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Information × Registration Number 0221U102503, 0116U003103 , R & D reports Title Investigation of models of mathematical physics, which describe the deterministic and stochastic processes in complex systems of natural sciences popup.stage_title Head Rebenko Oleksii L, д.ф.-м.н. Registration Date 04-02-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2  Object of research - systems that describe the models of mathematical physics in which processes occur due to the collective interaction of a large number of their subsystems. Such research is important both for the development of the theory of complex systems and for applied applications in models of physics, models of biological evolution, ecological models of cleaning the polluted environment, in modeling conflict situations in business, sociology, etc. Within the framework of research work the results are obtained, the most significant of which are the following. The problem of describing the interaction between clusters for an infinite system of interacting particles is solved. New equations for correlation functions of clusters are derived, their solutions are represented by contributions from forest diagrams. The resulting formula summarizes the known Kelly formula of the number of tree diagrams with a given number of vertices. Periodic and quasi-periodic solutions of Coulomb motion equations for charges in the field of fixed positive charges are found with the help of Lyapunov's central theorem. A new approach to the problem of constructing singularly perturbed perators is presented, on the basis of which the theory of constructing a self - adjoint operator for arbitrary singular drilling is developed. An original mathematical theory of the description of conflict processes in nature and society has been developed. А number of specific models of dynamic systems of conflict have been developed. The Gaussian problem of minimizing α-rice energies in the presence of external fields in a qualitatively new formulation is solved - for a (generalized) condenser, the oppositely charged plates of which intersect at a set of arbitrarily large capacity. A new alternative concept of α-Riss energy is introduced into the analysis, which is based on Riesz's law of decomposition of nuclei and resonates with the well-known definition of Danny of α-Riss energy. Product Description popup.authors Zorii Natalia V Karataieva Tetyana V Koshmanenko Volodymyr D Petrenko Sergii M Satur Oksana R Skrypnik Volodymyr I Kharchenko Nataliya V popup.nrat_date 2021-02-04 Close