http://dspace.nbuv.gov.ua:80/handle/123456789/150374 Mon, 20 Apr 2026 14:26:28 GMT 2026-04-20T14:26:28Z http://dspace.nbuv.gov.ua:80/bitstream/id/472504/ http://dspace.nbuv.gov.ua:80/handle/123456789/150374 http://dspace.nbuv.gov.ua:80/handle/123456789/158441 Sergei Nikolaevich Chernikov. Memoirs Plotkin, B. Dedicated to the 100th anniversary of the birth of Sergei Nikolaevich Chernikov. Sun, 01 Jan 2012 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/158441 2012-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/152235 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. Sun, 01 Jan 2012 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/152235 2012-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/152234 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. Sun, 01 Jan 2012 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/152234 2012-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/152233 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. Sun, 01 Jan 2012 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/152233 2012-01-01T00:00:00Z