СЕРИЯ ФИЗИКО-МАТЕМАТИЧЕСКИХ НАУК
Издатель: Институт математики НАН Беларуси, Минск, Республика Беларусь
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Известия Национальной академии наук Беларуси СЕРИЯ ФИЗИКО-МАТЕМАТИЧЕСКИХ НАУК Издатель: Институт математики НАН Беларуси, Минск, Республика Беларусь |
Summary: The upper estimates for Hausdorff dimension and Lebesgue measure of points of the plane R2 with the given approximation by algebraic numbers are obtained.
Krasovskii S.G.
On spectral set of a linear singular system with the coincident exponents. pp. 10--15
Summary: The singularly perturbed 2-dimensional linear system with infinitely differentiable coefficients and their derivatives which has the coincident characteristic exponents is constructed. The spectral sigma-set of this system is completely described.
Vol'vachov R.T., Yanovich L.A.
Linear interpolation of operators in rectangular matrix spaces. pp. 16--21
Summary: Necessary and sufficient conditions of existence of a linear interpolation polynomial of type XB + C, BX + C, XR + SX + T, or RXS + T, where X, B, C, R, S, T are rectangular matrices of required dimension are founded. Interpolation formulae for each of these cases are obtained.
Kopeikina T.B., Tsekhan O.B.
To the observability theory of linear nonstationary singularly perturbed systems. pp. 22--27
Summary: The problem of relative observability for linear nonstationary singularly perturbed dynamic systems of neutral type is investigated. Some effective conditions of relative observability in terms of algebraic defining equations are obtained.
Zhuk E.E., Pirshtuk I.K.
Statistical classification of autoregression time series. pp. 28--34
Summary: The statistical classification problem of observations described by autoregression time series is considered. The new decision rules of discriminant analysis and cluster analysis are proposed and their efficiency is analytically investigated.
Harin A.Yu.
On robustness of Bayesian forecasting under c2-distortions of parameters and observations distribution. pp. 35--37
Summary: We considered the problem of minimax robustness of Bayesian statistical forecasting for the case of hypothetical model distortions in c2-pseudometric. We have obtained the analytic expression for the guaranteed upper risk functional and the integral equation for the robust prediction statistic. From the latter we have derived the one-step robust prediction statistic and have analyzed its properties.
Summary: The linearity relations and naturalness conditions introduced by F. I. Fedorov in the framework of the three-dimensional vector parameterizations of the classical groups are extended on the case of four-dimensional quantum vector parameters of the q-deformed group GLq(2.C). The linear transformations of the quantum vector parameter caused by similarity transformations of the corresponding quantum matrix are defined and used.
Goncharenko A.M.
On the theory of spatial-temporal optical solitons. pp. 44--46
Summary: A spatial-temporal Gaussian form soliton is considered. It is shown that its dimensions and duration are defined by the energy and non-homogeneous parameters of medium.
Kudryashov V.V.
Quasi-uniform approximation for the solution of the one-dimensional Schrodinger equation with an arbitrary potential. pp. 47--52
Summary: The comparison equation method is applied to the Riccati equation related to the one-dimensional Schrodinger equation with an arbitrary potential. The approximation of a new type is obtained which is suitable near and far from turning points for the logarithmic derivative of the wave function. The continuous approximation for the wave function is constructed. New energy quantization rule for the problem with two turning points is found.
Novysh B.V., Dorozhkin N.N., Gololobov E.M., Anishchik V.M.
Calculation of angular components of the electron-ion potential in YBa2Cu3O7. pp. 53--57
Summary: Angular components of the electron-ion interaction potential for YBa2Cu3O7 for linear and quadratic with respect to atomic displacements components are calculated. It is shown that additional (with reference to Rigid Muffin-Tin Approximation) angular components of perturbing potential (L ¹ 1) can substantially change electron-phonon matrix elements in high-temperature superconductors.
Petrov A.V.
Deviations from Matthiessen's rule in Al-Ga alloys in strong magnetic fields. pp. 58--61
Summary: Results of the investigations of impurity part of electrical resistivity of Al-Ga alloys single crystals in the absence of magnetic field and in the field 8T in terms of the deviations from Matthiessen's rule (DMR) are analyzed. The correlation between the character of temperature dependencies of the DMR and the single crystal orientation in a transverse magnetic field is determined. It is explained by a diffusing character of electron-phonon scattering. The interpretation of negative values of the DMR which were observed in the experiment is given.
Girgel S.S., Shablovskii Ya.O.
Relationships between critical parameters of crystal dielectrics. pp. 62--65
Summary: The correlation of temperature anomalies of physical quantities in a critical region on the basis of the theory of thermodynamic stability is analyzed. Series of new relations for critical indices of thermodynamic and optical parameters of ferroelectric and ferroelastic crystals is obtained.
Ges' A.P., Guretskii S.A., Luginets A.M., Milovanov A.S., Fedotova V.V.
The growth of KTiOPO4 single crystals at high temperature gradients in the crystallization zone. pp. 66--69
Summary: Temperature gradients effect on growth kinetics of TiPO4 crystals from solution KO2 -- P2O5 -- TiO2 and their non-linear optical properties are investigated. It is established that correctly defined the temperature gradient on crystallization front is one of efficient factors providing high quality of crystals.
Belevich N.N., Makovetskii G.I.
Investigation of the diffusion and drift of the photo-exited charge carriers in the polycrystalline films of CuGaSe2. pp. 70--73
Summary: Results of ambipolar transport measurements made at 300 K with a steady-state photocarrier grating technique on 0.2-3 µm thick p-type films of CuGaSe2 are presented. It has been found that the diffusion length varies between 40 and 200 nm. The products of mobility-life time for minority and majority carriers have been also obtained. Results of the investigations of the diffusion length dependence on electric field value are presented.
Danilyuk A.L., Uglov V.V., Cherenda N.N., Zelenkovskii V.M., Pushkarchuk A.L.
The electronic structure of aluminium carbide atomic clusters. pp. 74--78
Summary: Results of the simulation of aluminium carbide clusters electronic structure are presented. Simulation was made by means of the modified neglect of diatomic overlap-parametric method.
Cherkas S.L.
About spin precession in electromagnetic wave. pp. 79--84
Summary: It is shown that two ways of the description of the 1/2 spin particle precession in a circulary polarized electromagnetic wave. First, on the basis of the Bargmann-Michel-Telegdi and second, on the basis of the Dirac equation with Pauli term give the same result in the second order of the wave's field for an arbitrary wave length.
Toumilovich M.A., Sementchik V.G.
On methods of base frequency evaluation for speech signals. pp. 85--87
Summary: The problem of accurate fundamental frequency measurement is important task in speech processing and identification. In this paper we investigate basic pitch extraction algorithms for patient with larynx disease. Median filtering for stable pitch estimation is used. The experimental results shown that the algorithm based on autocorrelation function is more applicable for fundamental frequency measurement.
Summary: A minimum-mean cycle can be found in Q(nm) time using an algorithm of Karp. Here we present a very simple algorithm which runs in O(n2m) time and has been proved to be very efficient in practice. An implementation of this algorithm which uses dynamic trees and Fibonacci heap data structures runs in O(nm log n) time. Proposed algorithm has the same complexity as more efficient algorithms for sparse graphs.
Matalytskii M.A.
Sequential method of finding steady-state probabilities for queuing networks. pp. 92--96
Summary: The steady-state probabilities of closed queuing networks with an arbitrary message servicing in systems are obtained.
Orlovich Yu.L.
On locally connected graphs whose maximal vertex degree does not exceed four. pp. 97--100
Summary: A graph is locally connected if the subgraph induced by the neighborhood of each vertex is connected. In this paper we describe all connected locally connected graphs whose maximal vertex degree does not exceed four. Some new properties of connected locally connected graphs with maximal vertex degree five is are obtained.
Podkopaev D.P.
The formula for quasi-stability radius of the vector trajectorial bottleneck problem. pp. 101--106
Summary: We consider the problem of vector optimization on the system of subsets of the finite set with the bottleneck partial criteria (MINMAX). Parameters of the vector criterion are exposed to independent perturbations. The formula for quasi-stability radius of the problem has been found for the case of an arbitrary monotone norm which is given in the space of perturbations.
Gagarin A.V., Metel'skii Yu.M.
Characterization of (1,2)-polar graphs. pp. 107--112
Summary: It is known that a class of (a, b)-polar graphs is hereditary and can be characterized in terms of forbidden induced subgraphs. The finiteness of such a characterization for (l,2)-polar graphs is proved. The corresponding list of 18 graphs is found.
Likhoded N.A., Tiountchik A.A.
Scheduling function for the implementation of algorithms on three-dimensional array processors. pp. 113--118
Summary: Scheduling function for the mapping of parallel algorithms onto three-dimensional fixed-size array processors without long interconnections is described. Conditions of scheduling optimality are formalized and proved. The proposed procedure of the time mapping is constructive and ensures finding of the optimal parameters.
Chernyak A.A.
K-terminal networks with threshold system of connectedness. pp. 119--123
Summary: K-terminal nonoriented networks with threshold survival known as K-terminal cut-threshold graphs are effectively characterized. The characterizations of 2-terminal and allterminal cut-threshold graphs directly follow from the main result.
Summary: The theorem about existence and uniqueness of R-holomorphic solution for the entirely solvable system of equations in total differentials is proved.
Stel'mashuk N.T., Shilinets V.A.
The solution of the boundary value problem for one system of differential equations in formal derivatives. pp. 127--128
Summary: The boundary value problem for one system of differential equations based on F-monogenic functions is investigated.
In Belarusian Mathematical Society. pp. 130--132
Гайшун И.В., Олехнович Н.М., Анисович Г.А. и др.
Георгий Павлович Лопато (К 75-летию со дня рождения). С. 135--136
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