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Information × Registration Number 0217U007301, 0115U003027 , R & D reports Title Application of Hypercomplex Analysis to the Study Partial Differential Equations and Stochastic Differential Equations popup.stage_title Head Pogoruy Anatoliy Oleksandrovych, Registration Date 28-12-2017 Organization Zhytomyr State University named after Ivan Franko popup.description2 A new method for studying the problems of extremal decomposition of the complex plane was developed, which, in particular, allowed to significantly improving the results in known problems on maximum of product of inner radii of non-overlapping domains. An open Dubinin's problem on finding the maximum of product of inner radii of n non-ovarlapping domains containing the points of the unit circle with certain restrictions on the domain containing the point zero was solved. Also, this Dubinin's problem on n non-ovarlapping domains containing the points of the unit circle was solved for certain restrictions on the angles between the segments of the neighbouring lines. In addition, a partial solution of Dubinin's problem was obtained for n = 2, 3, 4 mutually non-overlapping domains without any restrictions. A method for solving partial differential equations with variable coefficients is described. We obtained renewal equations for the characteristic function for the density of the transition probability of a random walk of a particle with a non-constant velocity in some semi-Markov media for two-, three-, and four- dimensional spaces are obtained. The parameters of a system of particles with different interactions with collisions such as the energy of the system, the swirling effect and others are estimated. For the problem of finding the maximum of the product of inner radii of n non-overlapping symmetric domains, containing the points of the unit circle, and the degree of the inner radius of the domain, containing the point zero, for the first time a result for the degree of power more than one was obtained. Using the generalized notion of the inner radius for polycylindrical domains in multidimensional complex space, we obtain a solution the problem on product of the powers of generalized conformal radii of non-overlapping domains with poles on the boundary of a polydisk and in some more general cases. The advancement in the classical Dubinin's problem for functionals in the case of five free poles on the complex plane was obtained. In addition, problems when free poles oscillate around the corresponding rays are considered. Some interesting properties of a function harmonious in the unit disk are proved. The obtained results can be applied to various problems connected with the Bertram equation in inhomogeneous and anisotropic media. Product Description popup.authors Андрійчук Жанна Іванівна Бахтін Олександр Костянтинович Герасимчук Ілона Володимирівна Голуб Ольга Олександрівна Гусар Марія Василівна Денега Ірина Вікторівна Зелінська Наталія Миколаївна Котюк Тетяна Петрівна Поштарева Тетяна Вікторівна Римар Ольга Миколаївна Рязанов Володимир Ілліч Таргонський Андрій Леонідович popup.nrat_date 2020-04-02 Close