Mathematics

Symmetry Axes of Planar Polynomial Differential Systems

Authors: Tlyachev V. B., Ushkho A. D., Ushkho D. S.

The notion of N-type axis of symmetry is introduced. It is proved that the vector field defined by system of the differential equations with norder polynomials in a right hand, cannot have even number of axes of symmetry N-type at n =2m,m ∈N. For n =2,3 full research of the given system on N-symmetry is carried out.

Аbout Some Boundary Problems in the Semispace for a Class of Pseudo-Differential Equations with Degeneracy

Authors: Baev A. D.

Boundary problems in the halfspace for one class of the pseudodifferential equations are considered. The coercetive a priori estimations and theorems of the existence of solutions for these problems are established.

On Multiple Completeness of the Root Functions for a Class of the Pencils of Differential Operators

Authors: Rykhlov V. S.

A polinomial pencil of ordinary differential operators of n-th order generated by a homogeneous differential expression with constant coefficients and by two-point boundary conditions of a special structure with lcondition sinzero only (1 ≤ l ≤ n−1) isconsidered in the space L 2 [0,1]. The case is studied, when the roots of the characteristic equation lieonaray coming from theorigin. Asufficient condition of m-fold completeness of the system of root functions for m ≤ n−l inthe space L 2 [0,1] isfound. Anaccuracy of obtained result is shown.

Integrability of a Partial Case of the Lowner Equation

Authors: Prokhorov D. V., Zakharov A. M.

We give a quadrature solution to the partial case of the Lowner¨ equation for the upper half-plane.

Asymptotic Properties of Polynomials pˆα,βn (x), Orthogonal on Any Sets in the Сase of Integers α and β

Authors: Nurmagomedov А. А.

Asymptotic properties of polynomials pˆα,βn (x), orthogonal with weight (1−xj)α(1+xj)β∆tj on any finite set of N points from segment [−1,1] are investigated. Namely an asymptotic formula is proved in which asymptotic behaviour of these polynomials as n tends to infinity together with N is closely related to asymptotic behaviour of the Jacobi polynomials.

Cohomology Rings of Semicubecal Sets

Authors: Lopatkin V. E.

The aim of this paper is to define the structure of the ring over the graded cohomology group of a semicubecal set with coefficients in a ring with unity.