Search academic texts

Information × Registration Number 0221U107108, 0120U100222 , R & D reports Title Topological-analytical methods in complex and hypercomplex analysis and their applications popup.stage_title Head Shpakivskyi Vitalii S., Registration Date 27-12-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Constructive descriptions of three classes of mappings in some three-dimensional associative non-commutative algebra over a field of complex numbers are obtained using holomorphic functions of a complex variable. The real analytical dependence of the effective conductivity at perturbations of the form of inclusions, the periodicity structure and the conductivity of each material in the case of a periodic two-phase composite with imperfect contact at the interface is proved. The solution of the problem of the maximum product of the inner radii of two domains with respect to any 2-ray system of points of a complex plane by the degree yє[0,2] of the inner radius of the domain with respect to the origin is obtained, provided that all three domains do not intersect. Estimates of the products of generalized inner radii of mutually non-overlapping polycylindrical domains with poles at the boundary of the polydisk are established. Lower estimates of the area of the sphere image for homeomorphic mappings with respect to a nonconformal module in a multidimensional Euclidean space are established. The problem of restoring the functions of many variables from Hilbert spaces generated by the generating kernel in a uniform metric is solved. Asymptotic and pre-asymptotic estimates are obtained, which are performed with high probability for errors of restoration of functions from spaces of Sobolev type, which are related to differential operators of Jacobi type, as well as from classical classes of periodic functions of many variables of Sobolev type with common smooth weights. The properties of periodic potentials during perturbation of periodicity parameters and characteristics of the supporting hypersurface are established. In particular, it is proved that the periodic potentials of the simple and double layers for the Laplace operator depend analytically on the density function, supporting hypersurface and the periodicity parameters. Product Description popup.authors Denega Iryna Viktorivna Klishchuk Bogdan A. Pozharska Kateryna V. Pukhtaievych Roman Petrovych popup.nrat_date 2022-03-09 Close