Mathematics

Solution of Integral Equations via Resolvents of Simplest Differential Operators

Authors: Khromov A. A.

Families of operators for approximate solution of integral equations with unbounded inverse operators and right parts of equations specified by the root-mean-square approximations are constructed.

On Uniform Convergenceof Transformationsof Fourier Serieson Multiplicative Systems

Authors: Agafonova N. Y.

Necessary and suffiecient conditions for uniform Λ-summability of Fourier – Vilenkin series of Functions from Orlicz spaces LΦ[0,1) and L1[0,1) are obtained. Some corollaries for matrices with generalized monotone coeffiecients are given.

Harmonic Analysis of Periodic at Infinity Functions from Stepanov Spaces

Authors: Strukova I. I.

We consider Stepanov spaces of functions defined on R with their values in a complex Banach space. We introduce the notions of slowly varying and periodic at infinity functions from Stepanov space. The main results of the article are concerned with harmonic analysis of periodic at infinity functions from Stepanov space. For this class of functions we introduce the notion of a generalized Fourier series; the Fourier coefficients in this case may not be constants, they are functions that are slowly varying at infinity.

The Solution of the Homogeneous Boundary Value Problem of Riemann with Infinite Index of Logarithmic Order on the Beam by a New Method

Authors: Salimov R. B., Khasanova E. N.

In this paper we consider the homogeneous Riemann boundary value problem with infinite index of logarithmic order and boundary condition on the unlimited ray. This ray goes by the positive real axis and has a vertex. We solve the problem for analytic function with the cut along the ray. The value of the function at any point of the left bank equals the product of the coefficient and the value of the function at the corresponding point of the right bank of the cut. Let the modulus of the coefficient  meet the Holder condition at each point of the ray.

On Problem of Abstract Characterization of Universal Hypergraphic Automata

Authors: Molchanov V. A., Khvorostukhina E. V.

Hypergraphic automata are automata whose state sets and sets of output symbols are endowed with algebraic structures of hypergraphs preserving by transition and exit functions. Universally attracting objects in the category of hypergraphic automata are automata Atm (H1,H2), where H1 is a hypergraph of the state set, H2 is a hypergraph of the set of output symbols and S = EndH1 × Hom(H1,H2) is a semigroup of input symbols. Such automata are called universal hypergraphic automata.

Extended Structures on Codistributions of Contact Metric Manifolds

Authors: Galaev S. V.

In the paper, the notion of an AP-manifold is introduced. Such a manifold is an almost contact metric manifold that is locally equivalent to the direct product of a contact metric manifold and an Hermitian manifold. A normal AP-manifold with a closed fundamental form is a quasi-Sasakian manifold. A quasi-Sasakian AP-manifold is called in the paper a special quasi-Sasakian manifold (SQS-manifold). A SQS-manifold is locally equivalent to the product of a Sasakian manifold and a K¨ ahlerian manifold.

To Chang Theorem. II

Authors: Antonov S. Y., Antonova A. V.

Multilinear polynomials H +(¯x, ¯y| ¯ w), H −(¯x, ¯y| ¯ w) ∈ F{X ∪ Y }, the sum of which is a polynomial H (¯x, ¯y| ¯ w) Chang (where F{X∪Y } is a free associative algebra over an arbitrary field F of characteristic not equal two, generated by a countable set X ∪ Y ) have been introduced in this paper. It has been proved that each of them is a consequence of the standard polynomial S−(¯x). In particular it has been shown that the Capelli quasi-polynomials b2m−1(¯xm, ¯y) and h2m−1(¯xm, ¯y) are also consequences of the polynomial S−m (¯x).

On Recovering Differential Pencils on a Bush-type Graph

Authors: Yurko V. A.

We study the inverse problem of spectral analysis for differential pencils on a bush-type graph, which is an arbitrary compact graph with one cycle. We pay the main attention to the most important nonlinear inverse problem of recovering coefficients of differential equations provided that the structure of the graph is known a priori. We use the standard matching conditions in the interior vertices and Dirichlet and Neumann boundary conditions in the boundary vertices.

On Solvability of One Class of Urysohn Type Nonlinear Integral Equation on the Whole Line

Authors: Khachatryan K. A., Sardaryan T. H.

In present work one class of Urysohn type nonlinear integral equation on whole line is studied. Equations observed have applications in various fields of mathematical physics. It is assumed that Hammerstein type nonlinear integral operator with a difference kernel serves local minorant in terms of M. A. Krasnoselskii for the Urysohn initial operator.

A Minimal Non-extendable Partial Semigroup

Authors: Petrikov A. O.

This article discusses partial semigroups with a finite number of elements. Any partial semigroup can be extended to a full semigroup by adding elements to it, for example, a zero semigroup, in an external semigroup way. The author of the article is interested in the question of continuation of a partial semigroup without adding any elements to it in an internal semigroup way. The aim of this work is to find an internally non-extendable partial semigroup with a minimal number of elements.

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