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Information × Registration Number 0223U001235, 0122U001844 , R & D reports Title Development of new mathematical methods for the theory of optimal solutions popup.stage_title Head Nakonechnyi Oleksandr H., Доктор фізико-математичних наук Registration Date 26-01-2023 Organization Taras Shevchenko National University of Kyiv popup.description2 Research object: systems described by boundary value problems for ordinary differential equations and partial differential equations under conditions of incomplete information, evolutionary systems with perturbations, decision-making problems under conditions of vague information, asymptotic category of Booleans and macro-uniform morphisms. The purpose of the work: development of new mathematical methods of the theory of optimal solutions. Research methods: modern methods of the theory of decision-making under conditions of uncertainty, new methods of system analysis and optimization of stochastic and deterministic systems, modern methods of group theory. A technique for guaranteed evaluation of solutions of linear systems of ordinary differential equations of the first order with periodic boundary conditions and unknown right-hand parts, which belong to some special bounded set and satisfy the appropriate compatibility condition, has been developed. For the problem of linear estimation of unknown rectangular matrices based on observations, the guaranteed root mean square error of linear operators is obtained under the assumption that the unknown matrix is a solution of a matrix linear equation with an undefined right-hand side. Homogeneous and inhomogeneous models of diffusion processes with fractional derivatives in the spatial variable and in time were considered, solutions were obtained, and numerical calculations were carried out. Constructed and substantiated approximate controls and regulators for parabolic systems with disturbances in the coefficients. The concept of maximum and minimum of fuzzy numbers with a fuzzy set of operands is developed. A structural characterization of finite Boolean selectors of groups and graphs is established.  Product Description popup.authors Ivokhin Eugene V. Ivokhin Dmytro Ye. Vavrykh Petro R. Zinko Taras P. Kapustyan Olena A. Korobko Tetyana V. Kudin Hryhoriy І. Losyeva Mariya V. Mashchenko Serhii O. Protasov Igor V. Filonenko Svitlana M. Shevchuk Yuliia M. popup.nrat_date 2023-01-26 Close