Results 31 to 40 of about 69,814 (147)

On Bicomplex (p,q)-Fibonacci Quaternions

Mathematics
Here, we describe the bicomplex p,q-Fibonacci numbers and the bicomplex p,q-Fibonacci quaternions based on these numbers to show that bicomplex numbers are not defined the same as bicomplex quaternions.
Çağla Çelemoğlu
doaj   +2 more sources

A note on hyperbolic (p,q)-Fibonacci quaternions [PDF]

, 2020
In this paper, we introduce a new quaternion sequence called  hyperbolic (p,q)-Fibonacci  quaternions.  This new quaternion sequence includes hyperbolic Fibonacci, hyperbolic k-Fibonacci, hyperbolic  Pell, hyperbolic k-Pell, hyperbolic  Jacobsthal ...
Tülay Yaǧmur
semanticscholar   +2 more sources

Generalized commutative quaternion polynomials of the Fibonacci type [PDF]

Annales Universitatis Mariae Curie-Sklodowska. Sectio A. Mathematica, 2023
Generalized commutative quaternions is a number system which generalizes elliptic, parabolic and hyperbolic quaternions, bicomplex numbers, complex hyperbolic numbers and hyperbolic complex numbers.
A. Szynal-Liana, I. Włoch, M. Liana
semanticscholar   +2 more sources

Fibonacci–Lucas Recurrence-Indexed Quaternionic Unitaries: Channel Convergence, Clifford Proximity, and Controlled Entanglement

Mathematics
We investigate the normalized operator geometry of the mixed Fibonacci–Lucas quaternion Qn = Fn + Lni + Fn+1j + Ln+1k. Standard quaternion representations associate this sequence with single-qubit unitary channels.
Zafer Ünal, Can Doğan Vurdu
doaj   +2 more sources

A New Aspect of Dual Fibonacci Quaternions

Advances in Applied Clifford Algebras, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Salim Yüce, Fügen Torunbalcı Aydın
openaire   +5 more sources

Product Difference Fibonacci Identities Revisited: Quaternionic Generalizations of Everman and Koshy

European Journal of Pure and Applied Mathematics
In this paper, we investigate new identities involving generalized Fibonacci and Lucas sequences, as well as their associated quaternions. After establishing the fundamental properties of these generalized number sequences, we derive quaternionic ...
Bahar Demirturk, N. Topal
semanticscholar   +2 more sources

On Fibonacci Quaternions [PDF]

Advances in Applied Clifford Algebras, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sakarya Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü, Halıcı, Serpil   +1 more
openaire   +3 more sources

Pauli–Fibonacci quaternions [PDF]

Notes on Number Theory and Discrete Mathematics, 2021
The aim of this work is to consider the Pauli–Fibonacci quaternions and to present some properties involving this sequence, including the Binet’s formula and generating functions. Furthermore, the Honsberger identity, the generating function, d’Ocagne’s identity, Cassini’s identity, Catalan’s identity for these quaternions are given.
  +7 more sources

On the Solutions of Quaternion Difference Equations in Terms of Generalized Fibonacci-Type Numbers

Symmetry, 2022
The aim of this paper is to investigate the solution of the following difference equation zn+1=(pn)−1,n∈N0,N0=N∪0 where pn=a+bzn+czn−1zn with the parameters a, b, c and the initial values z−1,z0 are nonzero quaternions such that their solutions are ...
K. Gül
semanticscholar   +1 more source

On a Generalization of Incomplete Fibonacci Quaternions

The Journal of the Indian Mathematical Society, 2021
The aim of this article is to introduce a new class of quater- nions, namely, incomplete Horadam quaternions that are based on in- complete Horadam numbers which generalize the previously introduced incomplete Fibonacci and Lucas quaternions. Further, some identities including summation formulas and generating functions concerning these quaternions are
Bijan Kumar Patel, Narmada Behera
openaire   +2 more sources