Известия Нац. академии наук Беларуси. Сер. физ.-матем. наук, 2001, No.3
/ Издания академии / Научные журналы
Известия Нац. академии наук Беларуси. Сер. физ.-матем. наук, 2001, No.3
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Известия Национальной академии наук Беларуси
СЕРИЯ ФИЗИКО-МАТЕМАТИЧЕСКИХ НАУКИздатель: Институт математики НАН Беларуси, Минск, Республика Беларусь |
Номер 3, 2001
СОДЕРЖАНИЕ
МАТЕМАТИКА
Korzyuk V. I., Kiselyov V. B.
Boundary value problem for the third order linear non-classical equation generated with a heat equation. pp. 5--11
Summary: With methods of functional analysis using averaging operators with variable step on the basis of preliminary derived energetic inequality it is being proved existence and uniqueness of strong solution of boundary problem for the third order equation. Considered problem is equivalent to the mixed problem for one modified thermal conductivity equation, where term on time is set at the end of concerned time period.
Kalosha N. I.
On approximate properties of real algebraic numbers of the third degree. pp. 12--17
Summary: Let M(I, Q, l) be a set of real numbers lying in a given interval I and satisfying |P3(x)| < Q-l for some non-zero polynomial P3(x) of the third degree with integer coefficients, H(p) £ Q and 3 < l < 3• 9/38. An effective estimate of measure of the set M(I, Q, l) is obtained.
Starovoitov A. P.
About coincidence of the best rational and polynomial of trigonometric approximations. pp. 18--22
Summary: For any non-increasing sequence {an}n=0¥, an ® 0, an ³ 0, of real numbers the necessary and sufficient conditions have been obtained for the sequence {nk}k¥ = 0) for which there exists the continuous 2p-periodic function f, such that Rnk, mk (f) = Enk (f) = ank, k = 0, 1, 2, ... , where En(f) and Rn,m(f) are the best uniform approximations of the function f by trigonometric polynomials of degree not exceeding n and trigonometric rational functions rn,m(x) = pn(x)/qm(x) accordingly.
Levina T. I., Matsevich D. A., Sinkevich D. V.
About coefficients of determination of elements of the mistake matrix one statistical model for calculation of the estimation of transition probabilities of a homogeneous Markovian chain for the aggregated information. pp. 23--28
Summary: Formulas for coefficients of determination of elements of the mistake matrix one statistical model for calculation of the estimation of transition probabilities of a homogeneous Markovian chain for the aggregated information are given.
Malyutin V. B.
Approximations of matrix-valued functional integrals by numerical-valued functional integrals with respect to space of functions with finite number of values. pp. 29--32
Summary: Matrix-valued functional integral is approximated by numerical-valued functional integral and functional integral with respect to space of functions taking values ±1.
Demenchuk A. K.
On periodic partially irregular solutions of linear non-homogeneous differential systems. pp. 33--35
Summary: Necessary and sufficient conditions of existence of periodic partially irregular solutions for linear non-homogeneous differential systems are given.
Sobolevskii S. L.
The small parameter transform in the Painleve property analysis of differential systems. pp. 36--40
Summary: It is proved that if the system of ordinary differential equations with rational right side possesses Painleve property (i.e. all of its singularities are poles) then the simplified (in the sense of small parameter transform) system also possesses the same property.
Kilbas A. A., Dem'yanko S. V.
Solution of integral equations with power-logarithmic kernels in the class of integrable functions. pp. 41--46
Summary: One-dimensional Volterra integral equations of the first kind, containing power-logarithmic functions in kernels, are studied on a finite interval of the real axis. The necessary and sufficient conditions for the solvability of these equations in the space of absolutely integrable functions are proved, and their solutions in closed form are constructed.
Trush N. N., Markovskaya N. V.
On estimates of mixed cumulants of the third and fourth orders. pp. 47--54
Summary: The estimates of mixed cumulants of the third and fourth orders are built. Mathematical expectations, covariance, dispersion of constructed estimates are calculated. The estimates of mixed cumulants of third and fourth orders are asymptotically unbiased and consistent in mean-square sense. Limit distribution of the considered estimates is found.
Mandrik P. A.
The solution of two-dimension heat conduction problem with mixed boundary conditions for an isotropic half-space. pp. 55--59
Summary: An analytical distribution of temperature fields of an isotropic half-space is obtained. The change law of a density of a heat flow through a circle of a fixed radius and the constancy law of temperature on a surface of a half-space outside of this circle are given.
Demidenko V. M.
Extremal values of linear functionals on the set of cycles of symmetric group. pp. 60--64
Summary: The condition that guarantee attainability of extremal values of linear functionals on the given pair of cyclic permutations are proposed. The possibility of their use for obtaining the lower or upper bounds of values of the functional of the traveling salesman problem, as well their use under approbation and testing of the exact, approximate and heuristic methods of solution of the above-mentioned problem is discussed.
ФИЗИКА
Bogush A. A., Kisel V. V., Tokarevskaya N. G., Red'kov V. M.
On generalized scalar particle theory with extended set of irreducible Lorentz group representations. pp. 65--71
Summary: A generalized scalar particle theory with the use of an extended set of Lorentz group irreducible representations (scalar, two 4-vectors and antisymmetric 2-rang tensor) is investigated in tensor and matrix formalisms. A special basic in the space of 15-component wave function is found where instead of the four initial complex parameters li only one real quantity s is presented. It is shown that in this basis C-operation is reduced only to the complex conjugation of the wave function. C-matrix in the initial basis is calculated too. Invariant bilinear form matrices in both bases are calculated and the conserved current and Lagrangian formulation of the whole theory are established. Extension of the 15-component equation to a curved space-time is given.
Gurskii L. I., Dorozhkin N. N., Yakutovich N. G., Novysh B. V.
Linear augmented Slater-type orbital method for electronic structure calculations of solids with arbitrary basis. pp. 72--77
Summary: The linear augmented Slater-type orbital method (LASTO) is generalized for arbitrary atoms per unit cell. The LASTO method was applied to the electronic band structure and structural energy difference for fcc, bcc, and hcp phases of Al, Sc, Ti. The structural energy differences with fcc and diamond crystal structures for Si were calculated. The crystal structures for considered elements are correctly predicted by LASTO method.
Malik A. A., Satsunkevich I. S.
About the possibility to produce (µ- µ+)b atom. pp. 78--82
Summary: A schematic analysis of energy levels and decay rates of (µ- µ+)b has been done. All the contributions to the cross section of process e- e+ ® (µ- µ+)b have been calculated, taking into account all the final states after the decay of (µ- µ+)b. A conclusion has been given about the possibility to produce (µ- µ+)b in reasonable quantities in the corresponding experiments.
Hoang Quoc Khanh, Komarov L. I.
The simplified variant of the operator method in the theory of atoms. pp. 83--85
Summary: Within the framework of one-partial approximation the model of atom is proved with distinguish groups of particles forming electron shells.
Bokun G. S., Groda Ya. G., Vikhrenko V. S., Uebing C.
Generalized selfconsistent diagram approximation for the Gibb's grand canonical thermodynamic potential of a lattice system. pp. 86--91
Summary: The diagram expansion of the Gibbs' grand canonical thermodynamic potential in the four-site Mayer-like functions is considered. The mean potentials introduced to renormalize intermolecular interactions are calculated on the basis of a minimal susceptibility principle. The lowest order terms of the expansion reproduce thermodynamical properties and the liquid - gas coexistence curve of the lattice system with accuracy of an order of a per cent
Esman A. K., Goncharenko I. A., Kuleshov V. K.
Tuning the wavelength of laser radiation by use of controllable waveguide Bragg grating. pp. 92--96
Summary: The use of Bragg grating on the base of waveguide electrooptical modulator as external cavity for fast controllable tuning the wavelength of laser radiation is proposed. The reflectivity spectrum of such a grating with various values of controlling voltage has been calculated by the Method of Lines. Spectral parameters of laser radiation are obtained. The region of continuous tuning of such a laser for control voltage up to 5 V is about 0.2 nm and switching time is < 0.08 ns.
Kulak G. V., Khilo P. A.
Resonant acousto-optical interaction in single-mode fibre light guides. pp. 97--100
Summary: The peculiarities of Bragg's diffraction of light on longitudinal ultrasound waves in superlattices recorded in germanium silicate fibre is investigated. The possibility of 100 % intensity modulation of reflected waveguide mode by ultrasound wave of low frequency (about a few tens MHz) is demonstrated.
Bogatyrev Yu. V., Korshunov F. P., Lastovskii S. B., Kul'gachev V. I., Troshchinskii V. T.
The magnetic field effect on MIS structures with radiation defects. pp. 101--105
Summary: Several extremums in dependencies of gamma-irradiated MIS structures parameters on constant magnetic field induction (0.044 -- 0.3 T) have been determined. This effect is interpreted by the processes of dynamic polarization and relaxation of silicon magnetic isotope nuclei.
Shipilo V. B., Kovalevskii V. N., Shipilo N. V.
The physical and mechanical properties of ceramics from aluminum nitride in depending on conditions of its deriving. pp. 106--110
Summary: The influence of the high pressure (5 GPa) on the process of sintering (T = 1850 °C) of the ceramics from aluminum nitride was studied and its physical and mechanical properties was investigated.
It is established that the high pressures activate the process of sintering of the ceramics in result of plastic deformation of the grains and its higher characteristics is attained at 8 mas.% Y2O3 in result of more complete sintering of the material and a connecting of the oxygen dissolved in its.
Prosolovich V. S., Yankovskii Yu. N., Brinkevich D. I.
Radiation defects formation out the ion-implantation layer at high energy implantation of silicon. pp. 111--114
Summary: Defects formation processes at high energy implantation of silicon were studied by Hall effect and IR absorption methods. Point radiation defects formed at the interstitial-vacancy pair diffusion into the substrate were detected outside the ion-implantation layer. Effectiveness of this center formation at implanted ion mass increasing were decrease because of the interstitial and vacancy traps concentration increasing.
Gaiduk P. I., Larsen A. N.
Molecular-beam growth of SiGe/Si heteroepitaxial structure. pp. 115--119
Summary: A new procedure of stepwise equilibration for MBE growth of relaxed, low dislocation-density Si1-xGex alloy layers on a (001) Si substrate is presented. The stepwise buffer is prepared in a layer-by-layer manner. The growth of each layer includes two main stages, a low-temperature stage and an average-temperature stage, which allows to separate the processes of nucleation and multiplication of misfit dislocations and the propagation of the threading dislocations. An in situ equilibration annealing at considerably high temperature is proceeded before the next growth step to remove the threading dislocations from the layer. The dislocations in these stepwise graded Si1-xGex buffers are investigated by TEM and AFM. The ability to grow strain relaxed, almost dislocation-free, virtual substrates of different compositions is demonstrated.
Bordusov S. V., Spiridonov S. V., Starobinets G. G.
Energy dissipation in polar gases and liquids in alternating electrical field. pp. 120--123
Summary: The thermal power per unit volume due to dissipation of the energy of the alternate electrical field in viscous polar medium was calculated numerically for gaseous ammonia, water vapour and water.
ИНФОРМАТИКА
Lepin V. V.
The pebbling game on planar distributive lattices. pp. 124--128
Summary: The pebbling game on finite tight suborders P of the grid points of the first quadrant with (0,0) Î P and hence, in particular, on planar distributive lattices is considered. The upper and lower bounds for the pebbling number of such orders in terms of its width are given.
Malinkovskii Yu. V., Nueman A. Yu.
Multiplicativity of the stationary distribution in open networks with multi-mode service strategy. pp. 129--134
Summary: The open queueing networks with Poisson input, exponential service in the nodes and Markov routing are considered. Single server nodes can operate in several regimes, switching time from some regime to another one has the exponential distribution. Switch occurs only between the neighborhood regimes. The quasi-reversibility and ergodic conditions are established and the stationary network state distribution are determinated in product form.
КРАТКИЕ СООБЩЕНИЯ
Golubeva O. V., Pal'chik E. M.
On the Wielandt's theorem. pp. 135--136
УЧЕНЫЕ БЕЛАРУСИ
Богуш А.А., Гончаренко А.М.
Федор Иванович Федоров (К 90-летию со дня рождения). С. 137--139
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Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: 2 декабря 2006 г.
Создана при участии Игнатия И. Корсака
Копирайт © 2001-2006 Национальная академии наук Беларуси
Копирайт © 2001 Издательство "Беларуская навука"
