http://dspace.nbuv.gov.ua:80/handle/123456789/150397 Mon, 20 Apr 2026 23:45:35 GMT 2026-04-20T23:45:35Z http://dspace.nbuv.gov.ua:80/bitstream/id/448182/ http://dspace.nbuv.gov.ua:80/handle/123456789/150397 http://dspace.nbuv.gov.ua:80/handle/123456789/156645 Jacobsthal-Lucas series and their applications Pratsiovytyi, M.; Karvatsky, D. In this paper we study the properties of positive series such that its terms are reciprocals of the elements of Jacobsthal-Lucas sequence. In particular, we consider the properties of the set of incomplete sums as well as their applications. We prove that the set of incomplete sums of this series is a nowhere dense set of positive Lebesgue measure. Also we study singular random variables of Cantor type related to Jacobsthal-Lucas sequence. Sun, 01 Jan 2017 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/156645 2017-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/156644 A note on simplicity of contact Lie algebras over GF(2) Zargeh, C. In this note we investigate the structure of contact Lie algebras when the ground field is of characteristic 2. In order to describe the simple constituent of contact Lie algebras, by using computer algebra system, GAP, we make a conjecture which says that the quotient algebra of contact Lie algebra by its Nilradical is simple and there exits an isomorphism among this constituents and Witt Lie algebras and Hamilton Lie algebras. Sun, 01 Jan 2017 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/156644 2017-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/156643 Total global neighbourhood domination Siva Rama Raju, S.V.; Nagaraja Rao, I.H. A subset D of the vertex set of a connected graph G is called a total global neighbourhood dominating set (tgnd-set) of G if and only if D is a total dominating set of G as well as GN, where GN is the neighbourhood graph of G. The total global neighbourhood domination number (tgnd-number) is the minimum cardinality of a total global neighbourhood dominating set of G and is denoted by γtgn(G). In this paper sharp bounds for γtgn are obtained. Exact values of this number for paths and cycles are presented as well. The characterization result for a subset of the vertex set of G to be a total global neighbourhood dominating set for G is given and also characterized the graphs of order n(≥3) having tgnd-numbers 2,n−1,n. Sun, 01 Jan 2017 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/156643 2017-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/156642 On locally finite groups whose cyclic subgroups are GNA-subgroups Pypka, A.A. In this paper we obtain the description of locally finite groups whose cyclic subgroups are GNA-subgroups. Sun, 01 Jan 2017 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/156642 2017-01-01T00:00:00Z