http://dspace.nbuv.gov.ua:80/handle/123456789/150374 2026-04-20T14:27:34Z 2026-04-20T14:27:34Z Plotkin, B. http://dspace.nbuv.gov.ua:80/handle/123456789/158441 2019-09-01T22:25:24Z 2012-01-01T00:00:00Z

Sergei Nikolaevich Chernikov. Memoirs Plotkin, B. Dedicated to the 100th anniversary of the birth of Sergei Nikolaevich Chernikov.

2012-01-01T00:00:00Z Zhykharyeva, Yu. Pratsiovytyi, M. http://dspace.nbuv.gov.ua:80/handle/123456789/152235 2019-06-09T22:26:15Z 2012-01-01T00:00:00Z

Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers Zhykharyeva, Yu.; Pratsiovytyi, M. We describe the geometry of representation of numbers belonging to (0, 1] by the positive Lüroth series, i.e., special series whose terms are reciprocal of positive integers. We establish the geometrical meaning of digits, give properties of cylinders, semicylinders and tail sets, metric relations; prove topological, metric and fractal properties of sets of numbers with restrictions on use of “digits”; show that for determination of Hausdorff-Besicovitch dimension of Borel set it is enough to use connected unions of cylindrical sets of the same rank. Some applications of L-representation to probabilistic theory of numbers are also considered.

2012-01-01T00:00:00Z Skiba, A.N. http://dspace.nbuv.gov.ua:80/handle/123456789/152234 2019-06-09T22:26:15Z 2012-01-01T00:00:00Z

On the F-hypercentre of a finite group Skiba, A.N. Our main goal here is to give a short survey of some recent results of the theory of the F-hypercentre of finite groups.

2012-01-01T00:00:00Z Monakhov, V. Trofimuk, A. http://dspace.nbuv.gov.ua:80/handle/123456789/152233 2019-06-09T22:26:13Z 2012-01-01T00:00:00Z

Invariants of finite solvable groups Monakhov, V.; Trofimuk, A. The article contains the results about invariants of solvable groups with given structure of Sylow subgroups and information about the nilpotent π-length of π-solvable groups. Open questions are formulated.

2012-01-01T00:00:00Z