Mathematics

Refined asymptotic formulas for eigenvalues and eigenfunctions of the Dirac system with nondifferentiable potential

Authors: Burlutskaya M. S., Kurdyumov V. P., Khromov A. P.

This paper investigates the Dirac system with the continuous potential. Asymptotic formulas for the eigenvalues (including refined) and eigenfunctions are established. As an application we obtain a theorem P. Dzhakova and B. S. Mityagin on the Riesz bases with brackets. 

The theorem on existence and uniqueness of the solution of one boundary value problem in strip for degenerate elliptic equations of higher order

Authors: Baev A. D., Buneev S. S.

Theorem on the existence and uniqueness of the solution of the boundary value problem in the strip for one degenerate elliptic equations of higher order, which degenerate on one of boundary of the strip in the third-order equation by one variable, is proved. 

One-dimensional equations of motion of a viscous incompressible fluid in flexible tubes

Authors: Gulyaev Y. P.

This paper describes a new variant of the averaging of the Navier–Stokes equations for axisymmetric flow of a viscous incompressible fluid with a minimum number of simplifying hypotheses. The complete system is spatially one-dimensional differential equations describing the dynamics of blood flow in the large arteries. 

Approximation of Bounded p-variation Periodic Functions by Generalized Abel–Poisson and Logarithmic Means

Authors: Tyuleneva A. A.
An asymptotic estimate of approximation by generalized Abel–Poisson means in p-variation metric on the class of functions with given majorant of p-variational best approximation is proved. Several other quantity results on approximation by these means are
obtained.

Uniqueness of recovering arbitrary order differential operators on noncompact spatial networks

Authors: Yurko V. A.

An inverse spectral problem is studied for arbitrary order differential operators on noncompact graphs. A uniqueness theorem of recovering potentials from the Weyl matrices is proved. 

On idempotents of algebra of Boolean matrices

Authors: Poplavskii V. B.

The structure of idempotent matrices in partial semigroups of matrices of arbitrary sizes with elements from arbitrary Boolean algebra with conjunctive and disjunctive partial multiplications is investigated. The connection of solvability of the simplest matrix equations with some kind of idempotent matrices which are called “secondary idempotents” is shown. Also we show the connection of arbitrary idempotent matrices with secondary idempotents and investigate their properties. 

Three-element problem of Carleman type for bianalitic functions in a circle

Authors: Perelman N. R., Rasulov K. M.

The article is devoted to the investigation of three-element boundary value problem of Carleman type for bianalytic functions. A constructive method for solution in a circle was found for the case when the problem was not reducible to a two-element boundary value problems without a shift. 

Frames and periodic groups of operators

Authors: Kreis S. A.

 In this paper some properties of periodic groups of operators which connected with frames theory are considered. We proof that there are no strongly continuous and uniformly bounded periodic one-parameter group of operators in Banach space which eigenvectors are cross-frame. 

Pages