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Information × Registration Number 0218U000113, 0116U004525 , R & D reports Title Inverse problems on graphs with various input data. popup.stage_title Head Pivovarchik Vyacheslav Mykolayovych, Registration Date 18-01-2018 Organization South Ukranian State Pedagogical University named after K.D. Ushynskyy popup.description2 The objects of the investigation at this stage are inverse problems generated by infinite-dimensional and finite-dimensional, i.e. differential and difference equations on star graphs. The aim of investigation on this stage is to establish connection between possible multiplicities of eigenvalues of problems on a star graph in quantum mechanics and problems which appear in description mechanical vibrations of a star graph of Stieltjes strings. Also an aim was solution of the inverse problem of finding the parameters of Stieltjes strings using the spectrum of vibrations of a star graph of Stieltjes strings damped at the central vertex. The method applied at this stage lies in use of the results on majorizing of ordered vector of multiplicities of eigenvalues finite-dimensional problem on a star graph for description of possible multiplicities of eigenvalues of an infinite-dimensional problem generated by the Sturm-Liouville equation on a star graph with infinite edges. The inverse problem on a star graph of Stieltjes strings damped at the central vertex is completely solved. Upper estimates for the ordered vector of multiplicities of eigenvalues of the Sturm-Liouville problem on a star graph with the edges of infinite lengths. The inverse problem by parts of two spectra of the Sturm-Liouville problems on a finite interval with different Robin conditions at one end and the same Regge condition at the other end is solved. A wide class of M.G. Krein's strings is described for which Barcilon's formula is true. All the obtained results are new. It is known that for a wide class of nonhomogeneous strings with one end fixed and the other one damped together with the length of the string uniquely determine the density of the string. The novelty of the results lies in using of parts of two spectra of this string with different Robin conditions at one end and the same conditions at the other end. This project is of theoretical essence. However, the results of it may be used in synthesis of electrical circuits. Product Description popup.authors Бойко О.П. Болдарєва О.М. Пивоварчик В.М. popup.nrat_date 2020-04-02 Close