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Information × Registration Number 0211U013354, 0109U000182 , R & D reports Title Direct and inverse problems on graphs, in linear non-conservative systems theory and optimization problems of control theory. popup.stage_title Head Pivovarchik Vyacheslav, Registration Date 26-12-2011 Organization South Ukrainian State Pedagogical University popup.description2 One of the objectives of these investigations is location of spectra of boundary value spectral problems and scattering problems on graphs and solving of the corresponding inverse problems. Another objective is to develop further the 'state/signal' theory and to construct canonical models for 'state/signal' linear simple conservative stationary systems with discrete time based on de Branges-Rovnyak result generalizations on Hilbert spaces with generating kernels for the case of an arbitrary maximal non-negative subspace in Krein space. The theme of investigation is description of interlacing of eigenvalues of different boundary value problems of a graph. Another theme is connected with asymptotic expansions of solutions for partial differential equations on graphs. One of the aims of the projects is investigation of location and of multiplicities of eigenvalues of boundary value problems generated by the Sturm-Liouville equation and damped string equation on a graph. Another aim of this project is development of the theory of linear stationary passive systems in the new direction 'state/signal' and to develop the theory of impedance passive systems with applications to the problem of stochastic processes realizations. The method of investigation lies in expansion of S-functions into continuous fractions to find graph Stieltjes string parameters As the result of the project we obtained general rules in eigenvalues location for spectral problems generated by the Sturm-Liouville equation and also by Stieltjes string equation. Generalizations of Krein-Gantmaher result are obtain for the case of a spectral problem on a graph which is a tree and also for a figure-of-eight graph. It is proved that the spectra of Dirichlet and Neumann problems on the graph are interlaced. Another result of the project is a constructive method of recovering parameters of a spectral problem on a graph by known spectra. In comparison with the results of M.Mihor and G.Teschl (Austria) the results of this project are more convenient due to found explicit formulae for masses and partial intervals of the Stieltjes strings. It is possible to apply the obtained results in the theory of syntheses of electrical circuits and in syntheses of quantum micro-schemes. Product Description popup.authors Волкова Марія Георгіївна Горохова Ірина Василівна Мартинюк Ольга Миколаївна Пивоварчик Вячеслав Миколайович popup.nrat_date 2020-04-02 Close