Eurasian Mathematical Journal

Construction of a discrete D-optimal design for a linear regression model with Haar basis functions

A.A. Adamov, M.B. Gabbassov, A.U. Kussebay — Tue, 30 Jun 2026 00:00:00 +0000

Parametrically linear regression models are widely used in practice to describe various types of dependencies. The goal of such experiments is to estimate the unknown parameters of the model and to verify the optimality of the chosen design points according to certain criteria.

On coincidence points of mappings on compact domains

A.V. Arutyunov, S.E. Zhukovskiy — Tue, 30 Jun 2026 00:00:00 +0000

In the paper, we study coincidence points of two mappings defined on a compact metric space. We assume that the first mapping satisfies the covering condition with a constant \(\alpha > 0\) and the second mapping satisfies the strict Lipschitz inequality with the same constant \(\alpha\). We prove that under certain continuity assumptions these two mappings have a coincidence point. An analogous result on the existence of a coincidence point and a generalized coincidence point of set-valued mappings is obtained.

Existence and uniqueness of solutions for third-kind linear Volterra integral equations

T.T. Karakeev — Tue, 30 Jun 2026 00:00:00 +0000

In this paper, there are studied third-kind linear Volterra integral equations with smooth data and the operator of multiplying by a smooth function that degenerates at the initial point of the integration interval. A theorem of existence, uniqueness, and continuity of a solution is proved. Conditions for smoothness and the degree of smoothness of a solution are obtained. Additionally, the existence and uniqueness of the solution in the \(L^p\) space are proved.

Pseudofinite unar theory with arbitrary number of semichains and antichains

A.A. Nuraly, N.D. Markhabatov, Ye.R. Baisalov — Tue, 30 Jun 2026 00:00:00 +0000

The paper focuses on constructing a pseudofinite theory of a unar with an arbitrary number of antichains and semichains and studying its model-theoretic properties. The question of elementary equivalence of unars with different numbers of antichains and semichains remains open. The obtained theory is shown to be omega-stable, strengthening the known result stating that all complete theories of unars are superstable. Prime models of this theory turn out to be omega-categorical, implying their smooth approximability.

The variational approach to time discretization of Birkhoff's equations for infinite-dimensional systems

V.M. Savchin, P.T. Trinh — Tue, 30 Jun 2026 00:00:00 +0000

Difference methods are widely used for the numerical solution of problems in mechanics and physics. When constructing discrete analogues, it is important to preserve the basic properties of the original differential problem. The main goal of this work is to discretize a system of equations of the form \(C(x,t,u)u_t + E(x,t,u_\alpha) = 0\), based on its functional — the Hamiltonian action. Necessary and sufficient conditions for potentiality with respect to a given bilinear form are obtained. The Hamiltonian action for this system is constructed and its representation in the form of Birkhoff's equations for infinite-dimensional systems is obtained. By approximating the constructed functional by its discrete analogue, a discrete-time analogue of Birkhoff's equations is obtained based on the variational principle. Theoretical results are illustrated by an example of a wave equation with axial symmetry.

On Kaiser class of unars in expanded signature

A.R. Yeshkeyev, A.R. Yarullina, M.T. Kassymetova — Tue, 30 Jun 2026 00:00:00 +0000

The present paper is connected with studying properties of Jonsson theories of a unar. The main idea is to study a structure of the signature with one unary functional symbol by expanding it with both a new constant symbol and a unary predicate symbol. We construct the semantic Jonsson quasivariety using the semantic models of enriched Jonsson primitives of unars and consider its Jonsson spectrum, divided by cosemanticness relation onto factor-set, and the obtained factor-set is divided by a new equivalence relation with regard to the Kaiser class. Additionally, we consider the notion of normal Jonsson theory and prove that the theory of all unars is normal, and obtain new results concerning components of unars and the Kaiser class of their theories.

On interpolation of local Morrey-type spaces

K.A. Bekmaganbetov, E.D. Nursultanov — Tue, 30 Jun 2026 00:00:00 +0000

In this paper, we study the interpolation properties of local Morrey-type spaces related to the interpolation method for anisotropic spaces. We define approximation local Morrey spaces \(\overline{LM}_{p,r}^{\lambda,q}\) and approximation spaces \(\widetilde{LM}_{p,r}^{\lambda,q}\), and in terms of these spaces we obtain a description of interpolation spaces for pairs of local Morrey-type spaces \(LM_{p_0,q_0}^{\lambda_0}\), \(LM_{p_1,q_1}^{\lambda_1}\) in the case \(p_0 \neq p_1\).