Yazar "Bektaş, Özcan" için listeleme
-
Dual octonions and rigid body kinematics
Çakır, Hasan; Bektaş, Özcan; Yılmaz, Ruşen (Wiley, 2024)In this paper, we first give the basic information about octonions and present the Euclidean rotation matrix formed by an octonion in seven-dimensional Euclidean space. Next, we define and introduce the -module and dual ... -
Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space
Bektaş, Özcan; Bekiryazıcı, Zafer (Ankara University, 2022)In this paper, we give a generalization of the osculating curves to the n-dimensional Euclidean space. Based on the definition of an osculating curve in the 3 and 4 dimensional Euclidean spaces, a new type of osculating ... -
Hyper dual number matrices
Bektaş, Özcan; Çakır, Hasan (Maejo University, 2023)We study hyper dual numbers and hyper dual number matrices. Firstly, we give some basic properties of dual numbers and hyper dual numbers. Next, we investigate hyper dual number matrices using the properties of dual number ... -
De Moivre's and Euler's formulas for the matrices of octonions
Bektaş, Özcan; Yüce, Salim (Natl Acad Sciences India, 2019)The purpose of this paper is to obtain de Moivre's and Euler's formulas for the matrices of octonions, and to find the powers and the roots of these matrices. A simple method is provided to find the powers of 8x8 matrices ... -
A new approach on electromagnetism with dual number coefficient octonion algebra
Chanyal, Bhupesh Chandra; Chanyal, Sunil Kumar; Bektaş, Özcan; Yüce, Salim (World Scientific Publ Co Pte Ltd, 2016)Dual number coefficient octonion (DNCO) is one of the kind of octonion, it has 16 components with an additional dual unit epsilon. Starting with DNCO algebra, we develop the generalized electromagnetic field equations of ... -
Normal curves in n-dimensional Euclidean space
Bektaş, Özcan (Springeropen, 2018)In this paper, we give a generalization of normal curves to n-dimensional Euclidean space. Then we obtain a necessary and sufficient condition for a curve to be a normal curve in the n-dimensional Euclidean space. We ... -
On the quaternionic focal curves
In this study, a brief summary about quaternions and quaternionic curves are firstly presented. Also, the definition of focal curve is given. The focal curve of a smooth curve consists of the centers of its osculating ... -
Quaternionic osculating curves in Euclidean and semi-Euclidean space
Bektaş, Özcan; Gürses, Nurten Bayrak; Yüce, Salim (Taylor & Francis Ltd, 2016)In this study, the osculating curves in Euclidean space E-3 and E-4, well known in differential geometry, are studied through the instrumentality of quaternions. We inoculate sundry delineations for quaternionic osculating ... -
Serret-frenet formulas for octonionic curves
Bektaş, Özcan; Yüce, Salim (Soc Paranaense Matematica, 2020)In this paper, we define spatial octonionic curves (SOC) in R( )(7)and octonionic curves (OC) in R-8 by using octonions. Firstly, we determine Serret-Frenet equations, and curvatures of the SOC in R-7. Then, Serret-Frenet ... -
Special smarandache curves in R3/1
In this study, we determine TN-Smarandache curves whose position vector is composed by Frenet frame vectors of another regular curve inMinkowski 3-space R. Then, we present some characterisations of Smarandache curves and ... -
Split-type octonion matrix
Bektaş, Özcan (Wiley, 2019)The split and hyperbolic (countercomplex) octonions are eight-dimensional nonassociative algebras over the real numbers, which are in the form X = x(0)e(0) + Sigma(7)(j=1)x(j)e(j) e(m)'s (0 <= m <= 7) have different ... -
ℂ, ℍ, O-katsayılı sedeniyonların özel matris gösterimleri ve bazı özellikleri
Bektaş, Özcan (Bitlis Eren Üniversitesi, 2021)Bu makalede ilk olarak sedeniyonlar ile ilgili temel kavramlar verilmiştir. Daha sonra sedeniyonların kompleks (ℂ), kuaterniyon (ℍ) ve oktoniyon (O) katsayılı gösterimlerinden yararlanılarak farklı türden eşlenikleri tanımlanıp, ...
