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Information × Registration Number 0217U000180, 0116U004525 , R & D reports Title Inverse problems on graphs with various input data. popup.stage_title Head Pivovarchik Vyacheslav Mykolayovych, Registration Date 23-01-2017 Organization South Ukranian State Pedagogical University named after K.D. Ushynskyy popup.description2 The objects of the investigation are inverse problems generated infinite-dimensional and finite-dimensional, i.e. differential and difference equations on graph domains. These differential equations describe quantum mechanics processes while the difference equations appear in the theory of mechanical vibrations of the so-called Sturm systems and Stieltjes strings . The aim of this investigation is to develop the theory of inverse problems on finite and infinite graphs and in the case of non-unique solution description of all the solutions, description of spectral data in concrete problems, description of spectral data of boundary value problems on graphs generated by the equations of smooth and Stieltjes strings under point-wise damping. The method applied at this stage is reducing the boundary value problems with point-wise damping (viscous friction) to spectral problems for operator pencils of certain form the theory of which is developed in [V.М. Pivovarchik. On spectra of a certain class of quadratic operator pencils with one-dimensional linear part. Ukrainian mathematical journal, Vol.59 (2007), No.5, 702-717]. Existence and uniqueness are proved for solutions to functional equations which occur in quantum mechanical inverse problems by three spectra in class of sine-type functions. The class of higher order Nevanlinna functions is introduced which is used to describe the spectra of problems with multipoint conditions. A method is proposed to solve three spectra problems, i.e. a method to recover of the data (the point masses and lengths of the intervals in the case of Stieltjes strings, and the potential in case of the Sturm-Liouville equation). All the obtained results are new. The majority of the previously known results on the three spectra problem were concerned with uniqueness of the solution but not with its existence. Also, functional equations were never considered in the class of sine-type functions on graphs. 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. Волкова М.Г. Драганюк С.В. Микитенко Н.О. Пивоварчик В.М. Смирнова С.В. popup.nrat_date 2020-04-02 Close