Browsing by Author "Alp, Murat"
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Balancing Diophantine triples with distance 1
Alp, Murat; Irmak, Nurettin; Szalay, Laszlo (SPRINGER, 2015)For a positive real number let the Balancing distance be the distance from to the closest Balancing number. The Balancing sequence is defined by the initial values , and by the binary recurrence relation , . In this paper, ... 
Cat1polygroups and pullback cat1polygroups
Davvaz, Bijan; Alp, Murat (Iranian Mathematical Society, 2014)In this paper, we give the notions of crossed polymodule and cat1polygroup as a generalization of Loday's definition. Then, we define the pullback cat1polygroup and we obtain some results in this respect. Specially, we ... 
Crossed modules of hypergroups associated with generalized actions
Alp, Murat; Davvaz, Bijan (HACETTEPE UNIV, FAC SCI, 2016)In this article, by using the notion of generalized action, we introduce the concept of crossed module of hypergroups, in the sense of Marty, and its related structures from the light of crossed polymodules. Hypergroups ... 
CROSSED POLYMODULES AND FUNDAMENTAL RELATIONS
Alp, Murat; Davvaz, Bijan (UNIV POLITEHNICA BUCHAREST, SCI BULL, 2015)In this paper, we introduce the notion of crossed polymodule of polygroups and we give some of its properties. Our results extend the classical results of crossed modules to crossed polymodules. One of the main tools in ... 
PELLANS SEQUENCE AND ITS DIOPHANTINE TRIPLES
Irmak, Nurettin; Alp, Murat (PUBLICATIONS L INSTITUT MATHEMATIQUE MATEMATICKI, 2016)We introduce a novel fourth order linear recurrence sequence {Sn} using the two periodic binary recurrence. We call it "pellans sequence" and then we solve the system ab + 1 = Sx, ac + 1 = Sy bc + 1 = Sz where a < b < ... 
Pullback and pushout crossed polymodules
Alp, Murat; Davvaz, Bijan (INDIAN ACAD SCIENCES, 2015)In this paper, we introduce the concept of pullback and pushout crossed polymodules and we describe the construction of pullback and pushout crossed polymodules. In particular, by using the notion of fundamental relation, ... 
Reduced diophantine quadruples with the binary recurrence G(n) = AG(n1)  G(n2)
Alp, Murat; Irmak, Nurettin; Szalay, Laszlo (OVIDIUS UNIV PRESS, 2015)Given a positive integer A not equal 2. In this paper, we show that there do not exist two positive integer pairs {a, b} not equal {c, d} such that the values of ac + 1, ad + 1 and bc + 1, bd + 1 are the terms of the ... 
SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES
Irmak, Nurettin; Alp, Murat (HACETTEPE UNIV, FAC SCI, 2013)In this study, we define a generalization of Lucas sequence {p(n)}. Then we obtain Binet formula of sequence {p(n)}. Also, we investigate relationships between generalized Fibonacci and Lucas sequences. 
TRIBONACCI NUMBERS WITH INDICES IN ARITHMETIC PROGRESSION AND THEIR SUMS
Irmak, Nurettin; Alp, Murat (UNIV MISKOLC INST MATH, 2013)In this paper, we give a recurrence relation for the Tribonacci numbers with indices in aritmetics progression, {Trn+s} for 0 <= s < n We find sums of {Trn} g for arbitrary integer r via matrix methods.