Özkan, Engin; Uysal, Mine

In this paper, we define Mersenne, Mersenne-Lucas hybrid quaternions. We give the Binet’s formula, the generating functions, exponential generating functions and sum formula of these quaternions. We find some relations between Mersenne-Lucas hybrid quaternions, Jacobsthal hybrid quaternions, Jacobsthal-Lucas hybrid quaternions and Mersenne hybrid quaternions.

Özdin, Tufan

In [8, Theorem 1], Jain and Prasad obtained a kind of symmetry of regular rings which is interesting and useful in the theory of shorted operators (cf. [9]). We show that this symmetry property indeed holds for endo-morphism rings of Leavitt path algebras. Using this property, we analyze a (strong/weak) regular inverse of an element of the regular the endomorphism ring A of the Leavitt path algebra L:= LK (E) (viewed as a right L-module). We also introduce some partial orders on the endomorphism ring A of the Leavitt path algebra L and investigate the behavior of regular elements in A.

Eser, Engin; Kuloğlu, Bahar; Özkan, Engin

In this paper, we introduce Mersenne and Mersenne-Lucas hybrinomial quaternions and present some of their properties. Some identities are derived for these polynomials. Furthermore, we give the Binet formulas, Catalan, Cassini, d’Ocagne identity and generating and exponential generating function of these hybrinomial quaternions.

Inam, Ilker; Özkan, Engin; Özkaya, Zeynep Demirkol; Uysal, Mine

In this paper, we introduce the Pell-Eisenstein Series which are obtained by Pell numbers and they are a new class of Eisenstein-type series. First we see that they are well-defined and then we prove that the Pell-Eisenstein series satisfies some functional equations. Proofs are based on properties of Pell numbers and calculations.