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: It is shown that the recession cone of a set characterizes in fact the star-shapedness of the set at the infinity.
Monastyrny P.I.
On calculation algorithms of hybrid type for grid and boundary problems. II. pp. 9--13
Summary: The new approach to the problem of the solution of grid equations is proposed. It is based on the hybrid principle of the joining of various calculations algorithms which are local adapted to the characteristic of equations. The method is provided by constructive using of the mechanism of closing of the calculations in boundary zones.
Laptinsky V.N., Livinskaya V.A.
On the periodic solutions of the Lyapunov second order matrix differential equation. pp. 14--17
Summary: The effective algorithm for the construction of periodic solution of matrix differential equation Lyapunov's type is proposed.
Zhuk E.E., Kharin Yu.S.
Interval approach to robustness in statistical classification. pp. 18--23
Summary: The case of distortions of probability distributions which describe classes is investigated. To construct the robust decision rules (DR) the interval approach is used. It is proved that under the Tukey -- Huber distortions the robust DR coincides with the minimax DR.
Troush N.N., Tsekhovaya T.V.
The investigation of statistical properties of the variogram and covariance function estimators. pp. 24--29
Summary: The estimators of the variogram and covariance function of stationary stochastic process with discrete time are constructed. The first two moments of examined estimators are found and their asymptotic behavior are investigated.
Lasyi P.G., Meleshko I.N.
Application of the l-polylogarithms to an approximate solution of the third boundary value problem for Laplace equation. pp. 30--36
Summary: New formulas for approximate solution of the third boundary value problem for Laplace equation are given. The proposed formulas use l-polylogarithms.
Vasilevich N.D.
The Fuch's system on Rieman sphere with the solvable monodromy group. pp. 37--39
Summary: The linear system of the second order with the Fuch's specialities on the Rieman sphere is construct. The monodromy group is solvable.
Bondarenko A.A.
A group structure existence criterion for the set of double classes of an adele group. pp. 40--43
Summary: Let G be a connected linear algebraic group defined over an algebraic number field K. For the set of double classes GA(¥)\GA/GK Of the adele group GA An existence criterion of the natural group structure is obtained.
Golubeva O.V.
On the existence of Schmidt groups in a finite group. pp. 44--47
Summary: The following proposition is proved. Let X be a finite group and p be an odd prime divisor of order of group X. If p = 3 then let X be {L2(7), L3(3)}-free group. Suppose that -X has no 2-nilpotent Schmidt 2d-subgroups whose orders is prime to p. Then X is a solvable group with a 2-closed Hall p'-subgroup.
Shpyrko O.A.
Hall subgroups and nilpotent p-lenght of the p-soluble group. pp. 48--50
Summary: New estimates of nilpotent, p-length and p-soluble group with respect to the structure of its p-Hall subgroup are obtained.
Gaiduk S.I.
The problem, concerning transverse vibration, generated by an mechanical impact, of the rectangular viscoelastic plate. pp. 51--57
Summary: The solution of the problem about transversal oscillations of a rectangular elastoviscous plate for the case when it was subjected to a mechanical impact in the point is constructed and is grounded.
Bakhanovich S.V., Likhoded N.A.
Two-dimensional scheduling of uniform loop nests. pp. 58--63
Summary: A formal method to schedule uniform loop nests for n-dimensional to (n - 2)-dimensional spatial mapping is proposed. The method is based on a technique of two-dimensional scheduling.
Mukha V.S.
Multivariate-matrix approach to the theory of orthogonal systems of vector variable polynomials. pp. 64--68
Summary: The general theory of system of orthogonal polynomials of vector variable based on multivariate-matrix approach is developed.
Summary: A set of binary operations, called relativistic vector algebra, over scalars, vectors and tensors which are transformed by irreducible representations (0,0), (1/2,1/2), (3/2,1/2), (1/2,3/2) and (1,1) of the Lorentz group is constructed and studied. An algebraic formulation of the relativistic first-order wave equations for a particle with spin 2 is given in terms of the introduced operations,
Kisel V.V.
Extended U(l)-invariant theory of vector fields and exception of the Goldstoune field. pp. 73--77
Summary: The applicability of the generalized variants of the vector field theories is considered. The Shamaly -- Capri approach to description of a spin I particle is extended on the massless particle case. The local U(l)-invariance of the equation of motion is established. The transition from massless case to the massive one is realized through the spontaneous symmetry breaking mechanism.
Goncharenko I.A.
The influence of the reflectivity coefficients on the efficiency of generation of cascaded fibre Raman laser. pp. 78--81
Summary: The generation of cascaded fibre Raman laser with various reflection coefficients of output fibre gratings and the cavity lengths is theoretically investigated. It has been shown that the efficiency of laser generation increases with decreasing the reflection coefficient down to optimal value. In case of absolute reflection of the first Stokes wave the efficiency of Raman laser generation enhances with decreasing the cavity length. For partial reflection of the first Stokes wave the efficiency of generation of fibre Raman laser with pump power below the definite limit increases when the laser cavity length increases.
Isaevich A.V., Kozlovskii A.S., Lutkovskii V.M., Misakov P.Ya., Nazarov P.V.
Increase of an accuracy in the measurement of the elements in the atom emission spectral analysis. pp. 82--87
Summary: The results of measurements of small concentration of lead and copper, conducted on a ICP-spectrometer are represented. The influence of various modes of mathematical handling of results to an error of the measurements of the elements in water solutions is investigated. In an outcome the diminution of an error of measurements in 1.2 -- 2.0 times is reached.
Petrova E.S.
The reflection and refraction of vectorial Bessel light beams. pp. 88--92
Summary: The boundary problem for vectorial Bessel light beams on the plane interface of two isotropic media is investigated. The refraction and reflection coefficients for arbitrary polarized Bessel light beams was represented as linear combinations of the refraction and reflection coefficients of TH- and TE-polarized Bessel beams. The polarization state of reflected and refracted fields in the special case of quasicircular polarized incident Bessel beams was calculated. The condition of neglecting of the change of polarization state is found. The interference between incident and reflected beams is predicted. This effect occur only for Bessel beams of higher orders and enhanced with increasing of the conicity angle.
Khilo P.A.
Light polarization reflected from absorbing supergratings. pp. 93--96
Summary: Polarized effects under inclined falling of light wave on a supergrating are investigated while having the linear absorption in it.
Primak I.U., Tomov A.V.
On possibility of reconstruction of the refractive index profile of waveguides with leaky modes. pp. 97--101
Summary: Conditions of applicability of the WKB approximation to the leaky mode waveguides are considered. Variations of complex propagation constants of the modes due to leakage are appreciated. The possibility of the refractive index reconstruction for the waveguides of that kind is shown numerically. A technique of its refinement with allowance for leakage is developed.
Makovetskii G.I., Smolik Ch.K. †, Severin G.M.
Calculation of the phonon density states function of aluminum from temperature dependence of specific heat. pp. 102--105
Summary: The extrapolation method for solution of ill-posed problem described by the first kind Fredholm integral equation for calculating the phonon spectrum of aluminum from temperature dependence of the specific heat is used. The optimal values of minimal and maximal temperatures for the measurements of the specific heat which provide minimal error of the calculated phonon density states function were established,
Novysh B.V., Dorozhkin N.N.
On calculation of electron structure of quasi-two-dimensional systems. pp. 106--110
Summary: A new method for calculation of electron structure of quasi-two-dimensional systems (e.g., thin films) using linear augmented-Slater-type-orbital formalism is developed. It is shown that an independence of Hamiltonian and overlap matrix elements on energy increase the speed of energy band calculations for given systems.
Sheleg A.U., Iodkovskaya K.V., Kurilovich N.F.
Investigation of the influence of g-irradiation on dielectric properties of the (CH3)2NH2Al(SO4)2 • 6H2O crystal in the ferroelectric phase transition range. pp. 111--114
Summary: Measurements of the dielectric permittivity (e) and dielectric losses (tgd) of the (CH3)2NH2Al(SO4)2 • 6H2O crystal (DMAAS) in the ferroelectric phase transition range against the irradiation dose were made. It is shown that the e and tgd values decrease under g-irradiation. A significant dispersion of e in this crystal was establish from the measurement at various frequencies (0.1 kHz -- 1 Mhz).
Sukhvalo S.V., Vlasov V.V.
Temperature evolution of the magnetic characteristics of films of an alloy FeNiCo. pp. 115--118
Summary: The features of temperature changes of the magnetic characteristics of films of an alloy 14%Fe 56%Ni 30%Co in a range of temperatures 290 -- 550 K are considered. The spin-reorientation transformation close 400 K, accompanying by abnormal behaviour of a coercivity, field and dispersion of a field of an anisotropy is revealed.
Potapenko I.P., Syrtsov S.R.
Thin films of BaTiO3 in free state for infrared detectors. pp. 119--120
Summary: BaTiO3 films were prepared onto a fused-quaitz substrates by RF planar-magnetron sputtering apparatus with high-deposition rate using a target of BaTiO3 ceramic. Then films (~ 2 -- 4 µ m) separated from a substrates by special heat treatment. The pyroelectric properties of BaTiO3 films were measured.
Summary: A graph G with the vertex set V belongs to the polar class (¥, 1) if there exists a stable subset S Ì V such that the induced subgraph G(V\S) is complete k-partite (k is not fixed). Let Llr be the class of the edge intersection graphs for linear r-uniform hypergraphs and Ll(r) be the same for linear r-partite hypergraphs. The recognition problems "G Î Ll3" and "G Î Ll(3)" are both known to be NP-complete. It is proved in the paper that the graphs in Llr which belong to (¥, 1) can be characterized by a finite list of forbidden induced subgraphs. The same holds for Ll(r). An algorithm for recognizing whether G Î Llr or G Î Ll(r) (under the same assumption) with complexity O(m) is given (m is the number of edges).
Martynchik V.N.
Optimal placements of polygons. pp. 126--132
Summary: The planar placement problems for a finite set of polygons with edges parallel to the coordinate axis (orthogons) are considered. The placement objectives are the maximization of area of orthogon intersection and the minimization of area of orthogon union. The algorithms for computing optimal solutions of the problems are obtained.
Emelichev V.A., Pokhil'ko V.G.
On the stability radius of a multicriteria problem of minimizing linear forms over a set of substitutions. pp. 133--138
Summary: Lower and upper bounds for the stability radius of the Pareto set for a multicriteria problem of minimizing linear forms over a subset of the symmetric group have been obtained.