# Доклады Академии наук Беларуси, 1996, Том 40, No.3

/ Издания академии / Научные журналы

Доклады Академии наук Беларуси, 1996, Том 40, No.3

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Benyash-Krivets V.V., Chernousov V.I.*
**On the varieties of two-dimensional representations of the fundamental groups of surfaces.** pp. 5--9

*Summary:* For the fundamental group **Ã**_{g} of the compact non-orientable surface of genus *g* the structure of the two dimensional representation variety is described.

*Bernik V.I., Dodson M.*

**The exact order of zero approximation by values of integral polynomials of complex variable.** pp. 10--13

*Summary:* For the curve *G*=*(z*^{m}, z^{n}), *z* Î *C*, *n*£*m*, the complete analogy of the famous theorem of A.Khinchine in the metric theory of diophantine approximations is proved.

*Kovalevskaya E.I.*

**Simultaneous approximation and the effective estimate for the measures of the sets with the given diophantine properties.** pp. 14--17

*Summary:* The effective estimate for Lebesgue measure of the points on the smooth manifolds simultaneously well approximated by rational numbers is obtained.

*Metelsky N.N., Martynchik V.N.*

**The cone of convexity directions for closed sets in ***R*^{n}. pp. 18--20

*Summary:* Vector n Î *R*^{n} is called a direction of convexity for a set *X* Ì *R*^{n} if for any point *x*_{o} the intersection of line *x *= *x*_{o} + l n, l Î *R*, and *X* is empty or connected. The cone of convexity directions for a closed set in *R*^{n} is described. A relation of the cone of convexity directions for a polygonal region to the structure of its border is under research. Complexity bounds for computing the cone are obtained.

*Lepin V.V.*

**Complexity of nondeterministic algorithms for front constrained problems.** pp. 21--25

*Summary:* Frontwidth constraints on problems: 3-SATISFIABILITY, HAMILTONIAL CIRCUIT and PEBBLE are considered. We show that 3-SATISFIABILITY, when restricted to n-clause collections of frontwidth *f(n)*, is in the complexity class NTISP(*poly, f(n)*); HAMILTONIAL CIRCUIT for *n*-vertex graphs of frontwidth *f(n) *is in the class NTISP(*poly, f(n)* log* f(n)*); and PEBBLE for *n*-vertex graphs of frontwidth *f(n)* is in the class NSPACE(*f(n)* log^{2}*n*).

*Metelsky Yu.M., Tyshkevich R.I.*

**Line graphs of linear 3-uniform hypergraphs.** pp. 26--30

*Summary:* In the paper it is proved that there is a finite list *A* of graphs such that any graph *G* with minimum degree at least 19 is the line graph of a linear 3-uniform hypergraph if and only if none of the members of *A* is an induced subgraph of *G*.

*Zverovich E.I.*

**On the problem of the linear conjugation for analytic functions in a bidisk.** pp. 31--35

*Summary:* The problem of finding two functions j*(z)* and y*(w)* analytic on the discs |*z*|<1 and |*w*|<1 respectively which satisfy the functional equation is considered: *a(z)* j*(z)* + *b(w)* y*(w)* = *c(z, w)*, (*z, w*) Î W, where W is a Riemann surface defined by the non-reducible algebraic correspondence *A(z,w)*= 0. For the investigation of this problem is proposed a method based on the global uniformization of the correspondence *A(z,w)* = 0.

*Marchenko V.M., Yakimenko A.A.*

**On the distribution of quasipolynomial roots.** pp. 36--41

*Summary:* The situation of the roots of the quasipolynomial l + *a*_{1} + *a*_{2} e^{- lh} + *a*_{3} l e^{- lh} with respect to its coefficients is studied.

*Rovba Je.A.*

**Quadrature formulae of interpolation-rational type.** pp. 42--46

*Summary:* Quadrature formulae of Gaussian type are introduced with the help of interpolated rational functions. Remainder estimates have been obtained in the class of continuons functions.

**ФИЗИКА**

*Bogush A.A., Otchik V.S.*
**On the motion of a charged particle in the field of two remote coulomb centres. ** 47--51

*Summary:* For the two Coulomb centres problem with large inter-centre separation, a new relation between solutions of the Schroedinger equation is found as a limit of the corresponding relation for the similar problem in the Lobachevsky space. As an application, the expression for the term splitting at a pseudocrossing is obtained.

*Kudryashov V.V.*

**Quasi-harmonic approximation for solution of the two-dimensional Schroedinger equation.** pp. 52--55

*Summary:* The method for obtaining the approximate solutions of the two-dimensional Schroedinger equation with an arbitrary smooth potential which does not allow separation of variables is proposed. The approximation is constructed with the employment of a new procedure of a transition from known solutions in the neighbourhood of a fixed point to solutions in the whole two-dimensional space.

*Olekhnovich N.M., Pushkarev A.V.*

**Birefringence and depolarization phenomena of X-ray many-wave scattering in Laue case for highly distorted crystals.** pp. 56--60

*Summary:* The birefringence and depolarization effects of the transmitted beam in Laue case many-wave X-ray diffraction for highly distorted crystals were revealed. The characteristics of these effects were found to depend on the turn angle of the polarization vector of the incident beam.

*Virchenko V.A., Kuzmin V.S., Tkachenko T.M., Shablovsky A.V.*

**Temperature dependence of quadrupole splitting of **^{57}Fe Moessbauer spectra in high temperature superconductor. pp. 61--65

*Summary:* Direct experimental proof of adequacy of the unharmonically unstable oxygen atom's sublattice model in the YBa_{2}Cu_{3-x}Fe_{x}O_{7-y} base high temperature superconductor was received on the bases of temperature dependence of Quadrupole Splitting of Moessbauer spectra.

*Ryzhkovsky V.M., Dymont V.P., Yerofeenko Z.L., Nekrashevich E.M.*

**The magnetic ordering in the solid solutions Mn**_{2-x}Fe_{x}Sb (0.05 £ x £ 0.7). pp. 66--69

*Summary:* The solid solutions of the Mn_{2-x}Fe_{x}Sb (0.05 £ x £ 0.7) system with the Cu_{2}Sb-type crystal structure have been obtained. The specific magnetization vs temperature has been investigated. The model of magnetic ordering Fe and Mn in this system is proposed.

*Dailyudenko V.F., Krot A.M.*

**The local-topological method of determining the minimal embedding dimension of the chaotic attractor.** pp. 70--75

*Summary:* The new topological method for determination of minimal embedding dimension of the chaotic attractor is proposed. It is shown that the suggested method makes it possible to reduce by an order the quantity of the required experimental data. to spare essentially computer resources and provides a good convergence of the calculation process and reliable definition of the minimal embedding dimension value.

**ХИМИЯ**

*Krutko N.P., Opanasenko O.N., Ovseenko L.V., Starostina O.I.*
**The regulation of colloid-chemical properties of cationic surfactants.** pp. 76--80

*Summary:* The colloid-chemical properties of the aqueous solution of long-chain aliphatic amines and their oxyethylene derivatives have been investigated by the tensiometric and viscosimetric methods. The correlation between the structure of surfactant molecules and their behavior in solution has been established that makes it possible to predict the possibility of application of different surfactants for emulsification of various hydrocarbons changing their hydrophilic-lypophilic balance by regulation of the polyoxyethylene chain length.

*Potkin V.I., Zapolsky V.A., Nechai N.I., Kaberdin R.V.*

**Synthesis of polyfunctional heterocyclic derivatives of nitrohalogenbutadienes.** pp. 81--85

*Summary:* Synthesis of different nitrogen-containing polyheterocyclic systems occurred by use of 2-nitroperhalogenbutadiene derivatives.

**БИОЛОГИЯ**

*Konoplya E.F., Bagel I.M., Shafranovskaya E.V.*
**The influence of low-dose ionizing radiation on Ca**^{2+}-ATPase activity of sarcoplasmatic reticulum membrane of skeletal muscle. pp. 86--89

*Summary:* An external gamma-irradiation with doses of 0.25 and 0.5 Gy results in an increase in Ca^{2+}-ATPase activity in SR of skeletal muscle, while 1 Gy exposure at early terms increases enzyme activity, but later on decreases it. The alterations revealed indicate disturbances of structural and metabolic processes in SR membranes which are redoubled with dose load increase.

*Chirkin A.A., Pristavko V.T., Chirkina A.A.*

**Integral characteristic of blood plasma lipid transport system in radiation-induced dyslipoproteinemia development.** pp. 90--93

*Summary:* Mathematical characteristics of blood plasma lipid transport system (LTS) of rats exposed to 0.25 -- 5.0 Gy radiation are given. Radiation-induced transitory dyslipoproteinemia is described by means of integral indices of direct and reverse cholesterol transport and integral index of LTS. Mathematical apparatus for calculating integral indices is worked out.

**НАУКИ О ЗЕМЛЕ**

*Bulkin Yu.S., Makhnach A.S.*
**Metallogenic specialization of granitoids from the Mostovsky and Vygodsky massives of Belarus.** pp. 94--97

*Summary:* On the basis of geochemical study it is shown that rare metal orebodies, particularly the molybdenite ones, can he found within the Mostovsky and Vygodsky granitoid massives of Belarus. Areas for ore prospecting are suggested.

*Kruchek S.A., Obukhovskaya T.G., Golubtsov V.K.*

**New evidence for the Upper Devonian Rechitsa deposits in the Belarus area.** pp. 98--103

*Summary:* The Rechitsa horizon deposits of the Frasnian stage of the Devonian are represented by three section types: normal-sedimantary showing a wide occurrence; volcanogenic-sedimentary confined to volcanic pipe calderas (diatremes); volcanogenic associated with volcanic pipes without caldera-like depressions. The above deposits were formed under continental and marine conditions.

*Kiselev P.A.*

**The assessment of the underground fresh water zone capacity in water-bearing complexes of various tectonic structures.** pp. 104--107

*Summary:* The equations for revealing the existence of interaction between fresh and mineralized underground waters were proposed. Evaluation of this interaction was fulfilled in the central part of Belarus.

*Pap A.M.*

**On granitization of the Okolovo series rocks.** pp. 108--111

*Summary:* Granitization of the Okolovo series rocks displayed in less degree and at later stage than in the Shchuchin gneisses that gives the possibility to recognize the primary origin of the Okolovo series rocks.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Boiko B.B., Zubovich G.K., Uvarova N.N., Shipilo V.B.*
**Disposal of graphite from synthetic diamond powders by pulse laser radiation.** pp. 112--114

*Summary:* The possibility of selective disposal of graphite from the diamond-graphite mixer by the action of IR-laser radiation pulses has been proved experimentally.

*Veinik A.I., Komlik S.F.*

**The influence of crown discharge on the cast crystallization process.** pp. 115--116

*Summary:* Structure and mechanical properties of metal at hardening of cast near crown discharge are shown to change.

*Soika A.K., Vashkevich I.M.*

**Forming pulses of strong magnetic fields in discharge vibratory circuits.** pp. 117--121

*Summary:* The paper describes a new method for forming pulses of strong magnetic fields in discharge oscillator circuits distinguished from the known ones by its exceptional engineering simplicity, universal character and reliability.

/ 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 © 1997-2008 Национальная академия наук Беларуси

Копирайт © 1996 Издательство "Беларуская навука"