Leveraging the defined hyperbolic spinor and the recurrence relation of the Horadam sequence, a novel sequence is delineated, and its foundational equations, akin to generator function and Binet formula, are expressed through theorems.
📌 3 Maddede Bu Makale
🎯
Amaç & Hipotez:In this study, a new definition of hyperbolic spinors is being introduced through a transformation from the Horadam split quaternion, which holds significant importance in both mathematics and physics.
📊
Temel Bulgular & Veri:Subsequently, fundamental concepts such as conjugate and norm are elucidated.
💡
Sonuç & Katkı:Leveraging the defined hyperbolic spinor and the recurrence relation of the Horadam sequence, a novel sequence is delineated, and its foundational equations, akin to generator function and Binet formula, are expressed through theorems.
In this study, a new definition of hyperbolic spinors is being introduced through a transformation from the Horadam split quaternion, which holds significant importance in both mathematics and physics. Subsequently, fundamental concepts such as conjugate and norm are elucidated. Leveraging the defined hyperbolic spinor and the recurrence relation of the Horadam sequence, a novel sequence is delineated, and its foundational equations, akin to generator function and Binet formula, are expressed through theorems.
Özçevik, S. B., Dertli, A., Karaahmetoğlu, S. (2024). HYPERBOLIC HORADAM SPINORS. Journal of Universal Mathematics, Cilt: 7 Sayı: To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI" Özel Sayı, 119–127. https://doi.org/10.33773/jum.1531576
Y. Alagoz, K. H. Oral, and S. Yuce. Split quaternion matrices. Miskolc Mathematical Notes,13(2):223-232, 2012.
D. Brod. On some properties of split horadam quaternions. Acta Universitatis Sapientiae, Mathematica, 12(2):260-271, 2020.
E. Cartan. The theory of spinors. Courier Corporation, 2012.
G. Cerda-Morales. Some properties of horadam quaternions. ariv preprint ariv:1707.05918, 2017.
J. M. Cooke, M. J. Zyda, D. R. Pratt, and R. B. McGhee. Npsnet: Flight simulation dynamic modeling using quaternions. Presence: Teleoperators Virtual Environments, 1(4):404-420, 1992.
S. De Leo and G. C. Ducati. Quaternionic groups in physics. International journal of theoretical physics, 38(8):2197-2220, 1999.
I. Frenkel and M. Libine. Quaternionic analysis, representation theory and physics. Advances in Mathematics, 218(6):1806-1877, 2008.
W. R. Hamilton. Elements of quaternions. Longmans, Green, Company, 1866.
A. Ipek. On (p, q)-bonacci quaternions and their binet formulas, generating functions and certain binomial sums. Advances in Applied Cli ord Algebras, 27:1343{1351, 2017.
T. Koshy. Fibonacci and Lucas Numbers with Applications, Volume 2. John Wiley Sons, 2019.
B. K. Patel and P. K. Ray. On the properties of (p, q)-bonacci and (p, q)-lucas quaternions. Mathematical Reports, 21(71):15-25, 2019.
M. D. Vivarelli. Development of spinor descriptions of rotational mechanics from eulers rigid body displacement theorem. Celestial mechanics, 32(3):193-207, 1984.
S. Weinberg. Comments on relativistic supermultiplet theories. Physical Review, 139(3B):B597, 1965.