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Information × Registration Number 0223U005637, 0121U109525 , R & D reports Title Spectral problems and regularity properties of differential and integral operators, boundary value problems for planar structures popup.stage_title Head Derkach Volodymyr O., Доктор фізико-математичних наук Registration Date 26-12-2023 Organization Vasyl' Stus Donetsk National University popup.description2  The class of generalized boundary triplets for symmetric operators in Hilbert space has been introduced and the corresponding Weyl functions have been investigated. It is shown that the class of Weyl functions of generalized boundary triplets coincides with the class of strict non-Branlinn operator functions. The problem of implementing Nevanlinna’s function operators in the form of Weyl functions of symmetric operators in Hilbert space is solved. To do this, functional models of symmetric operators are built in Lebesgue space and in Hilbert space with a reproducing kernel. The wide classes of nonlinear elliptic equations with the nonstandardt Orlich growth and generalized nonlogarithmic conditions for coefficients are considered. For these type of equations, such qualitative properties as local continuity and Harnak inequality are established. These equations are used to describe non-linear diffusion filters, which are the most effective tools for reducing the image noise. Therefore, the obtained results can be useful in mathematical modeling of filters for image processing. The phenomenon of mutual synchronization of powerful oscillators (autogenerators) of class E, which are characterized by a high efficiency, has also been studied. Based on the results of calculations and experiments, the possibility of operating oscillators in frequency capture mode and obtaining a fixed phase difference at their outputs (loads) is shown. There were proposed and tested a new design of mutually synchronized oscillators for installation in the communication circle of a high-yield resonator, which allowed to obtain high frequency stability of oscillators. Product Description popup.authors Buryachenko Kateryna O. Hryniv Rostyslav O. Dobosevych Oles M. Kryzhanovskyi Volodymyr H. Rassokhina Yuliia V. Savchenko Mariia O. Skrypnik Ihor I. popup.nrat_date 2023-12-26 Close