http://hdl.handle.net/123456789/4561 2026-04-15T20:09:23Z http://hdl.handle.net/123456789/4582 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 (Jn+2 = 2Jn+1 + Jn, J1 = 2, J2 = 1). 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. Pratsiovytyi M. Jacobsthal-Lucas series and their applications / M.Pratsiovytyi, D.Karvatsky // Algebra and Discrete Mathematics. - 2017. - Vol. 24. - Number 1. - Рp. 169-180 2017-01-01T00:00:00Z http://hdl.handle.net/123456789/4581 Identities related to integer partitions and complete Bell polynomials Mihoubi, M.; Belbachir, H. Using the (universal) Theorem for the integer partitions and the q-binomial Theorem, we give arithmetical and combinatorial identities for the complete Bell polynomials as generating functions for the number of partitions of a given integer into k parts and the number of partitions of n into a given number of parts. Mihoubi M. Identities related to integer partitions and complete Bell polynomials / M. Mihoubi, H.Belbachir // Algebra and Discrete Mathematics. - 2017. - Vol. 24. - Number 1. - Рp. 158-168 2017-01-01T00:00:00Z http://hdl.handle.net/123456789/4580 Cohomologies of finite abelian groups Drozd, Yu.; Plakosh, A. We construct a simplified resolution for the trivial G-module Z, where G is a finite abelian group, and compare it with the standard resolution. We use it to calculate cohomologies of irreducible G-lattices and their duals. Drozd Yu. Cohomologies of finite abelian groups / Yu. Drozd, A.Plakosh // Algebra and Discrete Mathematics. - 2017. - Vol. 24. - Number 1. - Рp. 144-157 2017-01-01T00:00:00Z http://hdl.handle.net/123456789/4579 Quantum Boolean algebras Díaz, R. We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces.We study quantum Boolean algebras from the logical and the set theoretical viewpoints. Díaz R. Quantum Boolean algebras / R. Díaz // Algebra and Discrete Mathematics. - 2017. - Vol. 24. - Number 1. - Рp. 106-143 2017-01-01T00:00:00Z