Dual quaternion theory over HGC numbers

SAÇLI G. Y., GÜRSES N.

Journal of Discrete Mathematical Sciences and Cryptography, cilt.27, sa.1, ss.117-142, 2024 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.47974/jdmsc-1611
  • Dergi Adı: Journal of Discrete Mathematical Sciences and Cryptography
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.117-142
  • Anahtar Kelimeler: Dual quaternion, Fibonacci number, Hyperbolic-generalized complex number, Lucas number, Q-matrix
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

Knowing the applications of quaternions in various fields, such as robotics, navigation, computer visualization and animation, in this study, we give the theory of dual quaternions considering Hyperbolic-Generalized Complex (HGC) numbers as coefficients via generalized complex and hyperbolic numbers. We account for how HGC number theory can extend dual quaternions to HGC dual quaternions. Some related theoretical results with HGC Fibonacci/Lucas numbers are established, including their dual quaternions. Given HGC Fibonacci/Lucas numbers, their special matrix correspondences have been identified and these are carried out to HGC Fibonacci/Lucas dual quaternions. Furthermore, we provide a more accurate way to quickly calculate HGC Fibonacci numbers and associate this with HGC generalized Fibonacci numbers. For implementation, we produce an algorithm in Maple. Lastly, we put the theory into practice.