Doklady of the National Academy of Sciences of Belarus, 1998, Vol.42, No.2
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Doklady of the National Academy of Sciences of Belarus, 1998, Vol.42, No.2

DOKLADY OF THE NATIONAL ACADEMY OF SCIENCES OF BELARUS
(Doklady Natsionalnoi Akademii Nauk Belarusi)Published by The Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Gaishun I.V.
Trajectory stabilization by impulse control under disturbances. pp. 57
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 deltadistributions are obtained.
Belousov M.V., Lebedev A.V.
Symbolic calculus nonlocal boundaryvalue problem with shifts on the boundary. pp. 812
Summary: The symbolic calculus and the Fredholmity conditions for the nonlocal boundaryvalue 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. 1317
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. 1824
Summary: A new class of vector special functions, Rfunctions 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^{n1}. The properties of Rfunctions 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. 2529
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.
PseudoHolderability and metric regularity of multivalued maps. pp. 3035
Summary: PseudoHolder multivalued maps are studied. The equivalence between pseudoHolder behavior and metric regularity of rate n is investigated.
Khomichkov I.I.
Retrial queue with probability of losses under double connecting. pp. 3639
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. 4044
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. 4548
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. 4951
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. 5255
Summary: Description of cyclic algebra representation of ntorsion part in Brauer group of curve over field of characteristic 0 is obtained.
PHYSICS
Sirota N.N.
On physical nature of metals strength. pp. 5659
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 quasifilaments, 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 quasifilaments 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 nonspheric correlational potential of interatomic interaction in solids. pp. 6065
Summary: Nonspherical 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 selfconsistent calculations of scattering waves (linear MuffinTin orbitals method).
Knyazev M.A.
Coupled states of three kinks in F^{4} theory with damping. pp. 6668
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. 6974
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.
CHEMISTRY
Nechai N.I., Potkin V.I., Kurman P.V., Kaberdin R.V.
Synthesis and some properties of 1,3dinitro1,2,4,4tetrachloro1.3butadiene. pp. 7578
Summary: For the first time 1,3dinitro1,2,4,4tetrachloro1,3butadiene has been obtained by nitration of available 1,1,3,4tetrachloro1,3butadiene 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 anitrob,bdichlorovinylic and bnitroa,bdichlorovinylic groups have been revealed in S_{N}Vin processes.
BIOLOGY
Koren L.V., Kaminskaya L.N., Khotyljova L.V.
Cytological investigation of wheatrye amphiploids with inclusion of Vrn genes. pp. 7984
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 wheatrye 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 wheatrye amphiploids have been revealed.
Nedvetsky P.I., Mongin A.A., Konev S.V.
Influence of arachidonic acid on the voltageoperated calcium channels in rat brain synaptosomes. pp. 8588
Summary: The effect of arachidonic acid on the activity of voltageoperated calcium channels, measured as voltagedependent ^{45}Ca^{2+} accumulation in rat brain synaptosomes, was studied. Arachidonic acid (5100 µM) dosedependent activated voltageoperated calcium channels. Inhibitor of phospholipase A_{2} 4bromophenacyl bromide, decreasing release of endogenous arachidonic acid, and inhibitor of cyclooxigenase aspirin, preventing prostanoid synthesis from arachidonic acid, suppressed voltagedependent ^{45}Ca^{2+} uptake by synaptosomes. The obtained data suggest that arachidonic acid and its metabolites participate in regulation of voltageoperated 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 gammairradiation. pp. 8994
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 girradiation and thymaline + solcoserile after it induces a pronounced effect of protectiontherapy (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 selffertile rye lines. pp. 9597
Summary: The influence of genotypic properties of selffertile 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 5aminolevulinic acid in etiolated leaves of barley. pp. 98100
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 5aminolevulinic 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 wavelike 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 atocopherol and glutathione in membrane defense under photodynamic action on erythrocytes. pp. 101103
Summary: Participation of atocopherol 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 (atocopherol; 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. 104106
Summary: In the current paper the best cultural conditions are determined for germination embryos of the cloudberry. Plantlets obtained were planted in the soil.
EARTH SCIENCES
Matveyev A.V., Nechiporenko L.A., Shishonok N.A.
Features of modem vertical movements of earth crust on territory of Belarus. pp. 107109
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. 110115
Summary: The U and Th contents of volcanicmagmatic rocks from the Zhlobin field diatrems have been studied for the first time by gammaspectrum 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. 116119
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.
TECHNICAL SCIENCES
Kuraev A.A., Popkova T.L.
Excitation of cavity resonators with finite conduction of the walls. pp. 120122
Summary: The exact excitation equations for the cavity with finite conduction of the walls were received by projection method.
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