(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: The article deals with exact relations between some constants characterizing different geometrical properties of nonnegative linear operators in Banach spaces ordered with a cone. The results generalize some not much known results for positive matrices by F. L. Bauer and A. M. Ostrowski.
Mandrik P. A.
About a solution of direct and inverse non-stationary heat transfer problems with heating of a half-space through infinite lengthy band. pp. 11--13
Summary: The isotropic semibounded solid is heated up by flows which one are various inside and outside of infinite lengthy band on a surface of a solid. The analytical expressions of the law of a temperature field development into considered solid with a given heat flows (direct problem) and of the law of a heat flow modification outside of a band on a halfspace surface with a given heat flow inside of a band (inverse problem) are defined.
Bakhtin V. I., Sarazhinskii D. S.
The Perron -- Frobenius operator for baker's transform. pp. 14--20
Summary: Two dynamical systems are under consideration here: the shift on a space of double-sided sequences and baker's transform. It is proved that they are the Perron -- Frobenius dynamical systems and so possess very strong stochastic properties.
Vorobei L. A.
On nilpotent transitive regular subgroup functors. pp. 21--25
Summary: It is considered the problem of classification of transitive regular subgroup functors. All such nilpotent subgroup functors are described,
Malyutin V. B.
Approximation for expectation of functionals from solution of linear stokhastic differential equation with noncommuting coefficients. pp. 26--29
Summary: Approximation for expectation of functionals from solution of linear stochastic differential equation with non-commuting coefficients is received.
Gous S. N., Sergievich N. V., Yudin M. D.
About influencing dependent of random items on limit distributions of their sums. pp. 30--34
Summary: Influencing a correlation of dependent random vectors and dependent random variables on limit distributions of their sums is considered.
Trelina L. A.
Cubic irrationalities with the power index. pp. 35--39
Summary: An effective bound for the height of algebraic integers a of the third degree with the discriminant of the form D(a) = BYz is obtained. This bound depends on the greatest prime factor of the norm of Ba.
Lyalikov A. S.
Approximation of functions with derivative from Lp by rational operators of Fourier type. pp. 40--46
Summary: Rational operators of Fourier type deviation from the functions with Riemann-Liouville derivative of Lp is estimated.
Kovalchuk A. N., Lazakovich N.V., Yablonskii O. L.
On approximation of the solutions of new classes of stochastic equations with q-integrals. pp. 47--54
Summary: The necessary and sufficient conditions of convergence of the solutions of finite-difference equations with averaging to the solutions of stochastic integral equations with q-integrals, q Î R are adduced. The estimates of the speed of approximations are found.
Summary: At the highly deep penetration of the disperse particle in the solid target the energy expended for making the volume and the surface of canal, the elastic deformation of its surrounded layers is compensated by the following slam of the canal and by the further push of the particle. Initial kinetic energy of the particle is sufficient to realize the whole process of the highly deep penetration.
Kudryashov V. V., Reshetnyak V. I.
Modified perturbative-variational approximation in quantum mechanics. pp. 60--63
Summary: Trial functions are constructed in the third order of the perturbation theory in the framework of the operator method with a variational parameter which value is chosen from condition of minimization of a relative discrepancy. The numerical verification of the new approach is performed by calculating expectation values of powers of two Hamiltoninans.
Ryabushko A. P., Nemanova I. T., Zhur T. A.
The relativistic equations of translational motion of two rotating bodies comparable masses in the medium. pp. 64--68
Summary: The post-Newtonian approximation of the Einstein equations was used to obtain the metric of gravitational field, which appears around two rotating bodies surrounded by a gas-dustlike globe. For such systems it is to derive the relativistic equations of translational motion.
Tunyak U. M.
Brans -- Dicke scalar field and Einstein -- Cartan torsion field in relativistic theory of gravity. pp. 69--71
Summary: The foundations of the theory of gravity in Minkowski space with more common, then Riemann space, effective Riemann -- Cartan space-time with non-zero torsion have been formulated. The equations of the gravitational field in case of the switching off the torsion transforms into equations of the scalar-tensor gravitational theory in Minkowski space for the spinless matter and non-gravitational fields.
Zakharov I. L, Lebedinsky Yu. A.
Geometrical aspect for an assessment of modulation transfer function of staring focal-plane-array. pp. 72--78
Summary: The analytical expression of the Modulation Transfer Function (MTF) of staring focal-plane arrays (FPA) with arbitrary pixel geometry is found. When there are no frequencies beyond of Nyquist frequency in the spatial object spectrum, it is proved that the object shift does not influence on MTF of FPA. For general case when there are such frequencies in spectrum) they were determined. The concept MTF averaged by shifts and orientations of a sinusoidal pattern is introduced. The concepts of mean square variation and dispersion of MTF are defined on this basis. They allow to evaluate the measure of the nonisotropic and the nonisoplanatic artifacts of FPA. The results of numerical calculations show that the quality of image is better when the form of pixel approaches to circular.
Sheleg A. U., Iodkovskaya K.V.
Electroconductivity and dielectric characteristics of TlGaS2 crystal in the temperature range of 200 -- 370 K. pp. 79--81
Summary: In the region of the temperatures 200 -- 370 K measurements of an electrical conductivity s and dielectric properties e and tgs on different frequencies of TlGaS2 crystals are carried out. It is shown, that with growth of temperature dielectric characteristics e and tgs, and also an electrical conductivity a are increased. The significant dispersion of the investigated properties is found out.
Shipilo V. B., Shipilo N. V., Dutov A. G., Comar V. A.
Kinetics of a crystallization of diamonds in a system Mn -- Ni -- C -- addition. pp. 82--86
Summary: The influence of the time of synthesis on the degree and speed of transformation of graphite in diamond in a system Mn -- Ni -- C -- addition is investigated at P = 5.5 GPa and T = 1620 °C, fractional and admixture makeup of diamond and their durability. It is shown that the kinetics of a crystallization of diamond in a considered system is characterized in basic local changes of supersaturation of a solute of beam-lead carbon in a melt of metals calling change of parameters of a crystallization and property of diamonds,
Plyushch O. B.
Structural investigations of polytypism of TlAIIIB2VI layer crystals. pp. 87--89
Summary: Analysys of diffraction spectra of X-ray scattering of TlInS2 and TlGaSe2 crystals with incommensurate modulation with wave vector qi = (l/4 ± d)c* was carried out. It was shown that these crystals are aperiodic polytypes.
Summary: The method for space-time mapping of n-dimensional algorithms with uniform dependencies onto p-dimensional fixed size parallel architecture in the framework of LSGP strategy is preseated. The procedure of synthesis of scheduling function is proposed. The procedure is based on technique of multi-dimensional scheduling.
Radyno N. Ya.
Algorithm of a PC user identification based on his keyboard typing. pp. 97--102
Summary: The algorithm of a PC user identification by his keystroke dynamics is proposed. Motivation of proposed algorithm is discussed. An example of manipulation of statistical data taken from the eight PC users is demonstrated.
Lepin V. V.
Profile minimisation algorithm for graph. pp. 103--109
Summary: A new method for minimizing the profile of graph is described.
Nikulin Yu. V.
On the strong stability and strong quasistability of a vector quadratic exicographic boolean programming problem. pp. 110--114
Summary: It is considered a vector quadratic Boolean lexicographic optimization problem. The formulae of the strong stability radius and strong quasi-stability radius have been found. Necessary and sufficient conditions of these types of stability were specified.
Summary: Some conditions for the convergence of some series with small denominators are found.
Silaeva N. A.
Simultaneous approximations zero by the vahies of normal functions in different metrics and the Khinchin theorem. pp. 118--120
Summary: It is proved a special case of analog of the Khinchin theorem about simultaneous approximations of zero by values of normal functions in different variations.
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