Search academic texts

Information × Registration Number 0216U008304, 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 23-12-2016 Organization Zhytomyr State University named after Ivan Franko popup.description2 We studied a system of interacting particles as a model of one-dimensional gas and investigated the problem of solution of certain types of partial differential equations by analysis of monogenic functions on commutative algebras. For the first time we presented the processes described by the Goldstein-Kac telegraph equation in two -, three - and five-dimensional space. We are preparing for publication a paper where the Brownian motion is modeled by particles with Maxwell distributed random velocities changing directions at Poisson times. We investigated the structure of the orthogonal square-integrated functionals on spaces of continuous functions with a measure defined by the transformation of the Wiener measure by some multiplicative functional. For a wide class of functionals we defined the procedure of multiple stochastic integration with respect to the appropriate measure and established analogue of the Ito-Wiener decomposition. We received a solution of the problem in which we finding the maximum of product of inner radius for n non-overlapping domains, containing points of the unit circle and for ? power of inner radius of domain, containing a zero point for certain values of n and ?. We got the generalization of some classical results of Dubinin and Kuzmina for some system of points for partly non-overlapping domains and open sets. We received a generalization in the case of arbitrary connectivity domains and significant clarify with the describing of the extreme configurations for Kuzmina's inequality for inner radius of non-overlapping simply connected domains relative to points on the unit circle. We got the result in the case of a variable number of points on the radials for spaces of dimension greater than 2. We developed an analytical method for constructing approximate solutions of differential equations, which describe stationary poly-harmonic fluctuations in nonlinear systems under mono-harmonic perturbation. The method is demonstrated for nonlinear systems such as dissipative oscillator with quadratic and cubic nonlinearities and visco elastic rod with quadratic and cubic characteristics of elasticity. We obtained important results for the analysis of so-called mono-harmonic approach of non-linear stationary vibrations. Product Description popup.authors Бахтін Олександр Костянтинович Дороговцев Андрій Анатолійович Зелінська Наталія Миколаївна Михайленко Василь Васильович Михайленко Станiслав Васильович Поштарева Тетяна Вікторівна Таргонська Ірина Ігорівна Таргонський Андрій Леонідович popup.nrat_date 2020-04-02 Close