# Доклады Национальной академии наук Беларуси, 2001, Том 45, No.4

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2001, Том 45, No.4

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Tikhonov S. V., Yanchevskii V. I.*
**Brauer groups of semisplit elliptic curves defined over the field of rational numbers.** pp. 5--8

*Summary:* The nontriviality criterion of the generators of 2-torsion part of the Brauer group of a semisplit elliptic curve over the field of rational numbers is obtained.

*Demidenko V. M.*

**The conditions for high solvability of optimization problems on substitutions and their application.** pp. 9--12

*Summary:* For functionals of general kind defined on subsets of the symmetrical group, conditions that guarantee reaching the extreme values on preassigned permutations are established.

*Demenchuk A. K.*

**Conditions of existence of almost periodic partially irregular solutions of differential systems.** pp. 13--14

*Summary:* We give necessary and sufficient conditions of existence of almost periodic partially irregular solutions for almost periodic differential systems.

*Yanovich L. A., Doroshko V. V.*

**Special cases of Hermite-Birkhoff-type polynomial operator interpolation.** pp. 15--20

*Summary:* Hermite-Birkhoff -- type interpolation formulae are constructed for the operators defined on functional spaces when the coincidence of differentials of lower orders at interpolation nodes is not required.

*Beresnevich V. V.*

**The distribution of rational points near the parabola.** pp. 21--23

*Trelina L. A.*

**The height of S-integral points on hyperelliptic curves and the relative rank of Jacobians.** pp. 24--26

*Summary:* Given a hyperelliptic curve *C* over **Q**, we explicitly construct elementary 2-extensions of **Q** for which the relative rank of the Jacobian of *C* grows unboundedly.

*Suprunenko I. D.*

**Identification of classical algebraic groups with the aid of matrices with big Jordan blocks.** pp. 27--30

*Summary:* A characterization of the classical algebraic groups as irreducible simple Zariski closed subgroups of the general linear group containing matrices with big Jordan blocks with respect to the degree of the group is obtained. In particular > 1 containing a it is proved that if *K* is an algebraically closed field, *G* Ì *GL*_{n}(*K*) is an irreducible simple Zariski closed subgroup of rank matrix with a Jordan block of size *k*, *n* > 248 and *n* < (*k*^{2} + 4*k* - 13)/8, then *G* is one of the classical groups *SL*_{n}(*K*), *Sp*_{n}(*K*), or *SO*_{n}(*K*). This characterization cannot be extended to semisimple subgroups.

*Osinovskaya A. A.*

**Restrictions of representations of classical algebraic groups to root A**_{1}-subgroups. pp. 31--33

*Summary:* Restrictions of irreducible representations of classical algebraic groups to root *A*_{1}-subgroups are studied. The composition factors of these restrictions for groups of types *A*, *B*, and *D* are found. The question is solved also for short root *A*_{1}-subgroups in groups of type *C*.

*Zabreiko P. P., Kovalenok A. P.*

**About the existence of nontrivial solutions for a class of elliptic problems.** pp. 34--37

*Summary:* The question about the existence of nontrivial solutions for a class of elliptic Dirichlet problems is considered. First we give conditions under which the index at infinity of the corresponding vector field equals I, so the task is to compare the index of a trivial solution with 1. The latter reduces the problem to either proving the oddness of a number of negative eigenvalues of the linearization at zero, when 0 is not an eigenvalue, or finding even higher order terms at zero which are nondegenerate on the kernel of the linearization.

*Gabasov R., Dmitruk N. M., Kirillova F. M.*

**A piecewise linear optimal observation problem.** pp. 38--41

*Summary:* An optimal observation problem for piecewise linear systems is under consideration. Algorithms for constructing program and positional solutions are given. They are based on a specific linearization of the piecewise linear problem with subseguent parametric optimization.

**ИНФОРМАТИКА**

*Likhoded N. A., Sobolevskii P. I., Tiunchik A. A.*
**Parallelizing of algorithms on the basis of splitting of macrooperations.** pp. 42--45

*Summary:* A new model for the representation of algorithms to solve a number of problems of parallel computations is developed. The use of the model for the construction of optimal scheduling functions and independent partitions is considered.

**ФИЗИКА**

*Knyazev M. A.*
**Kink in a nonlinear active medium.** pp. 46--48

*Summary:* One-kink and one-antikink solutions for a nonlinear equation of motion of the scalar field theory with fourth-order potential in the absence of a driven force and accounting the linear and nonlinear effects of damping are considered.

*Khomyakov P. A.*

**The operator method for solving the Schrodinger equation with a rational potential.** pp. 49--52

*Summary:* Exact numerical solutions of the Schrodinger equation with a rational potential are obtained by using the operator method. The effectiveness of nonunitary canonical transformations are shown. The energy of the ground and first excited states are calculated in the nonperturbation range of values of the parameters of the potential.

*Sosinovich V. A., Chornyi A. D.*

**Numerical solution of the equation for the one-point probability density function of turbulent passive scalar field fluctuations.** pp. 53--57

*Summary:* The problem of turbulent mixing, beginning from a state of full scalar unmixing, is considered. It is realized by meansof numerical integration of the equation for one-point probability density function *f*_{t}(Ã) of passive scalar fluctuations at a given conditional scalar dissipation rate c_{t}(Ã) with the aid of algorithms of retrospective problems solution. The evolution *f*_{t}(Ã) obtained is compatible with the results of numerous experimental and theoretical papers.

**ХИМИЯ**

*Shevchenko E. V., Kulak A. I.*
**Carbon fibers-based polyaniline-modified electrodes for measuring pH.** pp. 58--60

*Summary:* Polyaniline coatings doped with 12-tungstenphosphoric acid have been suggested for application to increase speed and linearity of the analytical response of carbon fiber pH-sensitive electrodes. It is shown that the annealing of doped electrodes at 200 °C made it possible to increase their stability and to provide the possibility of measurements in the range of pH 1.7--9.0 with an error ± 1.5 ¸ 4.3 mV for 46.9 mV slope of the dE/dpH curve.

*Potkin V. I., Zapol'skii V. A., Nechai N. I., Kaberdin R. V.*

**Condensation of 2-nitrosubstituted perhalogen-1,3-butadienes with ethyl vinyl ether.** pp. 61--63

*Summary:* The condensation reaction of 2-nitropentachloro- and 4-bromo-2-nitrotetrachloro-1,3-butadienes with ethyl vinyl ether proceeds by the substitution of the terminal chlorine atom in the nitrochloro vinyl group of initial nitro dienes and leads to the corresponding 6-etoxy-3-nitro-tetrahalogeno-1,3,5-hexatrienes. The cyclo addition products have not be en found in the reaction mixture.

*Babitskaya S. V., Kiselev P. A., Kisel' M. A.*

**A new approach to creation of lipide probes with intramolecularly quenched fluorescence.** pp. 64--67

*Summary:* New fluorescent analogues of phosphatidylcholine with intramolecularly quenched fluorescence containing a residue of 4-(1-pyrenyl)butyric acid as a fluorophore and a residue of bromine-labeled aliphatic acids as a quencher were synthesized. The spectral properties of substances obtained were described. A possibility of using these probes in investigations of biological and model membranes was demonstrated.

**БИОЛОГИЯ**

*Laznev K. V., Vorobei A. V.*
**Light-dependent binding of Merocyanine-540 (MC540) to erythrocytes: the role of the influx of the dye through the membrane.** pp. 68--71

*Summary:* The effect of a light dose on the time course of Merocyanine-540 (MC540) fluorescent dye binding to human erythrocytes and erythrocyte ghosts (open and sealed) was studied. It was found that the light-induced changes in the amount of MC540 bound to erythrocyte were concomitant with the changes in the bound dye fluorescense intensity, and the increase in MC540 influx into erythrocyte was the main reason for these changes. Our results support the evidence that both depolarization of erythrocyte membrane and direct increase in its permeability to amphiphylic molecules are the factors determining the light-induced influx of MC540 into erythrocytes.

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

**Evaluation of the fiber flax cultivar collection from isoenzyme spectra.** pp. 72--75

*Summary:* The analysis of the fiber flax cultivar collection for isoenzyme spectra of 6-phosphoglutamate dehydrogenase, glutamate dehydrogenase, and acid phosphatase has revealed genetic diversity of the forms studied. The obtained ratio of spectrum types in the analyzed enzymes maintains in the best way, in our opinion, homeostasis of fiber flax cultivars under artificial and natural selection.

*Rudenok V. V.*

**Age-related dynamics of neurofilament expression in paravertebral ganglia of a human.** pp. 76--78

*Summary:* A developmental pattern of neurofilament (NF)-immunoreactivity (IR) was investigated by the method of immunohistochemistry in the paravertebral ganglia of human fetuses and neonates. The results demonstrate age-related increase of NF-IR in sympathetic ganglia during maturation and growth. The NF can serve as a marker of differentiating neurons, as also as an index of the maturity of neonates.

*Domash V. I., Kaminskaya L. N., Pelageichik T. Ya., Volokhovich N. F., Khodortsova L. F., Koren' L. V., Matveenko S. N.*

**Proteinase and inhibitory activity of the grain proteins of spring and winter forms of triticale differing in tolerance to soil acidity.** pp. 79--82

*Summary:* The protein content, activity of neutral, acid, alkaline proteinases and inhibiting proteins were studied in grain of spring - and winter forms of triticale and genome-substituted wheat lines, tolerant to soil acidity, produced in vitro culture. The role of proteinase -- inhibitory system in resistance manifestation was revealed.

**НАУКИ О ЗЕМЛЕ**

*Starchik T. A.*
**The special features of the development of the Pripyat' paleorift basin boundaries.** pp. 83--86

*Summary:* Some differences in the formation of the regional closed structure of the Pripyat Trough in the cover and over the basement surface have been described. They are due to two major reasons: unconformable development of the Pripyat Trough relative to structures of the earlier stages and a difference in the evolution of the paleorift boundary faults.

*Mamchik S. O.*

**Jurassic and Lower Cretaceous deposit tectonics in the North-Pripyat shoulder area.** pp. 87--90

*Summary:* The special features of the Jurassic and Lower Cretaceous deposit structure in the North-Pripyat shoulder area: distribution boundaries, thickness variation, facies differences have been discussed. The tectonic movement inversion in post-Oxfordian and Aptian -- Early Albian time have been traced on the basis of drilling evidences.

*Avtushko M. I., Kovderko V. E.*

**Concerning the sources of radon contained in the interstitial air of the ground.** pp. 91--93

*Summary:* The probable sources of superfluous ground radon being by it self a difference between its actual contents in a soil and the contents, counted on ^{238}U concentration are reviewed. The data on the content and distribution of radon and uranium containing substance in the Earth atmosphere that make it possible to prove the assumption of atmospheric sources of radon into the formation of its redundant amount in the ground near the surface are being discussed. The outcomes of the experiment, that verifies this supposition are given.

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

**Geochemical special features of Pre-later Jurassic weathering cursts development on the granites of the West of Belarus.** pp. 94--96

*Summary:* The pattern of migration the of chemical and trace elements in the early Pre-later Jurassic weathering crusts developed on the garnets of Belarus both at the stage of weathering and in the postgenetic period is revealed. The attendant processes had the greatest influence on the behavior of potassium, magnium, silicom iron, and some trace elements (Ni, Cr, Hf, Nb, Y, Yb, Ba, Sr, Pb and Be).

*Zinovenko G. V., Voskoboinikova T. V.*

**Overbaltic Cambrian deposits of the Bug elevation of the Podlasie-Brest depression.** pp. 97--100

*Summary:* The paper contains the results of litological, paleontological and geophysical investigations of the Cambrian sequence of the Bug elevation of the Podlasie-Brest depression.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Samoilovich Yu. A., Timoshpol'skii V. I., Anisovich G. A., Trusova I. A.*
**Toward the selection of the regimes of vibrational effect on a steel ingot of electroslag refining (ERS).** pp. 101--105

*Summary:* Problem of the influence of vibration on an industrial ingot produced by ESR is considered. Results of experiments based on the possibility of control ling the process of the initial solidification of an ESR ingot are given. A technological possibility of executing an industrial melting in resonance frequency oscillation of a liquid steel bath is proved. A possibility of resonance oscillation use in a laboratory and industrial environment is proved theoretically.

*Yashcheritsyn P. I., Averchenkov V. I., Kheifets M. L., Kukhta S. V.*

**Analysis of the properties of ratios of technological solutions in designing combined methods of the treatment of materials.** pp. 106--109

*Summary:* The dominant characteristics of relations of technological solutions are suggested for using in automated design of the methods materials treatment. Criteria of transfer, which describe the domination of the controled parameters of the oftechnological system are considered.

*Chichko A. N., Likhouzov S. G.*

**Cell-automatic modeling of the process of melt flow in a mould.** pp. 110--114

*Summary:* Three-dimensional mathematical model for estimating the defects appearing during the flow of melted metal down the walls in gating systems on the basis of the Navier-Stokes and Fourier-Kirchoff is suggested equations. The results of the simulation of velocities and temperatures of the spatial elements of gating-casting system used in production of radiators are presented.

*Sviridenok A. I., Kovalevskaya T. I., Liopo V. A., Voina V. V., Kravtsov A. G., Sechko A. E.*

**Structure-charge correlations in polyethylene fibers.** pp. 115--118

*Summary:* The phisicochemical nature of volumetric defects which are responsible for the appearance of a residual charge in polyethylene fibers is investigated. The IR spectroscopy, X-ray structural analysis, thermally stimulated depolarization methods and mechanical tests were used. It is established that the residual charge is due to the defects caused by internal friction that accompanies the separation displacement of lamellas and inside and interlamellar sliding.

*Mariev P. L., Moiseenko V. I., Papkovskii P. I.,Kharitonchik D. I.*

**Bases of homogeneity and increase of the carrying ability of the nitride hardened surfaces of large-size machine parts.** pp. 119--122

*Summary:* The possibilities of increasing the load carrying ability of nitride hardened surfaces of machine steel parts by uniformily increasing a superficial hardened layer and increasing the hardness of the core details material are considered. The laws of change of hardness and mechanical uniformity of a layer from positions of constantly existing boundary limited copper concentration in a material which is not mutually soluble with nitrogen are investigated. The rational ways of protection of nitride hardened surfaces from oxidation in the ally thermstrengthened core of details are shown.

/ 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 © 2001-2008 Национальная академия наук Беларуси

Копирайт © 2001 Издательство "Беларуская навука"