De Moivre's and Euler's Formulas for the Matrices of Octonions

WOS: 000461480100011The 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 with the help of de Moivre's formula obtained from the matrices of octonions. We also show that any powers of these matrices can be found. Furthermore, we get the square, cubic and n-th roots for the matrices of octonions

Serret-Frenet Formulas for Octonionic Curves

YUCE, SALIM/0000-0002-8296-6495WOS: 000486984500003In 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 equations for the OC in R-8 are calculated with the help of Serret-Frenet equations of SOC in R-7

Some New Generalizations of the Lucas Sequence

In this paper, we investigate the generalized Lucas, the generalized complex Lucas and the generalized dual Lucas sequence using the Lucas number. Also, we investigate special cases of these sequences. Furthermore, we give recurrence relations, vectors, the golden ratio and Binet’s formula for the generalized Lucas and the generalized dual Lucas sequence

A new approach on electromagnetism with dual number coefficient octonion algebra

Chanyal, B C/0000-0003-3652-1601WOS: 000384454200001Dual 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 dyons regarding the DNCOS spaces, which has two octonionic space-times namely the octonionic internal space-time and the octonionic external space-time. Besides, the generalized four-potential components of dyons have been expressed with respect to the dual octonion form. Furthermore, we obtain the symmetrical form of Dirac-Maxwell equations, and the generalized potential wave equations for dyons in terms of the dual octonion. Finally, we conclude that dual octonion formulation is compact and simpler like octonion formulation

Gastroesophageal Reflux Disease in Children With Chronic Otitis Media With Effusion

Objective: We aimed to evaluate a possible relation between gastroesophageal reflux disease and middle ear effusion in children