Mathematics

Recovering singular differential pencils with a turning point

Authors: Yurko V. A.

Second-order pencils of differential equations on the half-line with turning points are considered. We establish properties of the spectrum and study the inverse spectral problem of recovering coefficients of the pencil from the spectral data.

An extension of the ordering to the set of probability measures

Authors: Rozen V. V.

A general method for extension of the ordering to the set of the probability measured. It based on the Galois connection between all such extensions and subsets of isotone mappings of the given ordered set in the real numbers. The canonical extension is defined as extension determined by the set of all isotone mappings. For canonical extension, an effective description is given and the maximal measures in convex polyhedra are found. Some applications of considered methods for decision making problems are indicated.

On regularity of self-adjoint boundary conditions

Authors: Minkin A. M., Khromov A. P.

In this paper we expound the favourable decision of Kamke's (Камке) hypothesis that self-adjoint boundary conditions are regular and we also establish an analogue of Jordan-Dirichlet theorem on uniform convergence of trigonometric Fourier series for the case of the expansions in eigen functions of self-adjoint integral operators from the certain class.

On optimal choise of interpolation spline on triangular net

Authors: Kupriyanova Y. V., Lukomskii S. F.

In this paper we find a Hermite Spline on atriangle for the approximation error of its derivatives with respect to a side of this triangle are inversely proportional to length of this side.

Rational interpolation processes on several intervals

Authors: Lukashov А. L.

It is considered the Lagrange interpolation processes such that rational functions with fixed denominators play the role of polynomials vanishing at interpolation nodes. An estimate for Lebesgue constants is obtained for the case of rational functions deviated least from zero on a given system of intervals with maximally possible number of deviation points, and when the matrix of fixed poles is contained in a compact set outside of the system of intervals. V. N. Rusak and G. Min found earlier particular case (for the case of one interval).

Siegеl disks and basins of attraction for families of analytic functions

Authors: Gumenuk P. A.

Let be a hyperbolic domain, , let ∆ be a Stolz angle at with respect to the unit disk D, and W a domain containing the point λ0 . Consider an analytic family ; consisting of analytic functions in the domain U with the following expansion , λ ∈ W, for small z. Let be the maximal domain A ⊂ U, such that 0 ∈ A and f l (A) ⊂ A, or the set {0} if there exist no such domains. We prove, that if a sequence converges to λ0 and , then the sequence of the domains converges to S as to the kernel.

Isometry groups of Lobachevskian spaces, similarity transformation groups of Euclidean spaces and Lorentzian holonomy groups

Authors: Galaev A. S.

In the present paper transitively and simply transitively acting isometry groups of Lobachevskian spaces and transitively acting similarity transformation groups of Euclidean spaces are classified. A geometrical proof of the result of L. Berard Bergery and A. Ikemakhen about the classification of weaklyirreducible not irreducible subalgebras of so(1,n+1) is given.