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Information × Registration Number 0222U001211, 0117U004091 , R & D reports Title Investigation of dynamical systems and evolution processes by topological, stochastic and algebraic methods popup.stage_title Head Drozd Yurii A., Доктор фізико-математичних наук Registration Date 24-01-2022 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2  The criterion of equivalence of categories of coherent sheaves over a noncommutative Noetherian scheme is obtained; it is proved that there are at least p non-isomorphic local near-rings on an elementary abelian group of order p^3; a representative type over the field of monoids or order 4 is determined and the classification of their irreducible matrix representations is obtained; the partial internal object of homomorphisms between the completed conilpotent cocategories is constructed as a tensor cocategory of the differentiation quiver, together with the coconfctor of value taking; foliated mapping class groups striped surfaces are calculated; for Morse functions on the 2-sphere the structure of the group of automorphisms of their Kronrod-Reeb graphs induced by diffeomorphisms preserving those functions is described, provided that those groups have fixed edges; for the class of Frechet MC^k-manifolds it is obtained analogues of known results on finite-dimensional manifolds, such as the theorems of existence and uniqueness of local flows of vector fields, implicit function theorem, and the theorem on invariance of the domain; for point processes arising in the Arratti flow, the boundary theorems for multiple integrals over a spatial variable are proved; the functional limit theorem for small Levi noise perturbation of a multidimensional differential equation with non-Lipschitz coefficients is established; the Wiener process in Euclidean space with a porous membrane on the hyperplane is constructed and the limit theorem for the number of membrane cross sections is proved by a discrete approximation of this process provided that the time sampling step goes to zero; the properties of the representation of real numbers by means of Denjoy's continued fractions are described Product Description popup.authors Bondarenko Vitalii M. Vlasenko Igor Yu. Dorohovtsev Andrii A. Drozd Yurii A. Eftekharinasab Kaveh A. Karvatsky Dmytro M. Lyubashenko Volodymyr V. Maksymenko Serhii I. Pilipenko Andrii Yu. Polulyakh Yevgen Portenko Мykola I. Pratsovytyi Mykola V. Raievska Iryna Yu. Raievska Maryna Yu. Ratushniak Sofiia P. Rudenko Oleksii V. Riabov Georgii V. Sysak Yaroslav P. Soroka Yuliya Yu. popup.nrat_date 2022-03-09 Close