# Доклады Национальной академии наук Беларуси, 1998, Том 42, No.2

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 1998, Том 42, No.2

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Gaishun I.V.*
**Trajectory stabilization by impulse control under disturbances.** pp. 5--7

__Summary:__ Let a system of control *x = A(t)x + b(t)u + w(t)* be given in the space **R**^{n}. Here *u(t)* is a control input and *w(t)* is a piecewise continuous disturbance. The conditions under which distributions of finite type may be used as control actions are established. Necessary and sufficient conditions for asymptotic convergence of all solutions to the given trajectory (curve) with the help Dirac delta-distributions are obtained.

*Belousov M.V., Lebedev A.V.*

**Symbolic calculus non-local boundary-value problem with shifts on the boundary.** pp. 8--12

__Summary:__ The symbolic calculus and the Fredholmity conditions for the non-local boundary-value problems generated by the Boutet de Monvel operators and normally acting shifts of the boundary are obtained.

*Erovenko V.A.*

**Analogs of classical Weyl theorem on invariance of the essential spectrum.** pp. 13--17

__Summary:__ A generalized Weyl theorem for the essential spectra of ordinary differential operators in *L*^{p}-spaces, 1£*p*£¥, is described.

*Tretjakova N.N.*

**Vector special functions and representations of the rotation group.** pp. 18--24

__Summary:__ A new class of vector special functions, **R**-functions of group *SO(n)*, is introduced. These functions are connected with the higher classes representations of this group and form the kernels of the Fourier series expansions for arbitrary quantities, defined on the sphere *S*^{n-1}. The properties of **R**-functions are studied. Their connection and analogy with some classical special functions is established.

*Kilbas A.A., Bonilla B., Rodriguez J., Trujillo J., Rivero M.*

**Compositions of fractional integrals and derivatives with Bessel type function and solution of differential and integral equations.** pp. 25--29

__Summary:__ The compositional relations of Liouville fractional integrals and derivatives with the special function of Bessel type generalizing modified Bessel function of the third kind are proved. It is shown that such a special function is invariant with respect to certain generalized fractional differentiation operators, in particular with respect to Bessel -- Clifford differential operator and differential operator of axisymmetric potential theory. Applications are given to obtain explicit solutions of differential equations of fractional and integer order and of Volterra integral equations of the third kind.

*Minchenko L.I., Satsura T.V.*

**Pseudo-Holderability and metric regularity of multivalued maps.** pp. 30--35

__Summary:__ Pseudo-Holder multivalued maps are studied. The equivalence between pseudo-Holder behavior and metric regularity of rate n is investigated.

*Khomichkov I.I.*

**Retrial queue with probability of losses under double connecting.** pp. 36--39

__Summary:__ An algorithm for computation of the generation function of the number of customers in a retrial queue is obtained.

*Tuzikov A.V., Hejmance H., Margolin G.L., Shemin S.A.*

**Similarity measures of convex polygons.** pp. 40--44

__Summary:__ Similarity measures of convex shapes are discussed. Their definitions are based on Minkowski addition and Brunn -- Minkowski inequality. All measures considered are invariant under translations; moreover, they may also be invariant under rotations, multiplying by a scalar, reflections, and linear transformations. In case of convex polygons, efficient algorithms for similarity measure calculation are proposed.

*Tchij O.P.*

**Hyperbolic Monge -- Ampere equations with transitive symmetry groups.** pp. 45--48

__Summary:__ It is shown that every Monge -- Ampere equation with transitive algebra of contact symmetries can be considered as a certain invariant geometric structure on homogeneous space. The local classification of generic equations is obtained (up to the group of contact transformations).

*Shiryaev V.M.*

**Identities at semibrauerian algebras.** pp. 49--51

__Summary:__ The class of semibrauerian algebras is investigated. It is shown that this class is a variety of universal algebras with a finite basis of identities, the latter with other relations is produced. Thirteen identities fulfilling at any brauerian but not at any semibrauerian algebras are given. It is proved that the variety of semibrauerian algebras is arithmetic.

*Guletskii V.I., Yanchevskii V.I.*

**Cyclic algebra representation of torsion in Brauer groups of curves.** pp. 52--55

__Summary:__ Description of cyclic algebra representation of *n*-torsion part in Brauer group of curve over field of characteristic 0 is obtained.

**ФИЗИКА**

*Sirota N.N.*
**On physical nature of metals strength.** pp. 56--59

__Summary:__ While considering the causes of the difference between technical and theoretical (physical) strength of solids by the example of carbon steel, a model is analyzed where quasi-filaments, separated by inclusions, are formed in breaking, as well as coefficient of their breakage synchronism j is introduced. This coefficient enhances with increasing inner surface of the phase interface, thus, ensuring the improvement of technical strength. At j ® 0 the break in the quasi-filaments occurs in turn resulting in a decrease of the technical strength, though each quasifilament exhibits the strength close to the theoretical one.

*Grushevskaya G.V., Gursky L.I., Dorozhkin N.N.*

**Modeling of non-spheric correlational potential of interatomic interaction in solids.** pp. 60--65

__Summary:__ Non-spherical correlation potential of interatomic interaction in solids has been calculated. The influence of atom electronic shell deformation on polarization effects has been established based on self-consistent calculations of scattering waves (linear Muffin-Tin orbitals method).

*Knyazev M.A.*

**Coupled states of three kinks in F**^{4} theory with damping. pp. 66--68

__Summary:__ Explicit solutions of the equation of motion for F^{4} theory with damping which correspond to the field configurations describing coupled states of various combinations of three kinks and/or antikinks are constructed.

*Primak I.U., Sotsky A.B.*

**On sensitivity of integral optic measurements of adsorbed layer parameters.** pp. 69--74

__Summary:__ The analysis of errors arised under reconstruction of thickness and dielectric permittivily of ultrathin adsorbed layers precipitated on the surface of the waveguiding structure farmed at the prism coupler was performed. Possibilities of minimization of the mean square errors for protein adsorbed layers were determined.

**ХИМИЯ**

*Nechai N.I., Potkin V.I., Kurman P.V., Kaberdin R.V.*
**Synthesis and some properties of 1,3-dinitro-1,2,4,4-tetrachloro-1.3-butadiene.** pp. 75--78

__Summary:__ For the first time 1,3-dinitro-1,2,4,4-tetrachloro-1,3-butadiene has been obtained by nitration of available 1,1,3,4-tetrachloro-1,3-butadiene with mixture of HNO_{3} and H_{3}PO_{4} (10 : 1). The interaction of dinitrodiene with some nucleophiles has been studied. Peculiarities of the chemical behaviour of a-nitro-b,b-dichlorovinylic and b-nitro-a,b-dichlorovinylic groups have been revealed in S_{N}Vin processes.

**БИОЛОГИЯ**

*Koren L.V., Kaminskaya L.N., Khotyljova L.V.*
**Cytological investigation of wheat-rye amphiploids with inclusion of Vrn genes.** pp. 79--84

__Summary:__ Cytologically stable forms of hexaploid and octoploid triticale marked with dominant V_{rn} genes have been isolated from an advanced generations (*F*_{4}) of wheat-rye amphiploids developed by crossing nearly isogenic common wheat lines with certain systems of the V_{rn} genes and winter rye variety Voskhod. Specific effects of wheat genotype on process of cytological stability of the wheat-rye amphiploids have been revealed.

*Nedvetsky P.I., Mongin A.A., Konev S.V.*

**Influence of arachidonic acid on the voltage-operated calcium channels in rat brain synaptosomes.** pp. 85--88

__Summary:__ The effect of arachidonic acid on the activity of voltage-operated calcium channels, measured as voltage-dependent ^{45}Ca^{2+} accumulation in rat brain synaptosomes, was studied. Arachidonic acid (5--100 µM) dose-dependent activated voltage-operated calcium channels. Inhibitor of phospholipase A_{2} 4-bromophenacyl bromide, decreasing release of endogenous arachidonic acid, and inhibitor of cyclooxigenase aspirin, preventing prostanoid synthesis from arachidonic acid, suppressed voltage-dependent ^{45}Ca^{2+} uptake by synaptosomes. The obtained data suggest that arachidonic acid and its metabolites participate in regulation of voltage-operated Ca^{2+} channels in brain nerve endings.

*Kraskovskiy G.V., Mironova G.I., Manina E.Yu., Migolienia T.I., Rosetskaya S.D., Pashatskaya T.V.*

**Study of protection and reparation of oncogenic and genetic damages induced by urethane and gamma-irradiation.** pp. 89--94

__Summary:__ Administration of solcoserile or thymaline after urethan to mice was revealed to reduce the level of chromosome damages in bone marrow and tumor formation in mice lungs. Administration of diethylnicotinamide (75 mg/kg) before urethan (1.5 mg/g) reduces the level of chromosome damages by 70% and tumor formation -- by 59%. Administration of thymogene before g-irradiation and thymaline + solcoserile after it induces a pronounced effect of protection-therapy (repair) of chromosomal damages.

*Kulminskaya I.V., Shilko T.S., Ukrainko A.P., Podunova T.V.*

**Cytological investigation of primary triticales produced on the basis of self-fertile rye lines.** pp. 95--97

__Summary:__ The influence of genotypic properties of self-fertile lines of diploid rye on cytological stability of primary triticales C_{0}--C_{3} was revealed.

*Radyuk M.S.*

**Stepwise character of protochlorophyleide accumulation from exogeneous 5-aminolevulinic acid in etiolated leaves of barley.** pp. 98--100

__Summary:__ A differential approach to the study of biological processes occurring in the developing plant plastids was used. It was shown that the process of protochlorophyllide accumulation from exogeneous 5-aminolevulinic acid in etiolated leaves proceeds in stepwise way from one steady level to another. Occurring during this process the alterations in protochlorophyll content have a wave-like character. A possible role of protochlorophyll in a stepwise process of protochloropliyllide accumulation is discussed.

*Vadetskaja T.N., Shukanova N.A., Vorobey A.V.*

**The role of a-tocopherol and glutathione in membrane defense under photodynamic action on erythrocytes.** pp. 101--103

__Summary:__ Participation of a-tocopherol and glutathione in defense of membrane from formation damages leading to haematoporphyrin photosensitized erythrocytes hemolysis is shown. Under intensive photodynamic action resulting in cell lysis directly on lighting main defense role plays membrane bound (a-tocopherol; under erythrocytes hemolysis in dark after shot photodynamic action -- decisive meaning has cytoplasm glutathione.

*Yatsyna A.A., Kontsevaya I.I., Yagodkina M.V.*

**Embryo culture of cloudberry (***Rubus chamaemorus L.*). pp. 104--106

__Summary:__ In the current paper the best cultural conditions are determined for germination embryos of the cloudberry. Plantlets obtained were planted in the soil.

**НАУКИ О ЗЕМЛЕ**

*Matveyev A.V., Nechiporenko L.A., Shishonok N.A.*
**Features of modem vertical movements of earth crust on territory of Belarus.** pp. 107--109

__Summary:__ It is shown that the territory of region is lowering at present with a predominent rate of about 2 mm a year. The central part of Belarus is rising because of heterogeneity of this process. Small areas of absolute uplifts (under 1 mm/year) and zones of high gradients of modern vertical movements are picked out. The conclusion concerning a formation of new structural pattern is made.

*Mikhajlov N.D., Avtusko M.I., Veretennicov N.V., Laptsevich A.G.*

**Radioactive elements in volcani formation of diatrems Zhlobin field.** pp. 110--115

__Summary:__ The U and Th contents of volcanic-magmatic rocks from the Zhlobin field diatrems have been studied for the first time by gamma-spectrum analysis. It has been found that rocks from various diatrems do not differ greatly in the U and Th contents, and these elements concentrations do not correlate with the potassium content of rocks. A close correlation has been determined between U and Th (K = 0.8). In U and Th contents and ratio the stulied rocks do not correspond to either kimberlites, or "classical" diamandiferous lamproites and, on this geochemical index, occupy an independent place between the alkali basalts -- alkali picrites and laproites -- kimberlites.

*Yakubovskaya T.V.*

**On three new plant species from cainozoic brown coal deposits in Belarus.** pp. 116--119

__Summary:__ New species of plants of genera *Tubela*, *Ludwigia* and *Myriophyllum* from brown coal deposits in Belarus are described in terms of fossil fruits and seeds.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Kuraev A.A., Popkova T.L.*
**Excitation of cavity resonators with finite conduction of the walls.** pp. 120--122

__Summary:__ The exact excitation equations for the cavity with finite conduction of the walls were received by projection method.

/ 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 © 1998 Издательство "Беларуская навука"