KaydedilenlerDerginizi ekleyin

Dergiler / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2022 / Cilt: 11 - Sayı: 2

Algebraic Construction for Dual Quaternions with GCN

Gülsüm Yeliz ŞENTÜRK
Nurten GÜRSES
Salim YÜCE
Sayfa
586–593
Yayın Tarihi
2022-10-12
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

More specifically, we algebraically examine this new type dual quaternion and give several matrix representations both as a dual quaternion and asa GCN.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we explain how dual quaternion theory can extend to dual quaternions with generalized complex number (GCN) components.
📊
Temel Bulgular & Veri:In this paper, we explain how dual quaternion theory can extend to dual quaternions with generalized complex number (GCN) components.
💡
Sonuç & Katkı:More specifically, we algebraically examine this new type dual quaternion and give several matrix representations both as a dual quaternion and asa GCN.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we explain how dual quaternion theory can extend to dual quaternions with generalized complex number (GCN) components. More specifically, we algebraically examine this new type dual quaternion and give several matrix representations both as a dual quaternion and asa GCN.

🔖

Bu Makaleye Atıf Yap

ŞENTÜRK, G. Y., GÜRSES, N., YÜCE, S. (2022). Algebraic Construction for Dual Quaternions with GCN. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Cilt: 11 - Sayı: 2, 586–593. https://ajindex.com/articles/466580

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (18)

  1. W. R. Hamilton, Elements of quaternions. New York: Chelsea Pub. Com.,1969
  2. W. R. Hamilton, Lectures on quaternions. Dublin: Hodges and Smith, 1853
  3. W. R. Hamilton, “On quaternions; or on a new system of imaginaries in algebra,” The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science (3rd Series), xxv-xxxvi, 1844– 1850
  4. W. K. Clifford, “Preliminary sketch of bi-quaternions,” Proceedings of the London Mathematical Society, vol. s1–4, no. 1, pp. 381–395, 1873
  5. J. D. Jr. Edmonds, Relativistic reality: A modern view. Singapore: World Scientific, 1997
  6. Z. Ercan and S. Yüce, “On properties of the dual quaternions,” European Journal of Pure and Applied Mathematics, vol. 4, no. 2, pp. 142–146, 2011
  7. V. Majernik, “Quaternion formulation of the Galilean space-time transformation,” Acta Physica Slovaca, vol. 56, pp. 9–14, 2006
  8. V. Majernik and M. Nagy, “Quaternionic form of Maxwell’s equations with sources,” Lettere al Nuovo Cimento, vol. 16, pp. 165–169, 1976
  9. V. Majernik, “Galilean transformation expressed by the dual four-component numbers,” Acta Physica Polonica, vol. 87, no. 6, pp. 919–923, 1995
  10. Y. Yaylı and E. E. Tutuncu, “Generalized Galilean transformations and dual quaternions,” Scientia Magna, vol. 5, no. 1, pp. 94–100, 2009
  11. I. Kantor and A. Solodovnikov, Hypercomplex numbers. New York: Springer-Verlag, 1989
  12. F. Catoni, D. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti and P. Zampetti, The mathematics of Minkowski space-time and an introduction to commutative hypercomplex numbers. Birkhäuser Basel, 2008
  13. F. Catoni, R. Cannata, V. Catoni and P. Zampetti, “Two-dimensional hypercomplex numbers and related trigonometries and geometries,” Advances in Applied Clifford Algebras, vol. 14, pp. 47–68, 2004
  14. F. Catoni, R. Cannata, V. Catoni and P. Zampetti, “N-dimensional geometries generated by hypercomplex numbers,” Advances in Applied Clifford Algebras, vol. 15, no. 1, 1–25, 2005
  15. A. A. Harkin and J. B. Harkin, “Geometry of generalized complex numbers,” Mathematics Magazine, vol. 77, no. 2, pp. 118–129, 2004
  16. S. Veldsman, “Generalized complex numbers over near-fields,” Quaestiones Mathematicae, vol. 42, no. 2, pp.181–200, 2019
  17. W. K. Clifford, Mathematical papers, R. Tucker, Ed., New York: Chelsea Pub. Co., Bronx, 1968
  18. P. Fjelstad, “Extending special relativity via the perplex numbers,” American Journal of Physics, vol. 54, no. 5, pp. 416–422, 1986