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Information × Registration Number 0222U003599, 0116U008181 , R & D reports Title Spectral analysis of operator models of mathematical physics, functional algebras on Banach spaces, and distributional algebras popup.stage_title Head Hryniv Rostyslav O., Кандидат фізико-математичних наукZahorodniuk Andrii V, д.ф.-м.н. Registration Date 03-05-2022 Organization Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine popup.description2 As a result of completing the research project, scattering problems for Schrödinger operators with generalized non-reflective potentials are investigated, generalized soliton solutions of the Korteweg-de Vries equations are constructed, a trace formula for Schrödinger operators with integrable potentials is obtained. Algebras generated by countable sequences of polynomials and composition operators on algebras of symmetric analytic functions of bounded type are studied. The continuity of composition operators on algebras of symmetric analytic functions of bounded type and the hypercyclicity of composition operators on these algebras are proved. Hilbert spaces of symmetric analytic functions on the space and algebraic bases in the space of symmetric polynomials on are investigated. The Cauchy problem for an infinite-dimensional heat equation in the space of polynomial -untradistributions of the Berling type is solved. Semi- and paratopological groups have been studied, in particular, their axioms of separation and sufficient conditions for the continuity of operations in them. The problem of detecting so-called Hirsch rings among known classes of topological rings is investigated and a positive solution of the Koch problem of locally compact monotheistic topological monoids for some partial cases is obtained. Algorithms for the image of a graph with low visual complexity have been developed and graphs with such images have been found. Estimates of visual complexity for the worst cases, at least for individual classes of graphs, and estimates of the computational complexity of finding the required images and the corresponding algorithmic problems were found.  Product Description popup.authors Lozynska Vira Ya Ravskyi Oleksandr V Cherneha Iryna V. popup.nrat_date 2022-05-03 Close