Nurlan Markhabatov | The L.N. Gumilyov Eurasian National University (original) (raw)

Uploads

Papers by Nurlan Markhabatov

Herald of the Kazakh-British technical university

This article deals with families of regular graph theories. Using invariants of regular graph the... more This article deals with families of regular graph theories. Using invariants of regular graph theory, a criterion for e-minimality, a-minimality, and α-minimality of subfamilies of the family of all regular graph theories is obtained. These ranks and degrees play a similar role for families of theories with hierarchies for definable theories, such as Morley's Hierarchies for a fixed theory, although they have their own peculiarities. The rank of families of theories can be thought of as a measure of the complexity or richness of these families. Thus, by increasing rank by expanding families, we produce richer families and get families with infinite rank, which can be considered "rich enough". The ranks for families of the theory of regular graphs with finite and infinite diagonals are described. The family of all regular graph theories has infinite rank. This follows from the fact that if a language consists of m-ary symbols, m≥2, then the family of all theories of the...

The Bulletin of Irkutsk State University. Series Mathematics

In this paper, approximations of acyclic graphs are studied. It is proved that any theory of an a... more In this paper, approximations of acyclic graphs are studied. It is proved that any theory of an acyclic graph (tree) of finite diameter is pseudofinite with respect to acyclic graphs (trees), that is, any such theory is approximated by theories of finite structures (acyclic graphs, trees). It is also proved that an acyclic graph of infinite diameter with infinite number of rays is pseudofinite.

Herald of Kazakh-British technical university

The paper [11] raised the question of describing the cardinality and types of approximations for ... more The paper [11] raised the question of describing the cardinality and types of approximations for natural families of theories. In the present paper, a partial answer to this question is given, and the study of approximation and topological properties of natural classes of theories is also continued. We consider a cycle graph consisting of one cycle or, in other words, a certain number of vertices (at least 3 if the graph is simple) connected into a closed chain. It is shown that an infinite cycle graph is approximated by finite cycle graphs. Approximations of regular graphs by finite regular graphs are considered. On the other hand, approximations of acyclic regular graphs by finite regular graphs are considered. It is proved that any infinite regular graph is pseudofinite. And also, for any k, any k-regular graph is homogeneous and pseudofinite.Examples of pseudofinite 3-regular and 4-regular graphs are given.

Sibirskie Elektronnye Matematicheskie Izvestiya, 2020

We consider sentence-definable and diagram-definable subfamilies of given families of theories, c... more We consider sentence-definable and diagram-definable subfamilies of given families of theories, calculi for these subfamilies, as well dynamics and characteristics of these subfamilies with respect to rank and degree.

Theoretical & Applied Science, 2014

This article discusses a number of points related to the numerical solution of differential equat... more This article discusses a number of points related to the numerical solution of differential equations of the second order, and the study of their stability in MathCad.