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Gamaliel Cerda-Morales

Publications and source records attributed to Gamaliel Cerda-Morales.

26 records · Page 2Linked to original sources
arXiv2018

Dual Third-order Jacobsthal Quaternions

In 2016, Yüce and Torunbalcı Aydın \cite{Yuc-Tor} defined dual Fibonacci quaternions. In this paper, we defined the dual third-order Jacobsthal quaternions and dual third-order Jacobsthal-Lucas quaternions. Also, we investigated the relations between the dual third-order Jacobsthal quaternions and third-order Jacobsthal numbers. Furthermore, we gave some their quadratic properties, the summations, the Binet's formulas and Cassini-like identities for these quaternions.

math.RA↗
arXiv2017

A note on dual third order Jacobsthal vectors

Dual third order Jacobsthal and dual third order Jacobsthal-Lucas numbers are defined. In this study, we work on these dual numbers and we obtain the properties e.g. some quadratic identities, summation, norm, negadual third order Jacobsthal identities, Binet formulas and relations of them. We also define new vectors which are called dual third order Jacobsthal vectors and dual third order Jacobsthal-Lucas vectors. We give properties of these vectors to exert in geometry of dual space.

math.RA↗
arXiv2017

The Third Order Jacobsthal Octonions: Some Combinatorial Properties

Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many different ways. In addition, formulas and identities involving these number sequences have been presented. In this paper, we aim at establishing new classes of octonion numbers associated with the third order Jacobsthal and third order Jacobsthal-Lucas numbers. We introduce the third order Jacobsthal octonions and the third order Jacobsthal-Lucas octonions and give some of their properties. We derive the relations between third order Jacobsthal octonions and third order Jacobsthal-Lucas octonions.

math.RA↗
arXiv2017

On Tribonacci and Tribonacci-Lucas Quaternion Polynomials

In this paper, we introduce the Tribonacci and Tribonacci-Lucas quaternion polynomials. We obtain the Binet formulas, generating functions and exponential generating functions of these quaternions. Moreover, we give some properties and identities for the Tribonacci and Tribonacci-Lucas quaternions.

math.RA↗
arXiv2017

Some Properties of Horadam quaternions

In this paper, we consider the generalized Fibonacci quaternion which is the Horadam quaternion sequence. Then we used the Binet's formula to show some properties of the Horadam quaternion. We get some generalized identities of the Horadam number and generalized Fibonacci quuaternion.

math.RA↗
arXiv2017

On a Generalization for Tribonacci Quaternions

Let $V_{n}$ denote the third order linear recursive sequence defined by the initial values $V_{0}$, $V_{1}$ and $V_{2}$ and the recursion $V_{n}=rV_{n-1}+sV_{n-2}+tV_{n-3}$ if $n\geq 3$, where $r$, $s$, and $t$ are real constants. The $\{V_{n}\}_{n\geq0}$ are generalized Tribonacci numbers and reduce to the usual Tribonacci numbers when $r=s=t=1$ and to the $3$-bonacci numbers when $r=s=1$ and $t=0$. In this study, we introduced a quaternion sequence which has not been introduced before. We show that the new quaternion sequence that we introduced includes the previously introduced Tribonacci, Padovan, Narayana and Third order Jacobsthal quaternion sequences. We obtained the Binet formula, summation formula and the norm value for this new quaternion sequence.

math.CO↗
arXiv2017

Identities for third order Jacobsthal quaternions

In this paper we introduce the third order Jacobsthal quaternions and the third order Jacobsthal-Lucas quaternions and give some of their properties. We derive the relations between third order Jacobsthal numbers and third order Jacobsthal quaternions and we give the matrix representation of these quaternions.

math.CO↗