Algebra and Discrete Mathematics. - № 1 (24). - 2017http://hdl.handle.net/123456789/45612024-03-29T10:49:23Z2024-03-29T10:49:23ZJacobsthal-Lucas series and their applicationsPratsiovytyi, M.Karvatsky, D.http://hdl.handle.net/123456789/45822020-01-08T15:07:43Z2017-01-01T00:00:00ZJacobsthal-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
2017-01-01T00:00:00ZIdentities related to integer partitions and complete Bell polynomialsMihoubi, M.Belbachir, H.http://hdl.handle.net/123456789/45812020-01-08T15:07:40Z2017-01-01T00:00:00ZIdentities 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
2017-01-01T00:00:00ZCohomologies of finite abelian groupsDrozd, Yu.Plakosh, A.http://hdl.handle.net/123456789/45802020-01-08T15:07:40Z2017-01-01T00:00:00ZCohomologies 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
2017-01-01T00:00:00ZQuantum Boolean algebrasDíaz, R.http://hdl.handle.net/123456789/45792020-01-08T15:07:42Z2017-01-01T00:00:00ZQuantum 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