# Доклады Академии наук Беларуси, 1996, Том 40, No.2

/ Издания академии / Научные журналы

Доклады Академии наук Беларуси, 1996, Том 40, No.2

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Gaishun I.V.*
**Stability conditions for discrete Volterra equations.** pp. 5--8

*Summary:* Some conditions of stability and asymptotical stability for discrete Volterra equations in Banach spaces and algebras are obtained.

*Benyash-Krivets V.V., Chernousov V.I.*

**On representation varieties of tile fundamental group of Klein's bottle.** pp. 9--13

*Summary:* For the fundamental group **Ã** of the compact non-orientable surface of genus *g* = 2 the structure of representation varieties of **Ã** into **GL**_{n} is described.

*Guletsky V.I., Yanchevsky V.I.*

**Reciprocity laws in Brauer groups of function fields of number curves with special Jacobians.** pp. 14--17

*Summary:* For smooth projective geometrically irreducible curve *C* over number field *k* with *k*-rational point the obstruction group to realization of sets of characters, satisfying reciprocity law, as sets of local invariants of elements of Brauer group of *k*-rational functions on *C* is calculated for the case where 2-torsion of Jacobian of *C* is *k*-rational.

*Dymkov M.P.*

**Existence and structure of the optimal solution to the quadratic optimization problem for linear 2-D control systems.** pp. 18--22

*Summary:* The two-parametric discrete (2-*D*) system with quadratic cost functional is considered. The existence and uniqueness conditions for optimal solution are expressed in terms of spectral properties of the system. The optimal closed-loop control is represented by means of state variables of the conjugate system.

*Borukhov V.T.*

**The Grassmann manifold of linear infinite dimensional control dynamic systems.** pp. 23--25

*Summary:* Topological structure of the set of the orbits of state feedback group action on the manifold of linear infinite dimensional control dynamical systems is studied. The set of the orbits is parametrized by points of an open analytical submanifold of Grassmannian.

*Baranov A.A.*

**Locally finite quotient algebras of universal enveloping algebras.** pp. 26--30

*Summary:* A bijective correspondence between the set of inductive systems of representations of a locally finite-dimensional locally perfect Lie algebra and that of semiprimitive ideals of its universal enveloping algebra with locally finite-dimensional quotients is proved.

*Tyshkevich R.I.*

**On hypergraph coverings connected with matroid intersections.** pp. 31--33

*Summary:* The parameter *eq(H)* is introduced and investigated for a hypergraph *H* without multiple edges. This parameter is a direct generalization of the equivalent covering number. Let *L(H)* be an independent system whose cycles are only minimal edges of *H* with respect to inclusion. Then *L(H)* can be represented as an intersection of *eq(H)* matroids.

*Zabreiko P.P.*

**Chebyshev envelopes and multivalued operators of superposition.** pp. 34--38

*Summary:* This article is devoted to the analysis of the pass from the given multivalued operator *A* to the singlevalued operator *B*, for which *Bx* is the Chebyshev center of a set *Ax* for all *x*. In particular the implicit formula of this pass are presented for usual superposition operators. As application a new solvability result for Hammerstein integral inclusion is given.

*Yerovenko V.A.*

**Essential spectra of linear differential operators with almost constant coefficients.** pp. 39--43

*Summary:* The paper describes various essential spectra of the minimal and maximal perturbated ordinary almost-constant differential operators in Banach spaces.

*Amelkin V.V.*

**Top estimation of the strong limit cycle number of polynomial dynamic systems.** pp. 44--45

*Summary:* S.P. Diliberto's estimation of the number of the strong limit cycles of the two-dimensional polynomial autonomous systems of the ordinary differential equations is ascertained.

*Vasiliev I.L., Plashchinsky P.V.*

**Discrete Mellin transformations and convolutions.** pp. 46--48

*Summary:* A new inversion formula for Dirichlet series is proved. The discrete Mellin transformations and convolutions are considered.

**ФИЗИКА**

*Efendiev T.Sh., Rubinov A.N., Katarkevich V.M.*
**Generation of ultrashort pulses by a solid-state DFB dye laser under nanosecond excitation.** pp. 49--52

*Summary:* Lasing of tunable ~0.5 ns pulses with spectral linewidth less than 0.01 nm was obtained in a DFB laser based on a dye doped epoxypolymer pumped with 14 ns second harmonic pulse of YAG:Nd-laser. The temperature sensitivity of the laser wavelength was 2.3·10^{-2} nm/K, which is seven times less than that of a DFB laser with ethanol solution.

*Kolovandin B.A., Vatutin I.A.*

**Conditional statistical description of surface dynamics in turbulence.** pp. 53--55

*Summary:* A general approach to description of turbulence parameters on conditional mixing surfaces is proposed. Justification of the statistical second-order model for the conditional averaged scalar field parameters in isotropic turbulence with strong vorticity of the velocity field is presented.

*Kuzmin V.S., Smirnova T.V.*

**Dynamics of pulse saturation of inhomogeneously broadened two-level systems.** pp. 56--60

*Summary:* It is theoretically shown that the Bloch description of pulse saturation of inhomogeneous broadened two-level systems is correct when after "burning-out of dip" in the spectroscopic line envelope the processes of energy transfer from the saturated spin packets to unsaturated ones don't occur. Otherwise the Bloch theory describes the delay of pulse saturation signal until the appearance of the indicated effect.

*Knyazev M.A., Vengrinovich V.L.*

**Inhomogeneous distribution of magnetization in domain.** pp. 61--63

*Summary:* Inhomogeneous magnetic state in anisotropic ferromagnet in the vicinity of phase transition of the second type is considered. It is shown that there is the rotation of the magnetic moment density vector in domain while moving from its centre to boundary.

*Ryzhkovsky V.M., Dymont V.P., Pashkovsky I.L.*

**Formation conditions and crystallochemical properties of manganese pnictides with the Cu**_{2}Sb structure. pp. 64--67

*Summary:* The conditions of formation of the Mn_{2-x}Ni_{x}As (0£x£0.6) alloys have been investigated by the methods of magnetometry and thermography. It has been ascertained that the single-phase alloys with stoichiometric composition having tetragonal structure of the Cu_{2}Sb type (d-phase) exist only at high temperatures (» 1100 K). The d ® e-phase transformation with the variation of the composition of the d-phase towards the increase of the content of the metallic component and appearance of the additional e-phase of the NiAs type occurs at *T* < 800 K. It has been shown that such character of crystallic behaviour is inherent also in other manganese pnictides with the Cu_{2}Sb structure.

**ХИМИЯ**

*Ulianova T.M., Krutko N.P., Titova L.V., Zub E.M.*
**Interaction between ceramic fibers LaPb(ZrTi)O**_{3} and polar polymer groups in piezocomposites. pp. 68--71

*Summary:* It was established that ceramic fibers LaPb(ZrTi)O_{3} added to PVA-based composite change the structure of polar polymer groups forming hydrogen bonds with them. Temperature dependencies of the dielectric permittivity and losses also vary, and piezoelectrical characteristics of the composite improve with an increase in the content of a fiber filler.

**БИОЛОГИЯ**

*Goncharova L.V., Reshetnikov V.N.*
**Proteinase activity of nuclear proteins in winter triticale.** pp. 72--75

*Summary:* Research of nuclear polypeptide composition was carried out. Endopeptide components of three nuclear fractions: nucleoplasma proteins, matrix proteins and matrix residual proteins were revealed. All revealed proteolytic components were characterized by their proximity among each other by molecular weights and differed from the protein basic group of nucleoplasma and cell nuclei matrix.

*Shalygo N.V., Averina N.G.*

**The influence of metal cations on chlorophyll accumulation in greening barley seedlings.** pp. 76--79

*Summary:* The effects of twenty metal cations on chlorophyll (Chl) biosynthesis in greening barley seedlings have been investigated. It was shown that relatively small concentrations of the cations stimulated Chl accumulation, while higher concentrations of the cations inhibited this process. The most strong activators of Chl biosynthesis were K^{+}, Rb^{+}, Ni^{2+} and Zn^{2+}. According to inhibitory actions the cations fall into the next order: Cd^{2+} > Cu^{2+} > Co^{2+} > Ni^{2+} > Hg^{2+} > Pb^{2+} > Zn^{2+} > Mn^{2+} > Al^{3+} > Fe^{2+} > Cs^{+} > Li^{+} > Ba^{2+} > Rb^{+} > Ag^{+} > Sr^{2+} > Ca^{2+} > Mg^{2+} > K^{+} > Na^{+}.

*Kholmetskaya M.O., Lobanok E.V., Chernin L.S.*

**Synthesis of indoleacetic acid with some phytopathogenic and nonpathogenic bacteria.** pp. 80--83

*Summary:* A collection of phytopathogenic and nonpathogenic bacteria falling into genera *Pseudomonas, Xanthomonas, Erwinia, Corynebacterium, Rhizobium, Agrobacterium* was examined for the ability to synthesize indoleacetic acid (IAA). The results obtained indicate that IAA-producing ability is the property that is peculiar to all examined bacteria regardless of their taxonomic belonging.

*Demidchik V.V., Sokolik A.I., Yurin V.M.*

**The copper ion influence on functioning of plant cell plasmalemma H**^{+}--ATPase. pp. 84--87

*Summary:* The effect of Cu^{2+} on light-induced H^{+}-ATPase of intact Nitella flexilis cells was studied by conventional voltage clamp microelectrode technique. Enhancing of H^{+}-ATPase light-induction and inhibition of dark H^{+}-ATPase activity by Cu^{2+} (10^{-5} -- 10^{-4} M) was demonstrated. Modification of active and light-activation sites of H^{+}-ATPase molecular complex was suggested as a probable mechanism of copper influence on the plant plasma membrane H^{+}-ATPase.

*Ostapenya A.P., Umnov A.A.*

**Radionuclide **^{137}Cs migration mechanism in a stratified lake. pp. 88--92

*Summary:* The problems of investigation of radionuclide transfer mechanism among components of lake ecosystem are discussed. On the basis of long-term investigations of lakes subjected to contamination by radioactive caesium after the Chernobyl accident a mathematical model of radionuclide transfer and accumulation in the lake ecosystem was developed. We managed to follow the redistribution process of radioactive caesium from the moment of the accident to the present time and succeeded to substantiate the key role of biota in the processes of ^{137}Cs-accumulation and burying in bottom sediments.

**НАУКИ О ЗЕМЛЕ**

*Levykh N.N., Makhnach A.S.*
**Paragenesis of newly-formed minerals of cryslalline base weathering crusts in Belarus.** pp. 93--95

*Summary:* A definition of a weathering crust is given. Criteria of crust recognition and paragenesis of authigenic minerals typical of weathering crusts are discussed.

*Konishchev V.S.*

**Formation of the Lower Permian secondary compensative synclines in the Pripyat River depression.** pp. 96--100

*Summary:* Formation of the secondary lower permian compensative synclines and the lower permian secondary salt strata is considered.

*Velichkevich F.Yu., Litvinyuk G.I.*

**Morphology and evolution of ***Caulinia minor (All.) Coss. et Germ.* seeds in Pleistocene deposits in Belarus. pp. 101--104

*Summary:* The characteristics of *Caulinia minor (All.) Coss. et Germ.* (*Najadaceae Juss.*) fossil seeds from the Late Pliocene and Pleistocene sediments of Belarus have been defined more precisely by scanning electron microscopy.

*Sanko A.F.*

**Morphogenetic classification of Pleistocene freshwater calcareous deposits.** pp. 105--108

*Summary:* A devised classification of the Pleistocene freshwater calcareous deposits based on genetic and relief features is proposed. The investigated deposits are classified into 4 morphogenetic species -- watershed slope, river (dolina), swamp and lacustrine ones.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Novikova L.N., Dostanko A.P., Khmyl A.A.*
**The influence of surface-active substances on kinetics of tin electrodeposition from sulfate electrolytes.** pp. 109--112

*Summary:* The paper deals with the study on the influence of different organic substances on the process of tin electrodepositing from the sulfate electrolyte. On the basis of the obtained kinetic regularities the conclusion about intensification of tin deposition process by adding trimethylcetylammonium iodide and ethylcetylmorpholinium bromide to the electrolyte was drawn. Besides, the presence of ethylcetylmorpholinium bromide in the solution increased a dissipating ability of the electrolyte.

*Starikov S.V., Bogdanovich P.N.*

**Correlation between plastic and eutectic alloy diagram behavior.** pp. 113--116

*Summary:* A binary alloy diagram characteristic that takes into account chemical and phasic composition of the alloy as well as the limiting solubility temperature gradient in both phases is suggested. This characteristic is shown to correlate with a maximal relative elongation of the alloy. The data confirming the necessity of high solubility in one of the phases for displaying alloy superplasticity are presented.

*Struk V.A., Ivchenko E.I., Ovchinnikov E.V., Gubanov V.A., Linkevich D.A.*

**The influence of energy factors on the structure of fluorine-containing oligomeres.** pp. 117--120

*Summary:* Energy influence leads to radical -- oxidation processes in thin films of oligomeres with fluorine (OWF) the result of which is structural configurations of OWF. Orientation of oscillation vector is close to isotropic when the temperature is about the destruction one. Orientation effects result in changes of OWF properties.

/ 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 © 1996-2008 Национальная академия наук Беларуси

Копирайт © 1996 Издательство "Беларуская навука"