In this study, generalized k-order Fibonacci hybrid quaternion is defined. We give recurrence relation, generating function, the summation formula and some properties for these quaternions. Furthermore, matrix representation quaternions determined. The Q_k defined numbers given By means of another matrices, several identities are also obtained.

Cayley-Dickson construction produces a sequence of normed algebras over real numbers. Its consequent applications result in complex numbers , quaternions, octonions, etc. In this paper we formalize the construction and prove its basic properties. The notation and terminology used here have been introduced in the following We use the following convention: u, v, x, y, z, X, Y are sets and r, s ar...

In this present study, we intend to determine the Padovan, Perrin and Pell-Padovan dual quaternions with nonnegative negative subscripts. line purpose, construct some new properties such as; special determinant equalities, recurrence relations, matrix formulas, Binet-like generating functions, exponential summation binomial for these quaternions.

This paper presents a motion control approach with focus on robotic manipulators based screw theory and dual quaternions. The stability analysis of general quaternion controller has been capitalized to design an additional bounded twist controller. is proposed limit the maximum end-effector within desired value, while preserving accuracy achievable high-gain feedback controllers. controllers co...

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

1. Introduction. The richness of the theory of functions over the complex field makes it natural to look for a similar theory for the only other non-trivial real asso-ciative division algebra, namely the quaternions. Such a theory exists and is quite far-reaching, yet it seems to be little known. It was not developed until nearly a century after Hamilton's discovery of quaternions. Hamilton him...

This note adds three annexes to my previous paper math/9904044 Annex 1. A sufficient condition for self-adjointness Annex 2. Invariant closed operators on locally compact abelian groups Annex 3. The trace of Connes for quaternions This last item is a minor variation on the evaluation of Connes’s trace (math/9811068), which is explained here in the setting of quaternions and can be applied also ...