Весці Нац. акадэміі навук Беларусі. Сер. фіз.-матэм. навук, 2004, No.2
/ Выданні акадэміі / Навуковыя часопісы
Весці Нац. акадэміі навук Беларусі. Сер. фіз.-матэм. навук, 2004, No.2
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Весці Нацыянальнай акадэміі навук Беларусі
СЕРЫЯ ФІЗІКА-МАТЭМАТЫЧНЫХ НАВУКВыдавец: Інстытут матэматыкі НАН Беларусі, Мінск, Рэспубліка Беларусь |
Нумар 2, 2004
ЗМЕСТ
МАТЭМАТЫКА
Zabreiko P. P., Kirsanova-Evkhuta O. N.
New theorem on convergence for the minimal residual method. pp. 5--8
Summary: The new result on the convergence of the minimal residual method for nonlinear operator equations in Hilbert spaces is presented.
Korzyuk V. I., Cheb E. S.
Mixed problem for the fourth order hyperbolic equation. pp. 9--13
Summary: Mixed problems with homogeneous boundary conditions are considered for the fourth order linear differential equation. Dominant part of this differential operator is a composition of two wave operators. For the considered mixed problems the existence and uniqueness of the strong solution are proved.
Kilbas A. A., Schetnikovich E. K.
Generalized H-transform on the weighted spaces of summable functions. pp. 14--20
Summary: Generalized integral transform involving Я-function in a kernel is studied on the weighted spaces of r-summable functions. Mapping properties such as the boundedness, the representations and the range of the considered transform are given, and the inversion formulae are established.
Radyna A. Ya.
Interpolation and approximation by p-adic linear splines of a function from C(Zp;R). pp. 21--24
Summary: Questions about interpolation and approximation of a continuous real valued function of a p-adic argument by p-adic linear splines are discussed. The theorem about uniform approximation of the function f : Zp ® R is proved.
Al-Shaihahmad Ahmad, Skiba A. N.
On finite factorable groups with given systems of c-normal subgroups. pp. 25--28
Summary: It is proved that a finite group G is soluble if G = AB and all maximal subgroups of A, B are c-normal in G.
Vasil'ev A.F.
New properties of finite dinilpotent groups. pp. 29--33
Summary: Finite groups which is the product of two nilpotent F-subnormal (F-composition) subgroups are investigated. The new criterion of supersolvability of finite groups is obtained.
Demesh N. N., Soboleva T.V.
The asymptotics of reciprocal periodogram moments of real stable stationary random processes. pp. 34--37
Summary: The definition of reciprocal spectral density of real multivariate stable stationary random processes whose second moments are infinite is introduced. According to the observations of the considered process, the Fourier transformation and a reciprocal modified periodogram used for the reciprocal spectrum estimation are constructed. The mean and variance of the reciprocal periodogram have been obtained, their asymptotic behavior have been investigated.
Lazakovich N. V., Rozin E. B.
Limit behavior of the solutions of the finite-difference equations with the averaging. pp. 38--42
Summary: It is shown convergence of the solutions of the finite-difference equations with the averaging to the corresponding solutions of the stochastic differential equations.
Kovalevskaya E. I.
Simultaneous approximations to zero by the values of integer polynomials of degrees 2 and 3 on different valuations. pp. 43--47
Summary: Analogues of Khintchine's theorem for the simultaneous approximations to zero in R x C x Qp by the values of integer polynomials of degrees 2 and 3 are proved.
Zverovich I.E., Orlovich Yu. L.
Implementation of the reducing copath method for specific homogeneous sets. pp. 48--55
Summary: Reducing Copath Method proposed by I. E. Zverovich for some types of homogeneous sets is considered.
ФІЗІКА
Kovalev A. A., Zhdanovich S. N.
The analysis of a microstructure of the relief-phase holograms on photothermoplastic materials with electron microscopy. pp. 56--60
Summary: The microstructure of the relief-phase holograms on photothermoplastic materials with electron-scan microscope is investigated. The holograms were developed with a pulsed Nd:YAG-laser (l = 1.064 µm, t = 4 ms). Surface appearance of signal and frost, in holograms of various diffraction efficiency is compared and discussed.
Ryabushko A. P., Nemanova I. T., Zhur T. A.
The relativistic rotational motion of two rotating bodies in the gravitational medium. pp. 61--65
Summary: In the post-Newtonian approximation the equations of the rotational motion of two rotating bodies comparable masses in the gravitating medium have been integrated. Some novel relativistic effects due to the proper rotation of bodies and the gravitational field of medium are detected.
Minkevich A. A., Feranchuk I. D.
Combinative rule for the force constants of the interatomic interactions and Debye temperature for crystals. pp. 66--71
Summary: Simple formula for microscopical estimation of the Debye temperature for polyatomic crystals is reported. It is based on the calculation of the force constants for arbitrary pair of interacting atoms by means of the phenomenological spectroscopy data for oscillation frequencies of homonuclear molecules. For that purpose a special combinative rule is suggested.
Chernichenko Yu. D.
Solution of the relativistic quasipotential equation involving non-local separable interaction. pp. 72--80
Summary: Within the relativistic quasipotential approach to quantum field theory, a method of solving a finite-difference quasipotential equation involving a non-local separable quasipotential simulating the interaction between two relativistic spinless particles of unequal masses is generalized to the case where the total interaction is the superposition of a non-local separable quasipotential and a local one. Besides, the local component of total interaction is supposed to be known and that it does not admit bound states. This has permitted to find an explicit expression for the additional phase-shift, to determine the conditions under which bound states may exist, and to generalize the Levinson theorem.
Shishkina T. V., Marfin I. B.
Production of polarized leptons in the deep inelastic scattering of polarized particles. pp. 81--85
Summary: The deep inelastic scattering (DIS) leptons on nucleons with and without registration of the polarization of final leptons are considered in the paper. We use two models of the quark distribution in nucleons to build the structure functions Wi(q2 ,v) (i = 1,...,5) and Gj(q2, v) (j = 1,...,9) which are included into the differential cross section of DIS. The registration of the polarization of a final lepton allows us to form and calculate new types of asymmetries that have significant values in the whole kinematic region of x at energies ~ 1 TeV. It is found that the new asymmetries give the additional information about structures of hadrons.
Pavlovich V. S.
Temperature dependence of the broademing of the B850 absorption bands of the light-harvesting antennas of the purple bacteria Rhodopseudomonas acidophila and Rhodobacter sphaeroides. pp. 86--92
Summary: An equation for the temperature dependence of full half-width which provides an excellent fit to known experimental data for B850 spectra of the light-harvesting antenna complex 2 (LH2) from the purple bacteria is found. After fitting to known data it is shown that the modulated broadening of the B850 spectra are caused by the 35 (± 7) and 54 (± 4) cm-1 polar modes for the LH2 from Rb. sphaeroides and Rps. acidophila, respectively. The nature of these polar modes is discussed.
Volodin V. A., Gatskevich E. I., Dvurechenskii A. V., Efremov M. D., Ivlev G. D., Nikiforov A. I., Orehov D. A., Yakimov A. I.
Influence of nanopulsed laser irradiation on Ge quantum dots in Si. pp. 93--96
Summary: The influence of a Q-switched ruby laser radiation on the system of Ge nanoclusters quantum dots (QD) in Si (100) matrix have been studied at the laser energy densities nearly to the silicon surface melting threshold. The Ge/Si nanostructures were formed by molecular beam epitaxy of Ge on Si (100) substrate. The change of nanocluster structure were analyzed by using spectroscopy of Raman scattering (RS). Initial RS spectra were compared with the calculated ones obtained by using Born-von-Karman and Wolkenstein models. It has been established that the nanopulsed irradiation changes the QD properties. The decrease of sizes of Ge clusters, increase of size dispersion and particular relaxation of compression stresses are observed at single pulsed irradiation. More considerable changes occur under irradiation by 10 laser pulses. Ge clusters are likely transformed into the clusters of GexSi1-x solid solution alloy likely due to the photo-thermostimulated break of inter-atomic covalent bonds on Si/Ge interfaces and due to the diffusion of Si atoms into melted Ge clusters.
Gaiduk P. I., Trautmann C., Toulemonde M., Larsen A.
Nylandsted Discontinuous latent tracks in relaxed Si1-xGex alloy layers: a composition effect. pp. 97--101
Summary: An effect of composition on discontinuous track formation in strain-relaxed Si1-xGex alloy layers irradiated with 0.7 GeV Uions is reported. Strongly non-monotonic dependence of the density of the track-related defects on the Si1-xGex alloy composition is disclosed by the transmission electron microscopy. The maximal probability of the track formation is registered in the compositional range around Si0.5Ge0.5. The results are discussed in the frame of the thermal-spike approach, which assumes both track melting and imperfect crystallization.
ІНФАРМАТЫКА
Naidenko V. G.
On a case of directional convexity. pp. 102--106
Summary: The generalized convexity (OC-convexity) which consists of the intersections of conic semispaces of directional convexity is investigated. The optimization problem on an OC-convex set is considered. The theorem of Krein--Milman type for OC-convexity has been proven in case of the vector set of directional convexity being infinite. The relation between OC-convex and functionally convex sets is considered.
Shilak A. N, Sotskov Y. N.
Minimization of project-network with given bounds of activity durations. pp. 107--113
Summary: The efficient algorithms are developed to delete from the given project-network all vertices and all arcs that cannot belong to a critical path for any possible realization of the uncertain activity durations.
Levin G. M., Guschinsky N. N., Burdo E.I.
Optimizing parameters of cascade multiplier transmissions taking into account stochastic nature of strength characteristics of materials. pp. 114--120
Summary: A problem how to optimize basic design parameters of power transmission systems taking into account the stochastic nature of strength properties of gears materials is investigated. The system can include a cascade multiplier gear box and operates in deterministic conditions. The mathematical model takes into account main kinematic and strength restrictions. The goal is to minimize the total mass of transmission elements. The suggested solution procedure is based on the methods of parametric decomposition and dynamic programming.
ВУЧОНЫЯ БЕЛАРУСI
Федор Павлович Коршунов (К 70-летию со дня рождения). С. 121--123
Націсніце тут, каб прачытаць артыкул
Анатолий Николаевич Сердюков (К 60-летию со дня рождения). 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.
Створана пры ўдзеле Ігната І. Корсака
Капірайт © 2004-2006 Нацыянальная акадэмія навук Беларусі
Капірайт © 2004 Інстытут матэматыкі НАН Беларусі
