Yazar "Tan, Elif" seçeneğine göre listele

Listeleniyor 1 - 4 / 4
  • [ X ]
    Öğe
    A New Class of Leonardo Hybrid Numbers and Some Remarks on Leonardo Quaternions over Finite Fields
    (Mdpi, 2023) Tan, Elif; Savin, Diana; Yilmaz, Semih
    In this paper, we present a new class of Leonardo hybrid numbers that incorporate quantum integers into their components. This advancement presents a broader generalization of the q-Leonardo hybrid numbers. We explore some fundamental properties associated with these numbers. Moreover, we study special Leonardo quaternions over finite fields. In particular, we determine the Leonardo quaternions that are zero divisors or invertible elements in the quaternion algebra over the finite field Zp for special values of prime integer p.
  • Küçük Resim
    Öğe
    Complex Factorization By Chebysev Polynomials
    (Univ Studi Catania, Dipt Matematica, 2018) Sahin, Murat; Tan, Elif; Yilmaz, Semih
    Let {a(i)}, {b(i)} be real numbers for 0 <= i <= r - 1, and define a r-periodic sequence {v(n)} with initial conditions v(0) , v(1) and recurrences v(n) = a(t)v(n-1) vertical bar b(t)v(n-)(2) where n t (mod r) (n >= 2). In this paper, by aid of Chebyshev polynomials, we introduce a new method to obtain the complex factorization of the sequence {v(n)} so that we extend some recent results and solve some open problems. Also, we provide new results by obtaining the binomial sum for the sequence {v(n)} by using Chebyshev polynomials.
  • Küçük Resim
    Öğe
    A note on bi-periodic Fibonacci and Lucas quaternions
    (Pergamon-Elsevier Science Ltd, 2016) Tan, Elif; Yilmaz, Semih; Sahin, Murat
    Motivated by the our recent work in Tan et al., 2016, related to the bi-periodic Fibonacci quaternions, here we introduce the bi-periodic Lucas quaternions that gives the Lucas quaternions as a special case. We give the generating function and the Binet formula for these quaternions. Also, we give the relationships between bi-periodic Fibonacci quaternions and bi-periodic Lucas quaternions. (C) 2016 Elsevier Ltd. All rights reserved.
  • Küçük Resim
    Öğe
    On a new generalization of Fibonacci quaternions
    (Pergamon-Elsevier Science Ltd, 2016) Tan, Elif; Yilmaz, Semih; Sahina, Murat
    In this paper, we present a new generalization of the Fibonacci quaternions that are emerged as a generalization of the best known quaternions in the literature, such as classical Fibonacci quaternions, Pell quaternions, k-Fibonacci quaternions. We give the generating function and the Binet formula for these quaternions. By using the Billet formula, we obtain some well-known results. Also, we correct some results in [3] and [4] which have been overlooked that the quaternion multiplication is non commutative. (C) 2015 Elsevier Ltd. All rights reserved.