Весці Нац. акадэміі навук Беларусі. Сер. фіз.-матэм. навук, 2004, No.4
/ Выданні акадэміі / Навуковыя часопісы
Весці Нац. акадэміі навук Беларусі. Сер. фіз.-матэм. навук, 2004, No.4
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Весці Нацыянальнай акадэміі навук Беларусі
СЕРЫЯ ФІЗІКА-МАТЭМАТЫЧНЫХ НАВУКВыдавец: Інстытут матэматыкі НАН Беларусі, Мінск, Рэспубліка Беларусь |
Нумар 4, 2004
ЗМЕСТ
МАТЭМАТЫКА
Gromak V. I., Zenchenko A. S.
On differential systems with the Painleve property. pp. 5--10
Summary: Classes of quasi-linear and Hamiltonian quasi-linear systems equivalent to the equations (P2) -- (P6) are considered.
Spichekova N. V.
Integral surfaces of one Pfaff equation with closed nonisolated singularity. pp. 11--14
Summary: The character of integral surfaces of one Pfaff equation with closed nonisolated singularity is investigated.
Monastyrnyi P. I., Kremen E. V.
Orthogonal pivotal for boundary-value problems with strongly changing coefficients. pp. 15--19
Summary: Problems with local infinitely great meanings of the heat conductivity medium are considered. The generalization of the pivotal for these problems is given. The theorems of the correctness and stability of the method are proved.
Martsynkevich G. L.
The local one-dimensional scheme of the second order of approximation for a multidimensional heat equation with a boundary condition of the third kind. pp. 20--25
Summary: The monotone local one-dimensional difference scheme of the second order of summarized approximation with respect to space variables without using the basic differential equations at the domain boundary for a p-dimensional heat equation with the boundary condition of the third kind is constructed. The a priory estimates of accuracy and convergence are established by means of the grid maximum principle in norm C.
Zbuk E. E.
Non-parametric stastistical classification of stationary time series. pp. 26--30
Summary: The problem of statistical classification of stationary time series is considered. The non-parametric classification procedures based on non-parametric estimators of covariance functions are proposed and their efficiency is analytically investigated.
Knyagina V. N.
Finite groups with Schmidt's subnormal subgroups. pp. 31--34
Summary: Finite groups with Schmidt's subnormal p-closed subgroups and groups with subnormal p-nilpotent Schmidt's subgroups are investigated, p-resolvability of such groups is established and the estimation of their p-length is given.
Gal'mak A. M.
Classes of n-ary group which are determined by classes of groups. pp. 35--37
Summary: Classes of n-ary groups of the X(n) and X*(n) form, where X is class of groups, are considered.
Ageenko A. V., Emelichev V. A.
On the stability radius of a strictly efficient solution of the vector Boolean problem of threshold functions minimization. pp. 38--41
Summary: Vector version of the well-known Boolean problem of threshold function minimization has been considered. Formula for the extreme level of independent perturbations of partial criteria parameters has been found where strictly efficiency of solution still remains.
Volosevich A. A.
Maximum principle and local selectors in control problem for discrete inclusions with delay. pp. 42--46
Summary: The necessary optimality conditions in control problem for discrete inclusions with delay are obtained. The connection between given results and Boltyanski local selectors method is established.
Demesh N. N. Chekhmenok S. L.
Asymptotics of the moments of the smoothed periodogram for symmetric homogeneous stable random fields with discrete time. pp. 47--50
Summary: The values of the bias and variance of the smoothed periodogram for symmetric homogeneous stable random fields with discrete time are investigated.
Vasilenko Zh. V., Trush N. N.
Estimation of the spectral density over overlapping observation intervals. pp. 51--54
Summary: The moments of the estimate of spectral density constructed from averaging of modified periodograms over overlapping observation intervals are calculated. Asymptotic behavior of the first two moments is investigated.
Adukov V. M.
The problem of the Pade approximation as the Riemann boundary problem. pp. 55--61
Levin G. M., Rozin B. M.
Optimization of the monotonous convex function on the convex polyhedral set generated by the parallel-sequential structure. pp. 62--67
Summary: The problem of minimization of the monotonous convex separable function on the convex polyhedral set, generated by the parallel-sequential structure is considered. The three-level decomposition scheme of this problem solving is proposed. This scheme is the modification of the constraints relaxation method. The scheme reduces the problem solving to the solving of finite consequence of subproblems with the equality constraints.
ФІЗІКА
Ivanov A. A., Feranchuk I. D.
Thermodynamic characteristics of gas of diatomic molecules with high degree of anharmonicity. pp. 68--73
Summary: The operator method and the cumulant expansion are used for the approximate calculation of the partition function and the free energy of a diatomic molecule with a high degree of anharmonicity. It is shown that the zeroth-order approximation of the method proposed interpolates these values with rather good accuracy in the entire range of both the Hamiltonian parameters and temperature. The method allows one to calculate also the corrections to the zeroth-order approximation.
Korshunov F. P., Kurilovich N. F., Prokhorenko T. A.
Annealing of radiation defects in irradiated gamma-quanta and fast electrons unalloyed n-GaAs crystals. pp. 74--78
Summary: The annealing behavior of unalloyed n-type GaAs crystals irradiated with gamma-rays and 4-MeV electrons has been investigated. It have been determined the radiation defects annealing activation energy of 0.65 ± 0.1 eV -- for irradiated with gamma-rays crystals and of 0.65 ± 0.1 eV -- at the first annealing stage and 1.5 ± 0.1 eV at the second annealing stage for irradiated with fast electrons crystals.
Kulak G. V., Kovchur S. N., Lutsenko E. V., Ropot P. I.
Acoustooptic light modulation in the conditions of Frenel reflection from a strengthening layer. pp. 79--82
Summary: The possibility of using three-layer structure, containing strengthening layer, for creation of lasers with modulated quality factor is shown.
Khapalyuk A. P.
On geometry of laser beams. pp. 83--90
Summary: The research of geometry of laser beams in optics is reduced to research of linear-fractional transformation in mathematics. The usual (classical) interpretation of this transformation, where the infinity is considered as one point (extended complex plane of Gauss), conducts to non-Euclidean geometry of laser beams. The axiom about the parallel straight lines requires existence of different infinities on a plane. The account of this feature conducts to Euclidean geometry of laser beams. Further is shown, that the definition by Euclid of a point as an object not having an interior structure contradicts an axiom about the parallel straight lines.
Brinkevich D. I., Prosolovich V. S., Yankovski Yu. N.
Impurity interaction at heat treatment of ytterbium implanted silicon monocrystals. pp. 91--94
Summary: The processes of doping and technological impurities interaction during high temperature heat treatment of silicon monocrystals with implanted ytterbium have been studied by the Rutherford backscattering spectrometry and secondary ions mass-spectroscopy methods. Boron and phosphorus atoms at heat treatment diffused into the bulk of monocrystal as well as to the surface. The presence of Yb leads to increasing of the last process efficiency. Sb impurity moves to the surface with the crystallization front during the heat treatment process. It is shown that ion implantation of the lanthanoids allow to form a effective getter for background technological impurities in silicon.
Makovetskii G. I., Dorofejchik S. S.
Magnetic properties of solid solution Cr1-x-CoxTe system. pp. 95--97
Summary: By X-ray analysis method is shown that in the Cr1-x-CoxTe system the solid solutions with the NiAs-type structure in the x = 0 ¸ 0.3 concentration range were obtained. From the specific magnetization temperature dependences is established that the solid solutions magnetic moment values decrease with the cobalt containing increasing.
Akimov A. I., Lebedev S. A., Letko A. K.
Refinement of crystal structure of ceramics Tl2Ba2CaCu2Ox received by a method of cold pressing at high pressure. pp. 98--101
Summary: Using by the Rietveld method parameters of crystal structure of Tl2Ba2C + Cu2Ox were refined in depending on compacting pressure. The Rietveld analysis of the room-temperature powder X-ray diffraction data showed that the parameter a, c and interatomic distances O2 -- O3, Ca -- O1 are decrease with increasing compacting pressure. Ba -- O1, Ba -- O2, Cu -- O1 distances are decrease at 5 Gpa. Positional parameters of the cations and O1, O2 are decrease in the same compacting pressure region.
Dymont V.P., Nekrashevich E.M., Pankov V.V., Budejko N. L.
Synthesis of carbon nitride at low temperature. pp. 102--104
Summary: Synthesis of carbon nitride in liquid ammonia was carried out. A carbon nitride was formed as a white powder. The results of X-ray diffraction and Fourier transform infrared absorption spectrum are obtained.
ІНФАРМАТЫКА
Baranouski A. K., Kuchinski P. V., Chernyavski A. F.
Entropy estimation of random number sequence produced with application of physical noise source. pp. 105--110
Summary: The method of entropy estimation in binary random number sequence is proposed. The method of counting of randomly generated noise pulses at the output of diode over a measured time interval are used for random number generation. Gaussian distribution law is proposed to depict events number produced from Poisson point process after dead-time resampling. The variance to mean ratio are proposed to use as a measure of entropy reduction in comparison with Poison random numbers. Proposals for diode operation mode and counting time interval are introduced.
Benediktovitch V. I.
Noncrossing k-factors in geometric graphs. II. pp. 111--116
Summary: It is proved that deciding the existence of a noncrossing 4-factor in 5-regular geometric graph G with r(G) = 3 and the existence of a noncrossing 5-factor in 6-regular geometric graph G with r(G) = 4, where r(G) is the index of intersection of geometric graph G, is WP-complete.
Kazantseva O. G.
Properties of the term structure functions in the stochastic financial analysis. pp. 117--122
Summary: The determination of so-called time structure of interest rates is the one of central problem of stochastic financial mathematics. In article this problem is examined for multifactor model of time structure of an affine class. Properties of functions of time structure of multifactor model are determined. The numerical example is given.
АНАТАЦЫІ ДЭПАНІРАВАНЫХ АРТЫКУЛАЎ
Dichkovskaya S. A.
Computing research of approximate algorithms and exact algorithms of the solution of a three-index axial decision problem. pp. 123--123.
/ 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
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Капірайт © 2004 Інстытут матэматыкі НАН Беларусі
