Dual Jacobsthal ve Dual Jacobsthal-Lucas Sedeniyonlar Üzerine

Year 2019, Volume: 12 Issue: 3, 1759 - 1766, 31.12.2019

Cennet Çimen

https://doi.org/10.18185/erzifbed.539189

Cited By: 1

Abstract

Sedeniyonlar üzerinde birleşmeli ve değişmeli olmayan 16 boyutlu bir cebirdir. Bu çalışmanın temel amacı
bilinen Jacobsthal sayıları ile ilgili sedeniyon sayıların yeni bir sınıfını sunmaktır. Rekürans ilişkilerini içeren
sedeniyon sayıların bu sınıfı için; Binet formülleri, üreteç fonksiyonlar, üstel üreteç fonksiyonlar, poisson üreteç
fonksiyonlar gibi çeşitli sonuçlar elde edildi ve aynı zamanda bu sayıların Binet formülleri yardımıyla Cassini
özdeşliği, Catalan özdeşlikleri ve d’Ocagne’s özdeşliği sunuldu.

Keywords

Sedeniyon sayılar, Jacobsthal sayılar, Dual sayılar

On the Dual Jacobsthal and Dual Jacobsthal-Lucas Sedenions

Abstract

The sedenions form a 16-dimensional non-associative and non-commutative algebra over the set of . . The
main object of this paper is to present a systematic investigation of new classes of sedenion numbers associated
with the familiar Jacobsthal numbers. The various results obtained here for these classes of sedenion numbers
include recurrence relations, Binet formula, generating function, exponentinal generating functions, poisson
generating functions and also we presented the Cassini identity, Catalan’s identities and d’Ocagne’s identity by
their Binet forms

Keywords

Sedenion numbers, Jacobsthal numbers, dual numbers

References

• Bilgici, G., Tokeser, U. and Unal, Z. (2017). “Fibonacci and Lucas Sedenions”, Journal of Integea Sequences. Vol. 20 Article 17.1.8.
• Bhupesh Chandra Chanyal et al. (2016). A new approach on electromagnetism with dual number coefficient octonion algebra, International Journal of Geometric Methods in Modern Physics, 13(9):1630013.
• Cawagas, R. E. (2004). “On the structure and zero divisors of the Cayley-Dickson sedenion algebra”, Discuss. Math. Gen. Algebra Appl., 24, 251--265.
• Cariow, A. and Cariowa, G. (2013). “An algorithm for fast multiplication of sedenions”, Inform. Process. Lett., 113, 324-331.
• Cimen, C.B. and Ipek, A. (2017). “On Jacobsthal and Jacobsthal-Lucas Octonions”, Mediterr. J. Math.,14:37.
• Cimen, C.B. and Ipek, A. (2017). “On Jacobsthal and the Jacobsthal-Lucas sedenions and several identities involving these numbers”, Mathematica Aeterna, Vol. 7, no. 4, 443-449.
• Clifford, WK. (1873). “Preliminary sketch of bi-quaternions”, Proc of London Math Soc; 4: 361–395.
• Daniilidis, K. and Bayro-Corrochano, E. (1996). “Dual quaternion synthesis of constrained robotic systems”, Proceedings of the 13th International Conference on Pattern Recognition, 1.
• Horadam, A.F. (1996). “Jacobsthal Number Representation”, The Fibonacci Quarterly; 34(1), 40-54.
• Halici, S. (2015). “On Dual Fibonacci Octonions”, Advances in Applied Clifford Algebras, 25(4):905-914.
• Imaeda, K. and Imaeda, M. (2000). “Sedenions: algebra and analysis”, Appl. Math. Comput. 115, 77-88.
• Kabadayi, H. (2016). “Homothetic motions with dual octonions in dual 8-space”, Turkish Journal of Mathematics, 40(1):90-97.
• Koltelnikov, AP. (1895). “Screw Calculus and Some of Its Applications in Geometry and Mechanics”, Kazan.(in Russian).
• Study, E. (1903). “Geometrie der Dynamen. Leipzig”, (in German).
• Ünal, Z., Tokeser, U. and Bilgici, G. (2017). “Some properties of dual fibonacci and dual lucas octonions”, Advances in Applied Clifford Algebras, Volume 27, Issue 2, pp 1907–1916.
• Yaglom, IM. (1979). “A Simple Non-Euclidean Geometry and Its Physical Basis”, New York, NY, USA: Springer-Verlag.