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Information × Registration Number 0219U003688, 0116U000850 , R & D reports Title Modelling and fractal analysis of dynamical systems with locally complex representation. popup.stage_title Head Turbin Anatoliy Fedorovich, Registration Date 19-01-2019 Organization National pedagogikal university named by M.P.Dragomanov popup.description2 A new parallel numerical method for solving a non-stationary Schrцdinger equation with a linear nonlocal condition and a time-dependent potential that does not commute with the stationary part of the Hamiltonian is developed. The methods and algorithms of the analysis of dynamic systems with complex local mapping were developed. Several application related mathematical models of dynamic systems were studied by the methods of operator interpolation. We studied and justified exponentially convergent methods for finding the solution of evolutionary and boundary-value and eigenvalue problems. New regularization methods and numerical solution algorithms were developed for the final value problem for an abstract differential equation of the first order with an unlimited operator coefficient. A grid method for numerical approximation of the solution to the first boundary value problem for ordinary differential equations and partial differential equations with fractional derivative of Riemann-Liouville type were developed and substantiated. A concise theory of generalized Rademacher functions as well the Walsh sequences, series and transformations have been proposed. In particular we established a series of meaningful functional and multiplicative relations for the aforementioned objects. A number of diverse applications were indicated, in particular, connected with the problems of fractal geometry and fractal analysis. The theory was applied to establish the subtle local properties of new mathematical objects associated with binary and Q_2-representation and the chain-type A_2-representations. Product Description popup.authors Біленко Валентин Іванович Василик Віталій Богданович Климчук Світлана Леонідівна Макаров Володимир Леонідович Маслова Юлія Петрівна Працьовитий Микола Вікторович Ситник Дмитро Олексійович popup.nrat_date 2020-04-02 Close