Eurasian Mathematical Journal

Stability of a programme manifold of indirect control systems with different feedbacks in the presence of an external load

A.T. Assanova — 2026-09-30

The problem of constructing indirect control systems of a special type for a given manifold is considered. This problem comes down to studying the stability of the programme manifold of the system under construction with respect to a given function. The stability of a given manifold of an automatic indirect control system with rigid and tachometric feedback is investigated, taking into account external load. By constructing Lyapunov functions, sufficient conditions for the absolute stability of the programme manifold are obtained. The obtained results can be used to construct stable automatic indirect control systems of a special type.

Application of a partial-order relation to the problem of absence of non-trivial solutions to inequalities in the complex space

E.I. Galakhov — 2026-09-30

This article examines the possibility of constructing a definition of an order relation of complex numbers and its applications to solving mathematical problems. As a result, we derive a condition for the absence of weak solutions to second-order semilinear equations and inequalities, and expand the concept of Hölder's inequality in the complex space based on the definition of a partial order.

On spectral problems for nonlocal analogues of the polyharmonic operator

V.V. Karachik — 2026-09-30

In this paper, using mappings of the unit ball in \(\mathbb{R}^n\), associated with orthogonal matrices, two types of nonlocal analogues of the polyharmonic operator are introduced. Spectral problems for the Dirichlet problem and Dirichlet-type problems for these operators are studied. The eigenfunctions and eigenvalues of the problems under consideration are found. Theorems on the completeness of systems of eigenfunctions in the space \(L_2\) are proved.

Group homomorphisms of small cohomological dimension

N. Kuanyshov — 2026-09-30

We characterize group epimorphisms of cohomological dimension one under the additional assumption that their Lusternik–Schnirelmann category is one. We further establish an Eilenberg–Ganea type theorem for epimorphisms between one-relator groups. Finally, we construct examples of epimorphisms between finite groups that have cohomological dimension two but infinite Lusternik–Schnirelmann category.

Riemann–Liouville integrals in Besov spaces

E.P. Ushakova — 2026-09-30

Criteria for the validity of inequalities in weighted smoothness function spaces of Besov type with Riemann–Liouville operators of natural orders on the real axis and semiaxes are found. The obtained estimates are refined under additional conditions on weights.

New cubature formulas for Korobov spaces

S. Bassarov — 2026-09-30

In this paper we present new cubature formulas for the Korobov spaces with a smoothness parameter \(\alpha > 1\) and an estimate of the worst-case error of the cubature formulas.

The BD property of a class of high-order singular difference operators

R. Oinarov — 2026-09-30

This paper establishes a criterion for the discreteness of the spectrum and its boundedness from below for a symmetric difference operator of the \(2n\)-order with two positive coefficients.