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Information × Registration Number 0224U002491, 0121U108117 , R & D reports Title The Research of mathematical models with relations of algebraic and topological types popup.stage_title Head Lukashova Tetiana D., Кандидат фізико-математичних наук Registration Date 16-02-2024 Organization Sumy State Pedagogical University named after A. S. Makarenko popup.description2  The authors of the project have enhanced research methods for groups with restrictions on its generalized norms. New methods have been developed in the theory of nonlinear oscillations, exploring the solvability conditions for weakly perturbed integro-dynamic systems with a degenerate kernel on the time scale, investigating the topological and fractal properties of sets of incomplete sums of absolutely convergent numerical series and distributions of random variables represented by incomplete sums with random elements. The obtained results are as follows: a constructive description of finite 2-groups with a cyclic center and the metacyclic non-Dedekind norm of Abelian non-cyclic subgroups was obtained; a characterization of infinite periodic locally nilpotent with a non-Dedekind norm of decomposable subgroups was obtained; a criterion for the solvability of linear weakly perturbed by a small parameter integro-dynamic systems with a degenerate kernel on the time scale was established. Іt was proved that the set of incomplete sums of an absolutely convergent numerical series, can be a perfect set, a finite union of intervals, or a nowhere dense set; the Lebesgue structure of the distribution of random variables represented by incomplete sums with random elements that satisfy certain conditions was investigated. The results of the study are obtained for the first time in the field of mathematical research. They are reliable, rigorously substantiated, meet international standards, and can be utilized by mathematicians engaged in the investigation of complex mathematical models with relationships of algebraic, functional, topological, and stochastic types both in Ukraine and abroad. Product Description popup.authors Drushliak Maryna H. Lukashova Tetiana D. Khvorostina Yurii V. popup.nrat_date 2024-02-16 Close