# Доклады Национальной академии наук Беларуси, 2001, Том 45, No.1

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2001, Том 45, No.1

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Bahtin V. I.*
**Superregular perturbation asymptotic of semigroup of operators.** pp. 5--8.

*Summary:* In this paper we construct an asymptotic expansion for the family of operators *A*_{e} ^{t/e } e^{zF/e} , where *A*_{e}^{t} is a superregular perturbation of a fiber ergodic semigroup.

*Benyash-Krivets V. V.*

**Representation varieties of ***F*-groups and their generalizations. pp. 9--12

*Summary:* It is found all irreducible components of the representation variety *R*_{n}(G_{g}) of an *F*-group G _{g} of genus g ³ 2 and proved their rationality.

*Rabtsevich V. A.*

**On nondecreasing singular solutions of Emden -- Fowler systems.** pp. 13--16

*Summary:* For Emden -- Fowler type systems of differential equations necessary and sufficient condition to have nondecreasing singular solutions with prescribed singular point is established. Two -- sided asymptotic estimates of the solutions are obtained.

*Tishchenko K. I.*

**On approximation of real numbers by algebraic integers of the third degree.** pp. 17--19

*Summary:* In this paper we prove the following. Theorem. For any real number x which is not a rational number or quadratic irrational, there exist infinitely many algebraic integers a of third degree such that |x - a| << *H*(a)^{-2,8}, where *H*(a) is the height of a, << is the symbol of Vinogradov. The implicit constant in << depends on x only.

*Lipnitsky A. A.*

*p*-Primary torsion of Bauer groups of elliptic curves with split multiplicative reduction over real formal power series. pp. 20--24

*Summary:* An abstract structure of odd *p*-primary torsion of Brauer groups of elliptic curves with split multiplicative reduction defined over real formal power series has been obtained. The presentation of elements of Brauer groups by crossed product algebras is provided.

*Gabasov R., Kirillova F. M.*

**Stabilization of nonlinear dynamic systems under large initial disturbing.** pp. 25--28

*Summary:* A method of constructing stabilizing feedbacks of nonlinear dynamic systems based on linear, piecewise linear or piecewise linear quadratic approximation of nonlinear elements and the optimal feedback control is under consideration. The method provides the maximal possible domain of stabilization and definite extremal properties of transients.

*Erovenko V. A., Severenchuk N. B.*

**Weyl's theorem and semi-Browder essential spectrums.** pp. 29--33

*Summary:* In this paper analogs of Weyl's theorem for Browder essential approximate point spectrum and Browder essential approximate defect spectrum of bounded operators in Banach space were established.

*Lomovtsev F. E.*

**Hyperbolic second-order differential-operatorial equations with variable domains of smooth operator coefficients.** pp. 34--37

*Summary:* The existence and uniqueness theorems of strong solutions of the Cauchy problem for hyperbolic second-order differential equations with variable domains of smooth operator coefficients are proved.

*Emelichev V. A., Stepanishina Yu. V.*

**Criterions of quasistablility for the vector trajectory problem of majority principle of optimality.** pp. 38--41

*Summary:* A quasistability criterion is given for the vector trajectory problem of discrete majority optimization.

*Tikhonov S. V., Yanchevskii V. I.*

**Unramified algebras of exponent 2 over function fields of split hyperelliptic curves.** pp. 42--44

*Summary:* The description of generators and relations of 2-torsion part of Brauer groups of hyperelliptic curves of even degree is obtained.

*Gaishun I. V., Goryachkin V. V.*

**Minimal realization of two-parameter discrete-continuous systems.** pp. 45--47

*Summary:* The method of construction of minimal realization for two-parameter discrete-continuous systems is proposed.

**ФИЗИКА**

*Ermolaev E. A., Shapovalov P. S.*
**For the polaron theory.** pp. 48--51

*Summary:* By a developed iterative method, the numerical solutions of the polaron problem discribing polaron's spherically symmetric states *ns* (n = 1, ..., 15) are obtained. The accuracies of the cases *n* = 1, ..., 6, having been calculated before, are improved. Asimple analytical approximation of the energy spectrum of studied states is found.

*Pilipovich V. A., Esman A. K., Goncharenko I. A., Kuleshov V. K.*

**Controllable radiation frequency tuning of fiber-optic and waveguide lasers.** pp. 52--55

*Summary:* The method for fast controllable tuning of the radiation wavelength of fiber-optic or waveguide laser is proposed. Bragg grating written on waveguide electrooptic modulator is used simultaneously as a wavelength selective element and a mirror of external laser cavity. Applying control voltage to grating electrodes it is possible to shift grating reflectivity spectrum and by this tune laser radiation region. Frequency tuning inside of grating reflectivity bandwidth is produced by the use of intercavity waveguide electrooptic cell. Spectral parameters of laser radiation have been calculated. It is shown, that the region of continuous tuning of such a laser for control voltage up to 5 Vis about 0.2 nm and the switching time is < 0.08 ns.

*Parashchuk V. V., Gribkovskiy V. P. †*

**Autooscillations of electron-photon system under streamer discharge.** pp. 56--59

*Summary:* The electron-photon-electric field system dynamics has been analysed taking into account the processes of impact ionization, the spontaneous and stimulated recombinations during streamer discharge in semiconductors. It has been shown that in given system the different autooscillation regimes and the spatially-inhomogeneous dissipative structures as the self-organization elements are possible. The efficiencies comparison of the possible generation mechanisms of nonequilibrium carriers show that the photoionization process prevail in these conditions.

*Goncharenko A. M.*

**For the light bullets theory.** pp. 60--63

*Summary:* Gaussin's functions are used to investigate properties of light bullets. It is shown that the light bullets oscillate in space and time.

**ХИМИЯ**

*Shchukin D. G., Kulak A. I., Sviridov D. V.*
**Ferrite microheterogeneous photocatalists on basic, of titanium dioxide.** pp. 64--67

*Summary:* The magnetorheological photocatalyst of core-shell type, which can be extracted from the treated aqueous media by applying magnetic field, is proposed. It has been demonstrated with a photocatalyst comprising TiO_{2} shell and ferrite or manganite magnetic core that the photocatalytic activity compatible to that of commercial TiO_{2} photocatalyst Sachtleben Hombikat UV 100 can be attained by deposition of SiO_{2} sublayer which separates the magnetic core and TiO_{2} shell thus preventing the parasitic trapping of photogenerated carriers in the core.

*Osipovich N. P., Streltsov E. A., Susha A. S.*

**Bismuth adatoms chemical and electrochemical deposition on the tellurium films surface.** pp. 68--71

*Summary:* Chemical underpotential deposition (UPD) of monolayers structures of Bi adatoms (Bi_{ad}) onto Te has been studied in solution containing Ti(IV)/Ti(III) redox pair. This process was compared with electrochemical UPD of Bi on Te. The stability of Bi_{ad} without the external polarization of the electrode has been investigated.

*Potkin V. I., Zelenkovsky V. M., Kaberdin R. V., Yanuchok A. A.*

**Quantum-chemical calculations for the reaction of 2-(1-nitro-2,3,3- trichloro-2-propenyliden)-4-ethoxybenzazatine with diethylamine.** pp. 72--74

*Summary:* By quantum-chemical calculatioas it was shown that the formation of the salt of 1-(4-ethoxybenzazet-2-yl)-2,3,3-trichloronitronic acid from corresponding tautomere of initial compound is more preferable thermodinamically in reacrtion of 2-(1-nitro-2,3,3-trichloropropenyliden)-4-ethoxybenzazetine with diethylamine then the nucleophilic substitution of chlorine atom in trichlorovinyl group.

**БИОЛОГИЯ**

*Lastovka A. S., Pereverzev V. A., Rudenok V. V.*
**Morphobiochemical substantiation of microsurgery method of organ preserving operations realization on submandibular glands.** pp. 75--78

*Summary:* The experiments on dogs have shown that the most atraumatic method of the organ preserving operation on the submandibular glands is a microsurgical method, as this method doesn't result in pathologic structural changes in the gland and content changes of biogenic amines in it (histamine and serotonine) during remote posoperative periods.

*Yurenkova S. I., Titok V. V., Hotyleva L. V.*

**Ontogenetic polymorphism of isoenzyme systems of fibre flax.** pp. 79--82

*Summary:* As a result of electrophoretic analysis of 6-phosphogluconate dehydrogenase, acid phosphatase, cytochrome oxidase and aspartate-aminotranspherase, considerable changes in isoenzyme spectra, caused by different expression of genes depending on the ontogenesis stage determining enzyme synthesis, were revealed in leaves of fiber flax Belinka. Isoenzyme profiles of cytochrome oxidase and aspartate-aminotransferase were revealed and loci controlling development of individual isoforms of these enzymes was determined.

*Gavrilov V. B., Mikhailov A. S., Konev S. V.*

**Main types of low-molecular weight hydrophobic ligands distribution between blood components.** pp. 83--86

*Summary:* The distribution between an aqueous phase, plasma proteins and blood cells of a number of fluorescent probes with a different charge as an analogues of low-molecular weight hydrophobic ligands was investigated. The simple method of account of ligand distribution between blood components on their distribution in plasma/erythrocytes and buffer/erythrocytes systems was suggested. It was shown, that for the most hydrophobic neutral ligand the binding with plasma proteins, namely with low-density lipoproteins. forms about 80% from its total. The anionic ligand having high albumin affinity only on 50% was binded by proteins, and the remaining part approximately is equally arranged between an aqueous phase and erythrocytes. The cationic ligands mainly binds by a1-acid glycoprotein, on 50% were sorbed by erythrocytes and only 30% were binded by plasma proteins.

*Pisarchik V. A., Kartel N. A.*

**Expression of b-galactosidase gene containing (AC)**_{20} repeat in a reading frame. pp. 87--90

*Summary:* There was investigated a possible impact of (AC)_{20} repeat insertion in a reading frame of b-galactosidase gene on its expression. It was found that simple repeat increases expression (1.5 times). Taking into account our previous results as well as the data from the literature we made a conclusion that the modulation of gene expression by simple repetitive sequences is not the main course of differences in the distribution of these repeats in translated and untranslated regions of eucaryotic genes.

*Voitovich A. M.*

**Bone tumors of grass frog (Rana Temporaria L.). under environmental radionuclide contamination.** pp. 91--94

*Summary:* The ecologogenetic study of amphibian populations in Belarus has been carried out from 1986 to 1998. In Cherikov city (Mogilev reg.) in Rana temporaria the chromosome aberration frequency in bone marrow cells was the highest among other frog populations in 1986. Only in Rana temporaria from Cherikov and in the so-called Pershay plume (Minsk reg, Volozin district) bone tumors were observed. Both populations are from the sites not heavily radionuclide contaminated, with ^{137}Cs and ^{90}Sr accumulation in animals being not so high as around the Chernobyl NPP.

**НАУКИ О ЗЕМЛЕ**

*Rylova T. B.*
**Evolutional features of Belarusian palynoflora at the end of Paleogene and during Neogene.** pp. 95--99

*Summary:* Main natural phenomena of the palynoflora evolution have been examined from the results of studying Upper Oligocene, Miocene and Pliocene deposits of the territory of Belarus and on the basis of the analisis of dinamics of palaeotropical and arctotertiary geoflora elements.

*Veretennikov N. V., Korzun V. P., Makhnach A. S., Laptsevich A. G.*

**Late Devonian volcanogenic formations in the area of Uvarovichi.** pp. 100--102

*Summary:* Volcanic rocks revealed by boreholes within the region of local positive megnetic anomalies at the distance of, 20-25 km to the northwest from Gomel mainly contain psephitic tuffs and xenotuffs of the alkaline ultrabasic suite. It form small subwater paleovolcanoes of the central type, which had been formed in the sea sedimentary basin of Voronozh time of the Late Devonian.

*Konishchev V. S.*

**Halokinesis rates in Pripyat flexure.** pp. 103--106

*Summary:* It is proved that the rates of grow of the salt structures depends on the rates of subsidence and sedimentation and were less during the breaks of sedimentation.

*Sokolik G. A., Ovsyannikova S. V., Kimlenko I. M.*

**Organic soil components influence on Plutonium and Americium mobility.** pp. 107--111

*Summary:* The results of investigation of ^{239,240}Pu and ^{241}Am distribution between humus substances (HS) fractions of organic and mineral soils are presented. It was established that HS mainly fasten ^{239,240}Pu and ^{241}Am in solid phase of soils, and ^{239,240}Pu more effectively than ^{241}Am. Mobility of radionuclides is essentially decreased as a result of formation of heavy soluble compounds of plutonium and americium not only with high-molecular humic acids but also with fulvic acids associated in soils with Ca, Mg, Fe, Al hydroxides and clay minerals. In majority of organic soils a share of heavy soluble HS constituents fastening radionuclides is higher than in mineral ones. That is one of the reasons of lower ^{239,240}Pu and ^{241}Am mobility in organic soils. Increasing of soil acidity increases the content of mobile ^{239,240}Pu and ^{241}Am fulvic complexes and americium cations involving into migration processes.

*Kudelsky A. V., Smith G. T., Ryabov I. N., Hadering R. H.*

**Experiment results on the application of potassium in a non-drainage lake as a countermeasure to the **^{137}Cs accumulation in fish. pp. 112--115

*Summary:* Three years' (1997--1999) full-scale experiment on the artificial application of potassium (as KCl) in a non-drainage lake as a countermeasure to the ^{137}Cs accumulation in fish was performed. The [K^{+}] content of water was noted to increase from I to 10 mg/l, and, as a consequence, a steady decrease of A^{137}Cs in fish by 9--76 % (red-eye on the average by 47%, roach and perch -- 37.5, pike -- 27.5 %) was recorded. An increase of the ^{137}Cs concentration in water from 3.8 to 10--15 Bq/l due to radiocaesium desorption from bottom sediments under the action of potassium occurred as a side effect.

*Khomchynska M., Matusevich V. V., Pawlowski L., Shymanska M., Vasong H., Soldatov V. S.*

**Recultivation of exhausted soils by means of the ion exchange substrates.** pp. 116--119

*Summary:* In the conditions of vegetation hall the influence of addition of 1--7 vol.% of the ion exchange substrate BIONA-312 (IS) on yield of Dactylis glomerata (L.) in three consecutive vegetations has been investigated. It has been demonstrated that addition of IS increases the yield in comparison to the pure sand. In the following vegetations the yield on the experimental variant has been dropping however being significantly higher then in control variant. The treatment of the experimental pots after the I vegetation by the nutrient solution has not influenced on the yield. The same procedure made after the second vegetation has raised the yield as much as twice.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Dobrolyubov A. I.*
**For superrotation theory of the Venus atmosphere.** pp. 120--123

*Summary:* The concepts of the travelling tidal gravitational and thermal waves and of the feedback mechanism were used to explain the driving mechanism generating the superrotation of the Venus' atmosphere.

*Sviridenok A. I, Kovalevskaya T. I., Kravtsov A. G.*

**Technological electretization features of polyethylene fibers and fiber-porous materials.** pp. 124--127

*Summary:* The residual electretization of polyethylene fibers and fiber-porous materials (FPM) was investigated. The fiber and FPM were made by extrusion and pneumoextrusion technology. IR-spectroscopy and thermostimulated depolarisation methods were used for researches. It was established, that the residual electretization of thies materials caused the charges, is localised on two type of defects: surface carbonil and carboxil groups and volume structural abnormalities. These data show that the principle of triboelectretization first revealed for friction of polymers is also applicable to the electretization at extrusion and pneumoextrusion technology.

*Samoilovich Yu. A., Anisovich G. A., Timoshpolsky V. I., Koshman V. M., Trusova I. A.*

**For choosing models of vibration influence of electric slag remelting (ESR) on steel ingot.** pp. 128--131

*Summary:* The report considers the method of vibration influence on a large steel ingot during vacuumarc remelting. It analyses ingot structure in diversifying combinations of electric and magnetic fields switcing. Experimental research data of different frequencies impact (frequency of switching) *f*_{exp} on Sn + Pb alloy structure and methods of vibration mode analysis arc given in this work.

*Migun N. P., Prokhorenko P. P., Chizh S. G.*

**On a new mechanism of defect development under capillary controlling.** pp. 132--135

*Summary:* By special experiments it is established for the first time that in the absence of direct penetrant-developer contact the liquid's drawing from a defect and subsequent formation of an indication takes place. A number of video-images of such a process for various liquids drawing from model defects are obtained. The explanation of new mechanism of development process based on liquid film flow due to the gradient of disjoining pressure is proposed.

/ Издания академии / Научные журналы / К началу страницы

Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: *6 сентября 2008 г.*

Создана при участии Игнатия И. Корсака

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Копирайт © 2001 Издательство "Беларуская навука"