# Mathematics

## On Inverse Problem for Differential Operators with Deviating Argument

Second-order functional differential operators with a constant delay are considered. Properties of their spectral characteristics are obtained, and a nonlinear inverse spectral problem is studied, which consists in constructin goperators from the irspectra. We establish the unique nessand develop a constructive procedure for solution of the inverse problem.

## Hermite Interpolation on a Simplex

In the paper, we solve the problem of polynomial interpolation and approximation functions of several variable sonann dimensional simplex in the uniform normus ingpoly nomials of the third degree.Wechoose interpolation conditions in terms of derivatives in the directions of the edges of a simplex. In the same

## Some Properties of 0/1-Simplices

Let n ∈ N, and let Q n = [0,1] n . For a nondegenerate simplex S ⊂ R n , by σS we mean the homothetic copy of S with center of homothety in the center of gravity of S and ratio of homothety σ. Put ξ(S) = min{σ > 1 : Q n ⊂ σS}, ξ n = min{ξ(S) : S ⊂ Q n }. By P we denote the interpolation projector

## Criterion for a Generalized Solution in the Class Lp for the Wave Equation to Be in the Class W1 p

In this paper we consider the question of whether a generalized solution of the wave equation belongs to different function spaces. Consideration of classical solutions imposes substantial restrictions on the initial data of the problem. But if we proceed not from differential but from integral equations, then the class of

## Non-reductive Homogeneous Spaces Not Admitting Normal Connections

The purpose of the work is the classification of three-dimensional non-reductive homogeneous spacesnot admitting normal connections, affine connections, their torsion tensors, curvature and holonomy algebras.The object of investigation arepointed-non-reductive spaces and connections on them. The basic notions,

## An Asymptotic Relation for Conformal Radii of Two Nonoverlapping Domains

We consider a family of continuously varying closed Jordan curves given by a polar equation, such that the interiors of the curves form an increasing or decreasing chain of domains.

Such chains can be described by the Löwner–Kufarev differential equation. We deduce an integral representation

## Classification of Prolonged Bi-metric Structures on Distributions of Non-zero Curvature of Sub-Riemannian Manifolds

The notion of the interior geometry of a sub-Riemannian manifold M is introduced, that is the aggregate of those manifold properties that depend only on the framing D ⊥ of the distribution D of the sub-Riemannian

manifold as well as on the parallel transport of the vectors tangent to the distribution D along the curves tangent to this distribution.The maininvariantsof the interiorgeometry of a sub-Riemannianmanifold M are

the following: the Schouten curvature tensor; the 1-form η defining the distribution D; the Lie derivative L ~

## Special Examples of Superstable Semigroups and Their Application in the Inverse Problems Theory

Special examples of superstable (quasinilpotent) semigroups and their application in the theory of linear inverse problems for evolutionary

equations are studied. The term “semigroup” means here the semigroup of bounded linear operators of class C 0 .

The standard research scheme is used. The linear inverse problem

with the final overdetermination in a Banach space for the evolution equation is considered.

A special assumption is introduced, related to the superstability of the main evolutionary semigroup.