Results 151 to 160 of about 1,605,720 (180)

Extending Mersenne Numbers to Bicomplex (p,q)-Mersenne Quaternions with Catalan Transformations

EQUATIONS
In our study we define bicomplex (p,q)- Mersenne numbers. Utilizing these numbers, we present bicomplex (p,q)- Mersenne quaternions which are a generalization of Mersenne quaternions. All these sequences have second order recurrence relations.
Engin Eser, B. Kuloǧlu, E. Özkan
semanticscholar   +1 more source

ON SOME ALGEBRAIC PROPERTIES OF THE HYPER-DUAL BICOMPLEX JACOBSTHAL QUATERNIONS

Journal of Science and Arts
In this article, we define the hyper-dual bicomplex Jacobsthal quaternions. We give some properties of these quaternions. Moreover, we investigate the Binet formula and calculate Vajda’s identity, Catalan’s identity, Cassini’s identity, d’Ocagne’s ...
C. Çimen
semanticscholar   +1 more source

Extended Generalized Fibonacci and Tribonacci Polynomials with some Properties

Sarajevo Journal of Mathematics
In this paper, we introduced the extended generalized Fibonacci polynomial sequence \{$Y_{2,n}$\} and extended generalized Tribonacci polynomial \{$Y_{3,n}$\} with arbitrary initial values and established a recursive matrix and then presented some ...
Vaishali Billore, Naresh Patel, Hemant Makwana   +2 more
semanticscholar   +1 more source

ON GAUSSIAN FUZZY LUCAS NUMBERS

Journal of Science and Arts
In the present paper, we introduce a new class of fuzzy numbers, which we will call Gaussian fuzzy Lucas numbers. We establish some fundamental properties and identities for these newly defined numbers, including the recurrence relation, Binet’s formula,
Tülay Yaǧmur
semanticscholar   +1 more source

A New Approach to k-Oresme and k-Oresme-Lucas Sequences

Symmetry
In this study, the k-Oresme and k-Oresme-Lucas sequences are defined, and some terms of these sequence are given. Then, the relations between the terms of the k-Oresme and k-Oresme-Lucas sequences are presented.
E. Özkan, H. Akkuş
semanticscholar   +1 more source

Balancing and Lucas-Balancing hybrid numbers and some identities

Journal of Information and Optimization Sciences
In this paper, we introduce Balancing and Lucas-Balancing hybrid numbers. We examine some identities of Balancing and Lucas-Balancing hybrid numbers. We give some basic definitions and properties related to them.
M. Uysal, E. Özkan
semanticscholar   +1 more source

The third order Nickel Fibonacci numbers

Logic Journal of the IGPL
Using the technique of characteristic equations and De Moivre-type identity, this article defines the third order Nickel Fibonacci sequence, the third order Nickel Lucas and a modified third order Nickel Fibonacci sequence.
S. Akbiyik
semanticscholar   +1 more source

A Note on Bivariate bi-periodic Mersenne Polynomials

PROOF
We introduce a new generalization mn(x,y), which we will call Bivariate Bi-periodic Mersenne polynomials depending on whether n is even or odd. We investigated the bivariate and biperiodic forms of Mersenne polynomials, focusing on their unique ...
B. Kuloǧlu, E. Cui, E. Özkan, J. F. Peters   +3 more
semanticscholar   +1 more source

Gaussian Quaternion Involving Leonardo Numbers

Sarajevo Journal of Mathematics
In this study, using the Leonardo numbers, we define a new type of quaternion that is called a Leonard Gaussian quaternion. We also give a negative-Leonardo Gaussian quaternion. These numbers are introduced from the set of complex numbers and quaternions.
Hasan Gökbaş
semanticscholar   +1 more source

On hyper complex numbers with higher order Pell numbers components

The Journal of Analysis, 2023
Hayrullah Özimamoğlu
semanticscholar   +1 more source