Results 11 to 20 of about 228 (120)
Properties of Generalized Bronze Fibonacci Sequences and Their Hyperbolic Quaternions
AxiomsIn this study, we establish some properties of Bronze Fibonacci and Bronze Lucas sequences. Then we find the relationships between the roots of the characteristic equation of these sequences with these sequences.
Engin Özkan, Hakan Akkuş, Alkan Özkan
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Some Identities of Fibonacci and Lucas Quaternions by Quaternion Matrices
Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2019 In this paper, we consider one of the most knownFibonacci matrix Qand the Fibonacciquaternion matrix MQFn, where Qnis the n-th Fibonacci quaternion.In particular we define some new quaternion matrices.
Bahar Demirtürk Bitim
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Dual Fibonacci Quaternions [PDF]
Advances in Applied Clifford Algebras, 2014 In this study, we define the dual Fibonacci quaternion and the dual Lucas quternion. We derive the relations between the dual Fibonacci and the dual Lucas quaternion which connected the Fibonacci and the Lucas numbers. Furthermore, we give the Binet and Cassini formulas for these quaternions.
Nurkan, Semra Kaya, Güven İ.A.
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Unrestricted Fibonacci and Lucas quaternions
Fundamental Journal of Mathematics and Applications, 2021 Many quaternion numbers associated with Fibonacci and Lucas numbers or even their generalizations have been defined and widely discussed so far. In all the studies, the coefficients of these quaternions have been selected from consecutive terms of these numbers.
Ahmet DAŞDEMİR, Göksal BİLGİCİ
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Journal of Science and Arts, 2021 In this paper, we define and study another interesting generalization of the Fibonacci quaternions is called k-order Fibonacci quaternions. Then we obtain for Fibonacci quaternions, for Tribonacci quaternions and for Tetranacci quaternions. We give generating function, the summation formula and some properties about k-order Fibonacci quaternions. Also,
Asci, Mustafa, Aydinyuz, Suleyman
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Pauli–Leonardo quaternions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this study, we define Pauli–Leonardo quaternions by taking the coefficients of the Pauli quaternions as Leonardo numbers. We give the recurrence relation, Binet formula, generating function, exponential generating function, some special equalities ...
Zehra İşbilir +2 more
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A Fórmula de Binet e representações matriciais para os Quaternions Complexos de Fibonacci
Revista Thema, 2018 Este trabalho investiga a complexificação do modelo de Fibonacci através do estudo sobre os Quaternions. Assim, são apresentadas as definições para os Quaternions de Fibonacci tanto na forma real como complexa.
Rannyelly Rodrigues de Oliveira +1 more
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On Bicomplex (p,q)-Fibonacci Quaternions
MathematicsHere, 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
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More Identities for Fibonacci and Lucas quaternions [PDF]
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2019 Summary: In this paper, we define the associate matrix as \[ F= \left( \begin{matrix} 1+i+2j+3k & i+j+2k \\ i+j+2k & 1+j+k \end{matrix} \right). \] By the means of the matrix \(F\), we give several identities about Fibonacci and Lucas quaternions by matrix methods.
Irmak, Nurettin
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Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2015 In this paper, we define the k-Fibonacci and the k-Lucas quaternions. We investigate the generating functions and Binet formulas for these quaternions. In addition, we derive some sums formulas and identities such as Cassini’s identity.
Ramírez José L.
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