Dual quaternion theory over HGC numbers

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dc.authoridGürses, Nurten/0000-0001-8407-854X
dc.authoridSaçlı (Şentürk), Gülsüm Yeliz/0000-0002-8647-1801
dc.contributor.authorŞentürk, Gülsüm Yeliz
dc.contributor.authorGürses, Nurten
dc.date.accessioned2024-09-11T19:53:20Z
dc.date.available2024-09-11T19:53:20Z
dc.date.issued2024
dc.departmentİstanbul Gelişim Üniversitesien_US
dc.description.abstractKnowing 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.en_US
dc.description.sponsorshipIstanbul Gelisim University Scientific Research Projects Application and Research Center [DUP-210720-GYS]en_US
dc.description.sponsorshipThis study has been funded by Istanbul Gelisim University Scientific Research Projects Application and Research Center. Project number: DUP-210720-GYS.en_US
dc.identifier.doi10.47974/JDMSC-1611
dc.identifier.endpage142en_US
dc.identifier.issn0972-0529
dc.identifier.issn2169-0065
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85183836218en_US
dc.identifier.startpage117en_US
dc.identifier.urihttps://doi.org/10.47974/JDMSC-1611
dc.identifier.urihttps://hdl.handle.net/11363/8120
dc.identifier.volume27en_US
dc.identifier.wosWOS:001195203500007en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.language.isoenen_US
dc.publisherTaru Publicationsen_US
dc.relation.ispartofJournal of Discrete Mathematical Sciences & Cryptographyen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmz20240903_Gen_US
dc.subjectHyperbolic-generalized complex numberen_US
dc.subjectDual quaternionen_US
dc.subjectFibonacci numberen_US
dc.subjectLucas numberen_US
dc.subjectQ-matrixen_US
dc.titleDual quaternion theory over HGC numbersen_US
dc.typeArticleen_US

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