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Information × Registration Number 0213U008282, 0111U010460 , R & D reports Title Inverse and half-inverse problems for quantum graphs and graphs of Stieltjes strings popup.stage_title Head Pivovarchik Vyacheslav Mykolayovych, Registration Date 10-01-2014 Organization South Ukranian State Pedagogical University named after K.D. Ushynskyy popup.description2 The object of investigations was establishing methods of solving interpolation problems related to polynomial identities. The aim of this investigation was to prove that in the finite-dimensional case the analogue of the equality of two parts of the interval in half-inverse problem established by F.Gesztesy, B.Simon is equality of the numbers of masses on the parts of Stieltjes string. Another aim was to generalize M.G. Kreins and F.R. Gantmakhers results on finite-dimensional inverse problem to the case of graph. The main methods of investigation of inverse problems generated be the recurrence relations of Stieltjes strings on graphs and half-inverse problems generated by these relations are expansions of the ratio of characteristic polynomials into branching continued fractions and in solving interpolation problems by constructing Lagrange polynomials. Analysis of half-inverse problems generated by the equations of a Stieltjes string on a finite interval with Robin conditions and on graphs of different form is proceeded. A constructive method of investigation of such half-inverse problems , i.e. a method of recovering of problems data (point masses and lengths of intervals of a Stieltjes string) is proposed. It is proved that the missing eigenvalue problem (related to Suzuki's theorem) does not exist in the case of half-inverse problem generated by the Stieltjes string equations. Formulae are obtained describing a branching continued fraction related to the problem of Stieltjes string graph vibrations. All the obtained results are new. All the earlier results on half-inverse problems were devoted to the question of uniqueness of solution, not to existence of such solution. Moreover, inverse problems for Stieltjes strings on graphs were not considered before. This project is of theoretical essence. However, the results of it may be used in synthesis of electrical circuits and in design of quantum microschemes. Product Description popup.authors Мартинюк Ольга Миколаївна Пивоварчик Вячеслав Миколайотич popup.nrat_date 2020-04-02 Close