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Information × Registration Number 0219U000513, 0116U002529 , R & D reports Title Development of new mathematical methods of system analysis and optimal solutions theory and ther applications popup.stage_title Head Nakonechnyi Oleksandr Grygorovych, Registration Date 04-02-2019 Organization Taras Shevchenko Kiev University popup.description2 Object of research: systems of equations of different types, stochastic equations, boundary value problems, flows in transport networks, pseudo transformations by Moore-Penrose, uncertainty, service networks, dynamic systems, random processes, balleans. Purpose: solving of new problems of system analysis of processes, described by equations with fuzzy or stochastic parameters, tasks of information grouping; study of stationary regimes for multidimensional controlled stochastic systems; optimization study on groups and graphs using the concept of ballean. Methods of research: modern methods of decision making theory under uncertainty, optimal control, forecasting, new methods of system analysis and optimization of stochastic and deterministic systems, modern methods of combinatorial optimization on groups and graphs. The mathematical methods of analysis and the theory of optimal solutions for systems described by models with fuzzy or stochastic parameters are developed. New methods of solving decision-making tasks with fuzzy structure are developed. New optimal control problems for the systems with distributed parameters are investigated. The forecasting process methods for dynamic of population under uncertainty are developed. New mathematical methods of clustering, classification and pattern recognition are developed. The expert system prototype that can manage the model of creation and improvement of decision support means for analyzing information flow in social networks is developed. The algorithms of optimal resource control for modern telecommunication networks are constructed. We investigated new classes of controlled Markov and semi-Markov processes, which consider the heterogeneity of information processing and explosive character of intensity of information flows. Under nonclassical assumptions, we constructed on-line algorithms for estimating the parameters, which have the smallest deviation norm from gravitational points for dynamic systems with perturbation. The optimal partition of groups and graphs into large and thick subset is constructed. A subset of balleans in terms of ultracompanions is classified. We found the conditions that guarantee a weak convergence of random processes with immigration to stationary processes. We carried out asymptotic analysis of stochastic differential equation solutions in Hilbert spaces. Product Description popup.authors Івохін Є.В. Іксанов О.М. Григор'єва Н.М. Доценко С.І. Зінько Т.П. Капустян О.А. Коробко Т.В. Лебєдєв Є.О. Лосєва М.В. Лукович О.В. Нікітін А.В. Назарага І.М. Пашко А.О. Подлипенко Ю.К. Пономарьов В.Д. Протасов І.В. Протасова К.Д. Самойленко І.В. Усар І.Я. Шестаков С.С. popup.nrat_date 2020-04-02 Close