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Information × Registration Number 0313U005250, 0109U000186 , R & D reports Title Differential eguations and systems on standart and nonstandart domains popup.stage_title Диференціальні рівняння та системи на стандартних та нестандартних областях Head Pivovarchik Vyacheslav, Registration Date 09-01-2014 Organization South Ukranian State Pedagogical University named after K.D. Ushynskyy popup.description2 The objective of these investigations is, firstly, solution of the inverse problem, generated by the recurrence relations of a Stieltjes string by four spectra of boundary value problems. The second objective was to establish existence of a minimal dissipative system transfer function of which coincides with the given operator-function in the neighborhood of the zero. The aim - Investigation of boundary value problems generated by the Sturm-Liouville, Dirac equations and by the equations of strings and beams and by canonical systems on domains which are finite intervals, half-axes, axes, finite graphs and infinite graphs. Solution of the corresponding inverse problems of recovering the parameters using known spectra and scattering data. Methods of investigation: the main methods of investigation of the inverse problems were decompositions of the ratio of the characteristic functions of Neumann and Dirichlet problems into branching continued fractions. Another method lied in decomposition of solutions of ordinary differential equations into the unconditional basis. Establishing analogues of known results to the case of problems on graphs which are trees. In this purpose results on theory of entire functions and control theory were obtained. All the obtained results are new and are published in Ukrainian and international journals. The results of this project were used by PhD student O.V. Taystruk in working on her thesis "Spectral problems related to damped vibrations of graphs and nets". Special courses for students in mathematics and computer science. Product Description popup.authors Аров Д.З. Бойко О. П. Волкова М. Г. Горохова І. В. Кобякова Л. М. Коваль Т. В. Мартинюк О. М. Олефір О. І. Сапрікін С. М. Третьяк О. І. Урум Г. Д. popup.nrat_date 2020-04-02 Close