(Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICAL-MATHEMATICAL SCIENCES
Published by The Institute of Mathematics of NASB, Minsk, Republic of Belarus
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Proceedings of the National Academy of Sciences of Belarus (Vestsi Natsiyanalnai Akademii Navuk Belarusi) SERIES OF PHYSICAL-MATHEMATICAL SCIENCES Published by The Institute of Mathematics of NASB, Minsk, Republic of Belarus |
Summary: Quasi-positive elements in ideal spaces are studied. Some characterizations of different classes of ideal spaces in terms of a quasi-positive elements are presented, in particular, it is described wide classes of ideal spaces without quasi-positive elements.
Zhuk E. E., Serikova E. V.
Cluster analysis of multivariate Gaussian observations in the space of principal components. pp. 10--15
Summary: The problem of cluster analysis of multivariate Gaussian observations in the space of principal components is considered. The clustering procedure based on maximum likelihood method is used and efficiency of transition to principal components is analytically investigated.
Troush N. N., Tsekhovaya T. V.
The variogram estimators of the stationary stochastic process. pp. 16--21
Summary: The variogram estimators of the intrinsic stationary stochastic process with discrete time are constructed. The statistical properties of the examined estimators are investigated.
Zelenyak D. M.
Description of a dissipation variety for relaxation systems. pp. 22--28
Summary: The boundary of the solution set of a dissipation inequality for relaxation systems is described as a part of a dissipation variety. The dimension of this variety is pointed out.
Shchukin M. V.
Non-trivial C* -algebra generated by three idempotents. pp. 29--34
Summary: Every homogeneous C*-algebra corresponds to the algebraic fiber bundle. C*-algebãa is called non-trivial if the corresponding algebraic fiber bundle is non-trivial. All C*-algebras generated by idempotents that was studied before corresponds to the trivial algebraic fiber bundles. A. Antonevich and N. Krupnik showed that non-trivial C*-algebra of dimension 2 can be generated by three idempotents. It is shown that non-trivial C*-algebras of any dimension n ³ 2 can be generated by three idempotents. It is studied the topology properties of C*-algebras generated by the idempotents to describe C*-algebras properly,
Dymkov S. M.
Linear optimization problem for repetitive continuous-discrete systems. pp. 35--41
Summary: The development of constructive methods for optimization problem of repetitive continuous-discrete systems is considered. The necessary and sufficient optimality conditions are obtained on the base of which the synthesis of optimal systems and design of optimal controllers for the proper dynamical processes can be realized.
Smotrytskii K. A.
On approximaton of differentiated in Riemann -- Liouville sense functions. pp. 42--47
Summary: Let WrV[-1,1] be the class of differentiated in Riemann -- Liouville sense on the segment [-1,1] functions with r-derivative of a byunded variation. It is showed in case of adequate selection of poles the degree of uniform deviation of the partial sums of rational Fourier -- Chebyshev series can potentially differ from the best one only in In n multiplier.
Naidenko V. G.
Finding the OC-convex hulls. pp. 48--53
Summary: It is investigated a generalized convexity (OC-convexity), which consists of the intersections of conic semispaces of directional convexity. Topological and numerical aspects as well as separability properties are described. The upper value of the Caratheodory number is estimated for OC-convexity. At the same time, the Helly and Radon numbers turned out to be infinite for OC-convexity. It is proved that the OC-convex hull of any finite point set represents the finite union of polytopes.
Benediktovich V. I., Sarvanov V. I.
On the relation of parameters of a regular polyhedron in R3. pp. 54--59
Summary: The extreme estimates of number of vertices, edges, triangles of a regular polyhedron and the least bodies, into which the regular polyhedron divides the three-dimensional Euclidean space R3 are obtained.
Summary: Gaussian's functions are used to consider properties of optical spatial-temporal solitons propagating in inhomogeneous elliptical waveguide with Kerr local nonlinearity. It is shown that the same as in the spherically symmetrical case both transverse dimensions and temporal duration of the light bullet oscillates along with the pulse propagating in the waveguide.
Pilipovich V. A., Esman A. K., Goncharenko I. A., Kuleshov V. K., Sergienya S. A.
Analysis of the basic parameters of optical fibre logic elements on the base of Bragg reflectors. pp. 65--69
Summary: The basic parameters (signal-to-noise ratio, switching energy, operation time) of optical logic elements "AND" with three inputs are estimated. The logical elements are based on complex fibre Fabry-Perrot resonators, formed by two Bragg reflectors and one end mirror, Such a logical element producing function of half-adder in a one switching tact can be used for algorithmic acceleration of optical computing. Considered optical logic elements can be used for preliminary information processing in fibre interconnections between chips or blocks of computing systems.
Kurilovich N. F., Korshunov F. P., Pashkovskii O. I., Yarunichev V. P.
The vacuum gamma-ray Co60 irradiation influence on characteristics of barium titanate posistor ceramics. pp. 70--74
Summary: The results of investigation of on air and in vacuum gamma-ray Co60 irradiation influence on characteristics of barium titanate posistor ceramics are given in this paper. It has been shown that larger decrease of posistor effect occurred in on air irradiated samples while for both cases of varistor effect were observed.
Tsionenko D. A.
The Dirac -- Kahler equation as a coordinate representation of the quantum-mechanical motion equation. pp. 75--83
Summary: The Dirac -- Kahler equation is investigated, Its wave function is transformed by the Lorentz group as a direct product of bispinor and charge conjugated bispinor. The possibility of using this equation as a coordinate representation of the quantum-mechanical motion equation is determinate. The systems of references permitting of this interpretation are defined. The positive Gilbert physical space on the solution of the Dirac -- Kahler equation is constructed.
Bordusov S. V.
Physical model of dissipation process of microwave electromagnetic field by molecular gases plasma. pp. 84--91
Summary: At the analysis of the interaction of microwave electromagnetic fields with ionization medium it is offered to consider the plasma of discharge in molecular gases as a dielectric with losses, which include the ohmic losses of energy, caused by raised eddy currents, and polarization losses stipulated by relaxation effects of the interaction of alternative fields with polar particles. The given model supplements physical representations of the interaction of an electromagnetic wave with multi composition ionized gaseous medium and makes it possible to explain a series of experimental data concerned with thermophysical performances of microwave discharge plasma.
Dymont V. P., Nekrashevich E. M., Goncharov V. S., Pan'kov V. V.
Synthesis tetragonal carbon-nitride phase synthesized by high-pressure technique. pp. 92--95
Summary: The new crystalline phase of carbon nitride was synthesized from precursor containing carbon and nitrogen by high-pressure technique. Tetragonal crystal structure was deduced from the X-ray diffraction patterns.
Karolik A. S.
Calculation of the grain boundary reflection coefficient of conductivity electrons as a function of the misorientation angle of grains in metals. pp. 96--100
Summary: Within the framework of the partial-wave method the grain boundary reflection coefficient R and porosity coefficient for simple metals (alkaline, noble and aluminium) are calculated. The good accordance with available experimental data is obtained. It is shown, that the coefficient R depends both on the crystal structure, on the misorientation angle of grains, and also on the character of scattering of carriers by the boundary,
Summary: The problem of scheduling for space-time mapping of n-dimensional algorithms with affine dependencies onto (n -- r)-dimensional parallel architectures is investigated. The procedure for multidimensional scheduling function synthesis based on Karp -- Miller -- Winograd decomposition is proposed.
Kravtsov M. K., Lukshin E. V.
On existence of non-integer vertices of a three-axial transportation polytope. pp. 108--114
Summary: Three-index axial transportation polytopes of order n x n x m, n ³ m ³ 3, defined by integer vectors are considered. The fact that each of these polytopes has r-non-integer vertices (i.e. vertices with the number of fractional components being equal to r) for any number r Î {4, 6, 7,..., 2n + m - 2} and only for it is proved.
Summary: The minimal w-composition non-H-formations are described where H is a formation of classical type.
In the Belarusian Physics Society. pp. 118--121
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