Весці Нац. акадэміі навук Беларусі. Сер. фіз.-матэм. навук, 2004, No.1
/ Выданні акадэміі / Навуковыя часопісы
Весці Нац. акадэміі навук Беларусі. Сер. фіз.-матэм. навук, 2004, No.1
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Весці Нацыянальнай акадэміі навук Беларусі
СЕРЫЯ ФІЗІКА-МАТЭМАТЫЧНЫХ НАВУКВыдавец: Інстытут матэматыкі НАН Беларусі, Мінск, Рэспубліка Беларусь |
Нумар 1, 2004
ЗМЕСТ
МАТЭМАТЫКА
Yanovich L. A., Ignatenko M. V.
About one class of operator interpolation formulas in the space of differentiable functions. pp. 5--11
Summary: The paper is devoted to the construction of Hermite type interpolation formulae for operators based on interpolation polynomials for numeral functions with respect to the Chebyshev system of functions. The obtained formulae are exact for a special class of operator polynomials of corresponding degrees typical for the considered systems of functions.
Kostyukova O. I.
Sensitivity Analysis for State Constrained Optimal Control Problems with Changeable Index. pp. 12--16
Summary: A family of parameter dependent optimal control problems is considered. The problems are subject to control and state constraints. It is assumed that parameter perturbations cause changing index of the problems. The implicit function theorem is used to investigate Frechet differentiability of the solution with respect to the parameter.
Alekhno E. A.
On some properties of irreducible positive operators in Banach lattices. pp. 17--20
Summary: The necessary and sufficient condition, which guarantee existence of s-order continuous band irreducible operator from Banach lattice E in E is proved. Examples of strong irreducible and super strong positive operators which are quasinilpotents, are built. Some examples of primitive matrices are considered.
Rusina T. I., Yablonski O. L.
Approximation of stochastic integrals in the non-homogeneous case. pp. 21--26
Summary: The approximations of stochastic q-integrals with non-homogeneous functions are investigated. Complete classification of the ways of approximations of stochastic q-integrals with non-homogeneous functions by process of Brownian motion in the convolution algebra has been given.
Kovalchuk A. N.
On the approximation of solution for the system of stochastic equations with q-integrals. pp. 27--32
Summary: The necessary and sufficient conditions of convergence of the solutions of system of finite-difference equations with averaging to the solutions of system of stochastic integral equations with q-integrals are obtained. The estimates of the speed of approximations are found.
Tikhonov S. V.
Brauer groups of hyperelliptic curves defined over real power series field. pp. 33--36
Summary: The presentation of 2-torsion part of Brauer group of a hyperelliptic curve with good reduction defined over real power series field by biquaternion algebras is obtained.
Rybak I. V.
Monotone difference schemes for equations with mixed derivatives in the case of boundary conditions of the third type. pp. 37--42
Summary: For elliptic and parabolic equations with mixed derivatives and boundary conditions of the third type monotone difference schemes of the second order of local approximation are developed without using the initial equation at the boundary. The appropriate a priori estimates in the norm C are obtained-
Troush N. N., Markovskaya N. V.
Research of statistical properties estimations of mixed cumulants of higher orders. pp. 43--49
Summary: The estimates of mixed cumulants of higher orders are built. Mathematical expectations, covariance, dispersion of this estimates are calculated. The estimates of mixed cumulants of higher orders are asymptotically unbiased and consistent in the mean-square sense.
Zadarazhniuk E. A.
New example of the Shemetkov's formation. pp. 50--54
Summary: This article is devoted to the investigation of the groups in which every minimal subgroup lies in the hypercenter of its normalizator. It is proved that the class of such groups is totally local formation. Furthermore, this class is the Shemetkov's formation.
Zalesskaya E. N.
Injectors for products of Fitting classes of finite groups. pp. 55--58
Summary: In this paper we give the generalization of the theorem of Blessenohl and Laue about the existence and conjugacy of quasinilpotent injectors in finite groups: we prove that all groups have a unique conjugacy class of cN*-injectors, where c is any non-empty Fitting class, N* is the class of all quasinilpotent groups, moreover the cN* -injectors of a group G are the maximal cN* -subgroups of G containing cN* -radical GcN* or of G.
Shmidt A. M.
On the influence of properties of stabilizer of coprime automorphism on the structure of finite group. pp. 59--64
Summary: The following main result is proved. Let X be a finite K-group, admitting automorphism y of prime order r. (|X|, r) = 1, C = Cx(y). Let P -- y-invariant Sp-subgroup in X and C Í Nx([y, P])- Let one of the following holds: (1) p > 2 but X has not y-invariant section L2(2r), Sz(2r), L2/2(3r); (2) p = 2, bat 2 not divided |C|; (3) p = 2, 2 divided |C|, but X has not y-invariant section X type (2, g, k, c), |Cx(y)| = 2, q Î p (X) or y-invariant section type X @ L2(2r), Sz(2r).
Then [y, P] ÑÑ X.
Kavalionak. N. N.
Construction of optimal feedback control with delays in feedback link. pp. 65--68
Summary: An optimal control problem with bang-bang controller is under consideration. Taking into account delays in feedback link caused by signal transmission and microprocessor performance we provide the algorithm for feedback control synthesis.
Mukha V. S.
Systems of orthogonal polynomials of vector variable in a space with the discrete weight. pp. 69--73
Summary: The general theory of system of orthogonal polynomials of vector variable in a space with the discrete weight is developed.
ФІЗІКА
Fedorovykh A. M.
Particle with spin 1/2 in non-Abeliari gauge field in formalism of relativistic vector algebra. pp. 74--79
Summary: A formulation of the Dirac equation describing spin-1/2 particle in an external gauge field (Yang -- Mills field) is given in terms of the operations of relativistic vector algebra and generalized relativistic vector algebra (GRVA) which extend the ordinary three-dimensional vector algebra to the reiativistic case. Some properties of GRVA are established. A solution of equation for a massless spin-1/2 particle in an external gauge field with constant and uniform potential is found in algebraic way.
Ryabushko A. P. Nenianova I. T., Zhur T. A.
The relativistic equations of rotating motion of two rotating bodies in the medium. pp. 80--83
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-dust-like globe. For such systems it is to derive the relativistic equations of rotating motion.
Chernichenko Yu. D.
Relativistic Inverse Problem for the Superposition of the Non-local Separable Interaction and Local Quasipotential which does not admit the Bound States. pp. 84--89
Summary: Within the relativistic quasipotential approach to quantum field theory, a relativistic inverse problem is considered for the superposition of a non-local separable quasipotential and a local one that simulates the interaction between two relativistic spinless particles of unequal masses. Besides, the local component of total interaction is supposed to be known and that it does not admit bound states. Then a non-local separable component of total interaction can be reconstructed on the basis of the additional phase-shift and bound-state energies.
Korneev S.V., Rakhno I, L., Chigrinov S.E., Martsynkevich B.A., Khilmanovich A.M., Krivopustov M. I., Sosnin A. N., Tumendelger T. S., Chultem D., Zaveyuha O.S., Pavluk A, V.
Unfolding of fast neutron spectra in the wide energy range (up to the 200 MeV) in a subcritical U/Pb-assembly of an electronurlear system. pp. 90--95
Summary: Experiment on irradiation of the two-section model of the U/Pb assembly is performed using proton beam from the Synchrophasotron at 1.5 GeV. Reaction rates are determined by means of the activation threshold detectors containing 23 elements from carbon-12 to neptunium-237 used to unfold fast neutron spectra. Experimental results of the unfolding of neutron spectra up to 200 MeV are in good agreement with calculated results obtained by means of statistical model.
Shishkina T. V., Makarenko V. V.
Production of fermion pair and photon in polarized photon collisions. pp. 96--100
Summary: Exclusive reaction gg ® f f -g is considered as the possible calibration process for J = 0 beams on the linear photon collider. We have analyzed the energy spectrum and total cross section dependence on the detector parameters at various initial beam helicities. It is discovered that the ratio of events on J = 0 and J = 2 beams strongly depends on the experimental cuts. We have obtained the region (the configuration of cuts) where the ratio is highest. It is the region of small cuts on polar angle, large cuts on collinear angle and high minimal energy of final-state photons. In this field the measurement of g+g+ beams parameters has the maximal precision.
Karanchuk D. J., Skiba P. A.
Some features of formation of optical elements based on glass-ceramics. pp. 101--104
Summary: The optimal regime of local heating of the thermally thing slades of glass-ceramics is defined, taking in account distribution of the temperature fields in material volume and the origin of the thermo strengthes near modified zone.
Liopo V. A.
The rule crystals forms and their short representations. pp. 105--109
Summary: It is supposed the method of determination of crystallographic indeces of rule simple form's faces for all crystal point groups. This procedure was done on basis of matrix representation of point groups in cristallophysic and cristallographic bodies.
Gaiduk P. I.
Vertical self-assembling of quantum dots in Si/Ge multilayered structures. pp. 110--113
Summary: Stacks of six or eight bilayers of Ge/Si were grown by molecular beam epitaxy (MBE) on Si/Si0.5Ge0.5 buffer layers modified with in situ implantation of 1 keV As+ or Ge+ ions. The structures were investigated by transmission electron microscopy (TEM). Vertically correlated Ge islands are observed by TEM. Results from variation of pre-implantation, thickness of Ge layers and temperature of MBE growth are presented.
ІНФАРМАТЫКА
Tikhonenko O. M., Klimovich K. G.
Two-priority queueing system with random volume demands and unreliable server. pp. 114--120.
Summary:
Single-server head-of-the-line two-priority discipline queueing system with random volume demands and the free state unreliable server is analyzed. It's supposed that the total demands volume of each priority is unlimited. In terms of Laplace and Laplace -- Stieltjes transformations the joint distribution of the total volume of both priority demands presenting in the system at given time moment is determined.
КАРОТКІЯ ПАВЕДАМЛЕННІ
Bernik V. I., Kalosha N. I.
Approximation of zero by values of integral polynomials in R x C x Qp. pp. 121--123
Summary: The relation between values of two integral polynomials without common roots and their degrees, heights, diameters of sets in R x C x Qp for which these values axe attained is established.
ВУЧОНЫЯ БЕЛАРУСI
Леанід Аляксандравіч Яновіч (Да 70-годдзя з дня нараджэння). С. 124--125
Націсніце тут, каб прачытаць артыкул
/ Выданні акадэміі / Навуковыя часопісы / Да пачатку старонкі
Распрацавана і падтрымліваецца Мікалаем М. Касцюковічам. Апошняе абнаўленне: 8 снежня 2006 г.
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