# Доклады Национальной академии наук Беларуси, 1998, Том 42, No.6

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 1998, Том 42, No.6

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Bernik V. I., Morozova I. M.*
**Diophantine approximation and zeros of the lacunary polynomials.** pp. 5--8

*Summary:* The upper bound for the degree of approximation of zero by the values of lacunar polynomials is improved.

*Shavel N. A.*

**Using nonmonotone Liapunov functionals for the boundedness investigation with respect to part of coordinates of delay differential equation.** pp. 9--12

*Summary:* By using nonmonotone Liapunov functionals it is investigated boundedness with respect to part of coordinates of nonautonomous delay differential equation. Uniform ultimate boundedness conditions of solutions with respect to part of coordinates of equations with unbounded right-hand part are obtained.

*Makarov E. K., Popova S. N.*

**The method of rotations for linear controllable systems.** pp. 13--16

*Summary:* We consider relations between control and multiplicative perturbations of the Cauchy matrix for a linear closed-loop control system under the condition of uniform complete controllability.

*Borukhov V. T., Korzhenevich S. K.*

**Factorization of transfer matrices of linear dynamical systems over a principal ideal domain.** pp. 17--21

*Summary:* The transfer matrix of dynamical systems (DS) factorization over a principal ideal domain definition is given and the factorization algorithm is proposed. The algorithm may be used by studying a disturbances rejection, a DS invertibility, a DS decoupling problems and others.

*Kopeikina T. B.*

**To the problem of stabilization of linear singularly perturbed systems with delay.** pp. 22--27

*Summary:* The problem of stabilizability of singularly perturbed dynamic systems with delay (SPDSD) is considered. Some sufficient stabilizability conditions of SPDSD are obtained in terms of stabilizability conditions of the reduced system and the boundary layer system.

*Gorokhovik V. V., Shinkevich E. A.*

**Stepped preorder relations on vector spaces.** pp. 28--31

*Summary:* On a real vector space a new class of preorder relations called stepped preorders is axiomatically introduced. Geometrical and analytical characterizations of stepped preorders are given.

*Kravtsov M. K., Krachkovskii A. P.*

**Asymptotic properties of the multi-index axial transportation polytopes.** pp. 32--37

*Summary:* It is considered problem of the asymptotic behavior for the classes multi-index axial transportation polytopes as the order of polytopes increases. In particular it is proved that almost all multi-index axial transportation polytopes have maximal number *k*-faces (for certain *k*).

*Jovanovich B. S., Matus P. P., Shcheglik V. S.*

**Finite difference schemes on nonuniform meshes for parabolic equation with variable coefficients and generalized solutions.** pp. 38--44

*Summary:* The convergence rate of finite difference schemes approximating the first initial-boundary value problem for one-dimensional heat equation with variable coefficient on nonuniform meshes is studied. For an implicit second order difference scheme with averaged right-hand side a convergence rate estimate in discrete *L*_{2}-norm of order *O* (*h*^{2} + t) is obtained for the case of generalized solutions from W_{2}^{2,1}(*Q*).

**ФИЗИКА**

*Kudryashov V. V.*
**Reconstruction of the WKB series as a new method of approximate solution of the Schrodinger equation.** pp. 45--49

*Summary:* The WKB series is reconstructed in the form of the sum of the new asymptotic expansions which compose an approximating sequence. The explicit form is found for the functions represented by the leading expansions. As a result, a new analytical uniformly valid approximation is obtained for solutions of the one-dimensional Schrodinger equation with an arbitrary potential.

*Pletyukhov M. V., Tolkachev E. A.*

**Berry's phase for a twice degenerated two-level system.** pp. 50--54

*Summary:* An expression is obtained for the *U*(2) gauge potential determining Berry's phase which arises in adiabatic description of a twice degenerated two-level system.

**ХИМИЯ**

*Shunkevich T. M., Ivashkevich O. A., Naumenko V. N., Pashkevich Zh. A., Sviridov V. V.*
**Thermal decomposition of silver acetylenide.** pp. 55--57

*Summary:* Elemental, chemical and X-ray analyses and IR spectroscopy were used to investigate the structures of condensed products formed thermal decomposition of silver acetylenide. It is shown that thermal degradation of silver acetylenide Ag_{2}C_{2} which upon proceeds as detonation is accompanied by formation of linear silver-intercalated carbine, apart from other products.

*Balabanovich A. I., Levchik S. V., Lesnikovich A. I.*

**Chemical processes in thermolysis of sodium 5-aminotetrazole.** pp. 58--60

*Summary:* Thermal decomposition of sodium 5-aminotetrazolate was studied in its first stage with FTIR. Two pathways of the tetrazole ring cracking are found: with evolution of sodium azide or hydrogen azide from the imino-form. The solid residue contains of sodium hydrocyanomide, sodium salt of cyanomelamine and trisodium salt of tricyanomelamine. The scheme of their formation is suggested.

*Dad'kov I. G., Kuzmitsky B. B., Antonevich I. P., Chernikhova T. V., Koroleva E. V., Lakhvich F. A.*

**Methyl ester of 6-oxo-6-[2,2-ethylenedioxy-5-(dimethoxycarbonylmethyl)-cyclopent-1-yl]-hexanoic acid as prototype of radiosensitizers of new type.** pp. 61--64

*Summary:* Radiosensitizing activity of 11-deoxy-PGE analogue series with malonic or heterocyclic fragment in w-chain was studied for the first time. In experiments with HeLa cell cultures of uterine cervix tumor it was revealed that one of prostanoids -- methyl ester of 6-oxo-6-[2,2-ethylenedioxy-5-(dimethoxycarbonylmethyl)-cyclopent-l-yl]-hexanoic acid -- caused practically significant increase of irradiated tumor cell death, in efficiency one compared well with metronidazole. The roles of 7-oxocarboxyalkylic a-chain and malonic ester fragment in w-chain in capacity of pharmacophores responsible for enhancement of tumor cell sensitivity to g-irradiation at relatively small doses were brought out. It was established that studied prostanoid in concentration 10^{-6} mol/l led to saturating effect, when it was incubated with HeLa cells for 30 and 60 min before irradiation, this prostanoid increased tumor cell radiodamaging by 32 and 25% after irradiation in dose range between 2 and 4 Gy. It was inferred that obtained prostanoid is a prototype of new radiosensitizing drug.

*Smolyak L. Yu., Prokopchuk N. R., Prokopovich V. P., Klimovstova I. A.*

**A photostabiliser of polypropylene.** pp. 65--68

*Summary:* A compound belonging to the group of structurally hindered amines (HA) was synthesized with the help of new technologies and investigated as a photostabiliser of polypropylene. The preservance of toughness of films and the quantity of carbonyl groups were estimated in accordance with the IR spectroscopic data in the process of exposure to ultraviolet radiation. A higher efficiency of bis-(2,2,6,6-tetramethyl-4-piperidinyl)terephtalate compared to industrial stabilizers is demonstrated.

**БИОЛОГИЯ**

*Rudenok A. N., Belyanovich L. M., Nikolskaya V. P., Konev S. V.*
**Light-induced deblocking of cytochrome oxidase inhibited by cyanide: the role of interheme electron transport.** pp. 69--73

*Summary:* It is shown that the respiratory activity of isolated cytochrome *c* oxidase, 95% of which is inhibited with cyanide, is restored under irradiation with visible light. It is suggested that the light-induced oxygen consumption is connected with photostimulation of intramolecular electron transfer with the cyanide complex of the enzyme.

*Gorbunova N. B., Kalyunov V. N.*

**The effect of Adrenoblockers on the blood concentration of the nerve growth factor in mice during psychological stress.** pp. 74--77

*Summary:* Using two-site immunoradiometric assay it was found that block of a- and b-adrenoreactive systems by separate or combined intraperitoneal injections of selective antagonists (phentolamine 25 mg/kg, propranolol 200 mg/kg) substantially limited an increase in the serum nerve growth factor (b-NGF) during psychosocial relations but did not affect its level in isolated mice. Thus, the content of b-NGF in blood serum in early stages of community formation is controlled by central and peripheral a- and (b-adrenoreactive structures.

*Sidorovich V. E.*

**Comparative analysis of the contents of trace elements in testes of mustelids (Mustelidae) in relation to their evolutionary similarity.** pp. 78--81

*Summary:* Comparative analysis of trace element contents in testes of mustelids was carried out. Nine species which comprise current mustelid fauna in Belarus (the otter, pine marten, the stone marten, the European mink, the American mink, the polecat, the stoat, the weasel, the badger) were involved in the study. The present data were compared with morphological, genetic and immunologic results. It was assumed that used character the trace element contents in testes could be used to obtain additional information on phylogenetic similarity of the taxa.

*Pavlyuchuk N. V., Akhramenko A. D., Palilova A. N.*

**The efficiency of clone selection for X-virus resistance within potato varieties-populations.** pp. 82--85

*Summary:* The behaviour of the character of *X*-virus resistance was studied in vegetative clone progenies produced with the two-stage selection method within four Belarus-bred potato varieties (Loshitsky, Aksamit, Altair, Yavar) by immunoenzyme analysis. The degree of variability of the character and conditions of its stabilization in the generations were determined. The relation between exhibition of the character of *X*-virus resistance, the genotype of the initial variety, the dosage of viral infection and the duration of its action on the plant was revealed. The efficiency of selection for *X*-virus resistance was shown to depend on the previous stabilization period of the selected clones against the background of natural infection.

*Davydenko O. G., Silkova T. A., Fomchenko N. S., Mavrishcheva E. B.*

**Investigation of the possibility of using Aegilops kotschyi cytoplasm to produce hybrid seeds of winter wheat.** pp. 86--89

*Summary:* Data on seed setting (in %) of sterile winter wheat lines with Ae. kotschyi cytoplasm under wind-pollinating conditions and the level of pollen fertility recovering in F1 hybrids are presented. Seed setting of F1 hybrids was found to depend on restorer variety genotype and reached 76.1%. Seed setting of male-sterile analogs varied from 29 to 54.9%, depending on the sterile line.

**НАУКИ О ЗЕМЛЕ**

*Kudelskii A. V., Smith J. T., Zhukova O. M., Matveenko I. I., Pinchuk T. M.*
**The role of the rive runoff in natural **^{137}Cs decontamination of contaminated areas. pp. 90--94

*Summary:* The several years (1987--1995) removal of ^{137}Cs within five river basins (the Dnieper, Pripyat, Sozh, Iput, Besed) is estimated and a series of basic differences between the intensity of decontamination of high and low river catchments is established. It is shown that the intensity of natural ^{137}Cs decontamination by river runoff varies from 0.95 to 3.18% (averaging to 1.55%), relative to radioactive decay within the river catchment areas.

*Bambalov N. N., Maryganova V. V., Prokhorov S. G., Strigutskii V. P.*

**The mechanism of formation of humic substances.** pp. 95--99

*Summary:* EPR spectroscopy can be used to reveal formation of true humic compounds directly in humifying plants. In the initial stage destruction of lignine macromolecules takes placse. After 50 days of humification in laboratory conditions molecular fragments of polyconjugation were formed in the straw. After 70 days, supramolecular associations characteristic of humic acids are formed. The humification process is variable.

*Levykh N. N., Bulkin Yu. S., Abramenko V. I.*

**Trends in migration of trace elements in Pre-Cambrian weathering crusts developed over granites of Belarus.** pp. 100--103

*Summary:* Geochemical studies of the Pre-Mid-Riphean weathering crusts developed over granites of Belarus were taken as a basis to ascertain the behaviour of trace elements in the hypergenesis migration cycle and their minerals-concentrators were revealed.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Vantsevich V. V., Vysotskii M. S.*
**The second dynamics problem as a base for the development of mobile machines theory.** pp. 104--110

*Summary:* A new direction for the development of the mobile machines theory (Vehicle Dynamics) has been proposed. The direction is oriented to search for a solution of the Second Dynamics Problem as the base for control of the vehicle running abilities. The main steps of the new theory have been formulated. The paper contains a method for optimizing mass and geometrical truck parameters as an example.

*Stavrov V. P., Dorozhko A. V., Zuev A. P., Kremenevskaya E. I., Markov A. V., Starinskaya T. V.*

**Relations of a thermoplastic polymers-based viscous flow of anisotropic fibrous composites with a thermoplastic polymer matrix.** pp. 111--115

*Summary:* The article contains results of an experimental study of viscous properties of anisotropic fibrous composites, produced with the film technology from polyethylene and glass roving. Parameters of the power law of the flow are determined. Their dependence on the content of fibres, the structure of the composites and the temperature is found. Anomalies of the viscous flow caused by the effect of the fibrous system are revealed.

**1998 Contents List of Doklady of the National Academy of Sciences of Belarus.** pp. 116--121

/ 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

Копирайт © 1999-2008 Национальная академия наук Беларуси

Копирайт © 1998 Издательство "Беларуская навука"