Makarov E. K.*

**Polynomial formulas for solution of the matrix equation AX - XA = C with the coefficient of simple structure.** pp. 10--14

*Summary:* An explicit formula for some particular solution of the matrix equation *AX - XA = C* is obtained when *A* is a simple matrix. This formula is polynomial with respect to *A* and *C*.

*Shishkcvich A. A.*

**Conjugation functor and aspherical pro-***p*-groups. pp. 15--17

*Summary:* The paper contains the results on the common properties of the conjunction functor in the category of finitely generated profinite *G*-modules. Besides, the structure of almost free aspherical pro-*p*-groups is investigated in detail.

*Matalytski M. A., Romaniuk T. V.*

**Mathematical analysis of the stochastic models for multi-type claim processing in insurance companies.** pp. 18--23

*Summary:* The mathematical analysis of the models for multi-type claim processing in insurance companies is made when the total number of insurance contracts may be a function of time. The closed in structure queueing networks serve as the models for claim processing.

*Osinovskaya A. A.*

**Restrictions of some representations of the symplctic group to the naturally embedded subgroups of type A**_{1}. pp. 24--26

*Summary:* Restrictions of the modular irreducible representations of the symplectic algebraic group to the naturally embedded long subgroups of type A_{1} are studied. Let w = m_{1} w_{1} + ... + m_{n} w_{n} be the highest weight of such a representation. The composition factors of such restrictions are determined in the case of m_{1} + ... + m_{n} + 3 £ *p* < m_{n-1} + 2m_{n} + 3, which completes the description of the restrictions of the classical algebraic groups to the naturally embedded *A*_{1}-subgroups.

*Pekarskii A. A.*

**One integral representation of the function of Hardy class ***H*_{p} for *p* £ 1. pp. 27--31

**ФИЗИКА**

*Ksenofontov M. A., Ostrovskaya L. E., Umreiko D. S., Vasilyeva V. S., Hatenko A. S.*
**Influence of intermolecular interactions on the oscillations of dioxibenzene molecules.** pp. 32--36

*Summary:* Based on the predictions of the frequencies and the forms of normal oscillations of the molecules of phenol and its derivatives (dioxibenzenes), the necessity is shown to transform the forced field of the above compounds in going from the model of free molecules (gas phase) to the condensed state that takes into account the onset of intermolecular interactions. A number of vibrational frequencies are estimated as characteristic ones, through which it is possible to make the spectral-structural analysis (including different conformations).

*Varaska Yu. A., Khodasevich M. A.*

**Gain equalization filter based on Fabry--Perots nonlinear interferometer for WDM systems.** pp. 37--40

*Summary:* A new type of a dynamic gain equalization filter for WDM systems is proposed. It is based on the use of Fabry--Perots nonlinear interferometer as a pump controlled amplitude mask in the scheme of Fourier-synthesis of short optical pulses. The results of numerical simulation show that the flat gain spectrum of wideband EDFA can be achieved in the proposed scheme at pumping power of units of mW and additional losses of units of dB.

*Artioukhina N. K., Shkadarevich A. P.*

**Classification of four-mirror anastigmats with a catoptic lens.** pp. 41--45

*Summary:* The classification of four-mirror anastigmatic optical objectives is given, and their aberrations are described. Different variants of designs are found. The problem of image plane protection from stray light is investigated. The plane -- field anastigmats are discussed.

*Saiko A. P., Markevich S. A.*

**Temperature hysteresis of the low-frequency combination-active phonon line in superconducting bismuthes.** pp. 46--49

*Summary:* A two-loop temperature hysteresis of the integral intensity of Raman light scattering for a line with a frequency of 50 cm^{-1} in a monocrystal of the superconducting oxide Ba_{1-x}K_{x}BiO_{3} is explained on the theoretical grounds.

*Lanin V. L.*

**Modeling of diffusion processes under the simultaneous action of ultrasonic and electromagnetic fields.** pp. 50--53

*Summary:* The modeling of the diffusion processes under the influence of US and EM fields at the formation of contact connections has increased a velocity and depth of components diffusion and has improved the properties of connections.

*Komarov F. F., Urbanovich A. I.*

**Temperature fields and track formation in the materials irradiated by highenergy ions.** pp. 54--58

*Summary:* The simulation of track formation in crystals irradiated by high-energy ions has been carried out in the framework of the two-temperature model. The hyperbolic equation for thermal diffusivity has been used for describing a lattice temperature. It has been shown that for short times the lattice temperature increases quadratically with time, while the usual parabolic equation gives a linear time dependence.

**ХИМИЯ**

*Ratko A. I., Shashkova I. L., Milvit N. V., Lesnikovich A. I.*
**Prospects for the use of calcium and magnesium phosphates for the chemosorptional removal of heavy and non-ferrous metals from solutions.** pp. 59--63

*Summary:* The features of the heavy and non-ferrous metal ion chemosorptional removal from the solution by calcium and magnesium phosphates have been discussed. The prospects for the use of calcium and magnesium phosphates as high ebbicient sorbents, including selective adsorption from bicomponent mixtures have been shown with the infent of their separation and utilization.

**БИОЛОГИЯ**

*Golubev A. P., Roshchina N. N.*
**Relationship between the somatic and generative growth increments at a compensatory growth in pond snail Lymnea stagnalis (Gastropoda, Pulmonata).** pp. 64--67

*Summary:* The quantitative aspects of the growth and reproduction of the largest (leaders) and smallest (outsiders) specimens of *L. stagnalis* families at a compensatory growth caused by the removal of the high-density pressure or the rearing in the experimental conditions have been determined. The outsiders are characterized by the most intense compensatory growth. The lower the body weight at the removal of the limiting factor the higher their compensatory growth. The abilities of the specimen to a compensatory growth decrease with increasing their body weight. The acceleration of the somatic growth of outsiders at the compensatory growth is followed by the intensification of their reproduction. It is expressed both in the decrease of the average weight of their body at the release of the first egg masses and in the increase of the daily generative increment. Therefore, in L. stagnalis the functional response to the removal of the limiting factor affects not only the somatic growth but the entire integrated system of plastic metabolism.

*Urbanovich O. Yu., Dolmatovich T. V., Malyshev S. V., Kartel N. A.*

**Brown rust resistance genes in the genome of common wheat cultivars.** pp. 68--72

*Summary:* The occurrence of brown rust resistance genes Lr1, Lr9, Lr 10, Lrl9, Lr21, Lr24 and Lr26 was analyzed in the genome of common wheat cultivars of Belarusian breeding. Molecular markers were used for the study. The results may be applied for characterization and certification of cultivars.

*Lukyanenko L. M., Kilanczyk E., Labieniec M., Bryszewska M., Slobozhanina E. I.*

**Protective effect of melatonin under the phenylhydrazine-induced oxidative stress in fibroblasts.** pp. 73--75

*Summary:* This work is concerned with studying the influence of melatonin on the DNA damage and the change of the physical state of a lipid bilayer under the phenylhydrazine -- induced oxidative stress in fibroblasts of a Chinese hamster. It is shown that the preliminary incubation of fibroblasts in the medium with melatonin protects DNA from damaging and stabilizes the microviscosity of a membrane lipid bilayer under phenylhydrazine -- induced oxidative stress in cells.

*Sidorovich E. A., Sergeichik S. A., Sergeichik A. A., Ljashuk A. M.*

**Stability of different species of aboriginal and introduction wood plants to the hydrogen chloride action.** pp. 76--78

*Summary:* In experiments with the leaves of 87 woody plant species, study was made of the changes in the concentration of chlorophyll a, b and carotinoids as well as in the photosynthetic pigment ratio environmental pollutant HCl. It was established that various plant species responded to the pollutant when affected differently. 4 groups of plant species were found: 1 -- very tolerant to HCl; 2 -- tolerant to HCl, 3 -- middle tolerant to HCl; 4 -- low tolerant to HCl. The plant species that demonstrated a high level of tolerance to HCl were the most promising for the environment optimization by means of landscaping.

*Belyanovich L. M., Rudenok A. N., Konev S. V.*

**Stomach chelicobasteriosis and associated diseases of internal organs.** pp. 79--81

*Summary:* Mass infection of the population by the *H. pylori* bacterium and, accordingly, the high communication of gastric diseases caused by it undoubtedly testifies to the insufficient efficiency of the present methods for treatment of the *H. pylori* infection. Owing to this, the development of new effective methods for treatment of the gastric *H. pylori* infection is an extremely significant and indispensable problem. The offered method is directed to realize the natural defending ability of the stomach, a high acidity of milieu, which is neutralized due to the activity of the *H. pylori* urease. The problems caused by urease-producing bacteria are not limited to the pathogenesis of gastric and duodenal ulceration. The damaging effects of urease have been shown to contribute to the pathogenesis of urinary calculus formation, pyelonephritis, and cardio-vasculas diseases. The mechanism of these states may be connected with the toxic effect of ammonia.

*Titok V. V., Kubrak S. V., Yurenkova S. I., Khotyleva L. V.*

**Expression of the proteins of the fiber flax stem in ontogenesis.** pp. 82--86

*Summary:* The electrophoretic analysis of the proteins of fiber flax stems has been carried out at various stages of the ontogenetic development of plants. The data obtained have shown that the variation of protein spectra is due to the differential activity of genes determining the protein synthesis during ontogenesis.

**МЕДИЦИНА**

*Shanko Yu. G.*
**Reconstructive surgery of facial nerve incontinence after the removal of parastemal posterior fossa tumors.** pp. 87--92

*Summary:* Reconstructive surgical treatment was made in 108 cases of facial nerve incontinence after the removal of parastemal posterior fossa tumors. Anastomoses of facial nerve with hypoglossal nerve was made in 64--65,3% cases, anastomoses of facial nerve with recurrent branch of hypoglossal nerve -- in 21--21,4% cases, anastomoses of facial nerve with hypoglossal and reinnervation of hypoglossal nerve by its recurrent branch -- in 13--13,3% cases.
Late results were estimated in 79--73,1% cases according to House-Brackmann scale. Good and satisfactory results (HB2--HB4) were achieved in 58--73,4% cases. Minimal mimic movements (HB5) were observed in 18--22,8% cases. Surgical treatment was non effective (HB6) in 3--3,8% cases. Autotransplantation of gracillis muscle from the hip to the face by means of neurovascular microanastomosis may be used for to remove the cosmetic defect in cases of degeneration of facial nerve and mimic muscles.

**НАУКИ О ЗЕМЛЕ**

*Tyumentsev V. L., Fursikov G. L.*
**Prospects for the oil content of the saline carbonate deposits of the Dubnyakovo-Savicheskoi zone of the uplifts of the Pripyat trough according to the hydrogeological data.** pp. 93--96.

*Summary:* Based on the complex of tone and local hydrogeological criteria of oil content, it is established that the saline carbonate deposits in the eastern and western parts of the Dubnyavsko-Savicheskoi zone of the uplifts hold more promise than in its central part despite the presence of oil deposits in the latter.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Timoshpolskii V. I., Postolnik Yu. S., Adrianov D. N.*
**Calculation of radiative and convective heating of steel ingots in circular furnaces.** pp. 97--102

*Summary:* In this article the main methods of solving the heat conduction problems when applied to metallurgical technologies are considered. Their advanfages and disadvantages and also the areas of their application are shown.

**СОЦИАЛЬНО-ГУМАНИТАРНЫЕ НАУКИ**

*Basetsky I. I., Bashan A. V.*
**Theoretical aspects of combating corruption.** pp. 103--109

*Summary:* The present work is conarned with the theoretical aspects of combating corruption and corruptional crime on the basis of the analysis and achievements in the chosen sphere. The authors have proposed the definitions of the terms "corruption" (wide, narrow, political, social-law and juridical sense), "corruptional offense", "corruptional crime".
The authors have made the well-grounded conclusions that corruptional offences can be divided according to the degree of social danger into: corruptional criminal crimes, corruptional criminal offences, corruptional administrative delicts. All this will need change and addition in the legislature of the country.

### AGRICULTURAL SCIENCES

*Kadyrov M. A.*
**Selection of the main crops in Belarus: state, problems, priorities.** pp. 110--114

*Summary:* In this article the present state of the selection of the main agricultural crops in Belarus is evaluated. The central reasons of its high outcome are found. The selection process is presented as an object of study, and the basic factors that provide its high efficiency are given. The necessity and the possibility of an organic combination of the traditional selection methods and the modern genetic-biotechnological methods, informatics and transgenesis are shown.

*Gusakov V. G., Likhatsevich A. P.*

**Variants and prospects for the use of reclaimed lands of Belarus in agriculture.** pp. 115--119

*Summary:* Analysis of possible consequences for the retransformation of reclaimed lands confirms that it is allowable on the area of up to 400 thousands of hectares.

*Sheyko I. P.*

**Deterrent factors and outlooks for the improvement of animal productivity.** pp. 120--123

*Summary:* A short analysis of animal production in Belarus as well as the scientific basis for its further development is given. Factors preventing from exposing the full potential of animal productivity are revealed and some ways of increasing the efficiency of animal production in the Republic are shown.

/ 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

Копирайт © 2005-2008 Национальная академия наук Беларуси

Копирайт © 2005 Издательство "Беларуская навука"