Известия Нац. академии наук Беларуси. Сер. физ.-матем. наук, 2005, No.4
/ Издания академии / Научные журналы
Известия Нац. академии наук Беларуси. Сер. физ.-матем. наук, 2005, No.4
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Известия Национальной академии наук Беларуси
СЕРИЯ ФИЗИКО-МАТЕМАТИЧЕСКИХ НАУКИздатель: Беларуская навука, Минск, Республика Беларусь |
Номер 4, 2005
СОДЕРЖАНИЕ
МАТЕМАТИКА
Gromak V. I., Goloubeva L. L.
The forth order generalized second painleve equation. pp. 5--10
Summary: Analytical properties of solutions of the forth order generalized second Painleve equation are investigated. Equivalent systems, Backlund transformations, functional relations between solutions are built, and the necessary and sufficient conditions of rational solutions existence are proved.
Zhestkov S. V., Zabreiko P. P.
One constructive variant of Meyers theorem for analytical ordinary differential equations. pp. 11--14
Summary: The constructive variant of Meyers theorem for the Cauchy problem x = f(t, x), x(0) = 0, where function f(t,x) is continuous on t and analytical on x, is proved.
Evtuhova S. M., Monakhov V. S.
On order core factors subgroups finite soluble group. pp. 15--18
Summary: It is investigated the rank dependence of the derivative length and p-length finite soluble group from values of orders core factors subgroups.
Lasy T. P.
On solvable aspherical pro-p-groups. pp. 19--24
Summary: The theorem describing solvable aspherical pro-p-groups in the cases p = 2 and p = 3 is proved without using homological methods.
Legchekova H. V.
Finite groups with X-permutable 2-maximal and 3-maximal subgroups. pp. 25--29
Summary: The evaluation of the p-length of the p-soluble groups is considered.
Kharin A. Yu., Kishylau D. V.
Performance and robustness analysis for sequential testing of hypotheses on parameters of Markov chains. pp. 30--35
Summary: The problem of sequential testing of hypotheses on parameters of Markov chains is considered. The special case of simple hypotheses is analyzed. Exact values for error probabilities and for conditional expected sequence lengths are obtained. Asymptotic robustness analysis for these characteristics is performed under "contaminations". A parametric family of modified sequential probability ratio tests is proposed and analyzed to get the robust test by the minimax risk criterion. Numerical results illustrate the theory.
Rusina T. I., Yablonski A. L.
The limiting behavior of multidimensional Ito sums with averaging in the nonhomogeneous case. pp. 36--42
Summary: The limiting behavior of multidimensional sums with averaging for functions f = f(t,x), t Î [0; a], x Î Rk are investigated. Complete classification of the ways of the approximations of multidimensional stochastic q-integrals with these functions in the convolution algebra of generalized stochastic processes has been given.
Kopeikina T. B.
Controllability of functional-differential systems. pp. 43--48
Summary: The wide class of linear time-variable functional-differential systems, such as ordinary and singularly perturbed systems without delay, with state delay, with deviating argument of neutral type are considered. The unified approach of constructing the defining algebraic equations is suggested. A criteria, sufficient conditions of controllability for singularly perturbed systems with respect to slow variable in standard form are obtained. All these conditions are formulated in terms of solutions of corresponding defining equations for systems under consideration.
Poddubnaya O. N.
Some criteria of hybrid system relative controllability. pp. 49--54
Summary: The problems of H-t1-controllability are considered for both non-stationary and stationary linear hybrid systems. Some geometrical properties of the attainability sets for such systems are investigated. As a result implicit criterion for non-stationary as well as parameter criterion for stationary hybrid systems is obtained.
Emelichev V. A., Kuzmin K. G.
On quasistability of the vector Boolean problem of threshold function minimization. pp. 55--58
Summary: The vector Boolean problem of threshold function minimization is considered. A kind of stability of this problem is studied, which assumes preservation of all the Pareto optimal solutions under "small" perturbations of parameters. The necessary and sufficient condition of stability is obtained.
Lepin V. V.
Minimizing diameters of edges in layout of a hypergraph into a d-dimensional grid. pp. 59--64
Summary: The hypergraph layout problem is considered. The hypergraph vertices are placed on a d-dimensional grid. Problem consist of the minimization of the total diameter of the hyperedges. The diameter of a hyperedge is the maximum distance between two vertices of the hyperedge. Approximation algorithm O((log n)2+2/d) for this problem is obtained.
Skums P. V., Suzdal S. V., Tyshkevich R. I.
On the some extension of the class of split graphs. pp. 65--71
Summary: The extension of the class of split graphs, retaining a number of its advantages connected with algorithmic problems, is considered. One of its variations -- the class of U-split graphs, is analyzed in detail. For this class solvability of the recognition problem and the problem of finding range of graph parameters in linear time concerning a number of verticies of a tested graph is proven. The generating function for the number of U-split graphs is given.
ФИЗИКА
Solovtsova O. P.
The Q2-dependence of the integral for the Gross -- Llewellyn Smith sum rule in analytic perturbation theory. pp. 72--76
Summary: A role of additional power corrections that are appear in analytic perturbation theory is investigated for the Gross -- Llewellyn Smith sum rule. It is shown that they are important in defining nonperturbative high-twist terms.
Ryabushko A. P., Nemanova I. T., Zhur T. A.
Riemann space-time due to the gravitating center surrounded by a nonhomogenous gas-dust-like globe in general relativity. pp. 77--85.
Summary: The post-Newtonian approximation of the Einstein equations has been used to obtain and discuss the metric of space-time, which appears around the gravitating center surrounded by a nonhomogeneous gas-dust-like globe.
Goncharenko I. A., Esman A. K., Kuleshov V. K.
Spectral demultiplexing of data streams in middle IR wavelength region. pp. 86--89
Summary: The fast method of demultiplexing and spectral routing of optical data streams transmitted in near and middle infrared wavelength region is proposed. With the help of numerical modeling the optimization of the parameters of the middle IR region demultiplexer based on the method proposed has been carried out. The proposed demultiplexer provides effective separation of the spectral components simultaneously to 300 channels with resolution about 50 nm. In general, the number of channels on the standard substrate is defined by permissible dimensions of the substrate, bend radius and the wavelength of information signal.
Belov V. V., Nemtsov V. B.
Statistical model of overstretching of DNA molecule. pp. 90--93
Summary: Two-state model of DNA molecule is proposed. On base of the statistical mechanics the curve of DNA overstretching is calculated and results of this calculation are corresponded to the experimental date. The plateau phenomena on the curve of deformation is described.
Tomov A. V., Huzouski V. G.
Optical sensor of ammonia based on porous aggregates. pp. 94--97
Summary: The possibility to improve sensitivity of a spectral-absorption sensor to ammonia vapors of low (below 1 v. %) concentrations using the methyl red as an indicator in a sensing element on the base of porous glass is considered.
Akimov A. I., Savchuk G. K.
The synthesys and physical properties of Ag5Pb2O6 compounds. pp. 98--103
Summary: New method of the synthesis of the Ag5Pb2O6 compound is elaborated. The optimum conditions to prepare the full stoichiometric Ag5Pb2O6 compound are determined on the basis of the XRD and EDX analyse. It is shown that an addition of strontium ions at the compound synthesis does not have a remarkable influence on the lattice parameters, electrophysical properties and thermal stability of the probes.
Shipilo V. B. †, Dutov A. G., Shipilo N. V., Komar V. A., Azarko I.I.
Effect of chromium, iron, cobalt and nickel on crystallization of diamonds in manganesenickel system. pp. 104--106
Summary: Dependence of change of a degree and phase transformation speed of graphite in diamond, its fractional and admixtures structure, paramagnetic defects, and also strength of diamonds from the contents in initial reactionary charge of systems Mn -- Ni -- C chromium, iron, cobalt and nickel are established.
ИНФОРМАТИКА
Adutskevich E. V.
Getting necessary and sufficient conditions for preservation of dependence when parallelizing algorithm. pp. 107--112
Summary: Necessary and sufficient conditions for preservation of dependence when parallelizing algorithms given by affine loop nests are obtained. A general approach of getting the conditions in the practically important cases is suggested. This approach allow to get less constraints which do not depend on external variables.
Zakharov I. L.
Super-resolution restoration from sequence of blurred and noised images. pp. 113--118
Summary: The image sequence processing method for restoration of high-resolution image from several shifted low-resolution images of the same object is described. The important property of the method is the possibility of theoretical quality assessment of restoration results in dependence on point spread function of imaging system and number of processed images. Numerical simulations and experiment show high efficiency of proposed super-resolution method.
КРАТКИЕ СООБЩЕНИЯ
Tyshchenko V. Yu.
On equivalence of complex many-dimensional Riccati equations with periodic coefficients. pp. 119--120
Summary: Topological and smooth classifications of the foliations, defined by general solutions of complex many-dimensional Riccati equations with periodic coefficients, are produced.
АННОТАЦИИ ДЕПОНИРОВАННЫХ СТАТЕЙ
Spichekova N. V.
On the behaviour of the integral surfaces of the Pfaff equation with sum of linear and bilinear operator. p. 121
Politaev D. N.
On the theory of methods of two-sided and multiple computational schemes. p. 121
УЧЕНЫЕ БЕЛАРУСИ
Николай Станиславович Казак (К 60-летию со дня рождения). С. 122--123
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Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: 2 декабря 2006 г.
Создана при участии Игнатия И. Корсака
Копирайт © 2005-2006 Национальная академии наук Беларуси
Копирайт © 2005 Издательский дом "Беларуская навука"
