Bazı kuaterniyon dizileri ve kuaterniyon polinomlarının kökleri
Yükleniyor...
Dosyalar
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Kırıkkale Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Kuaterniyonlar matematiğin çeşitli alanlarında görülen temel bir konudur. Hem teorik matematik hem de uygulamalı matematikte birçok uygulaması bulunmaktadır. Bileşenleri çeşitli sayı dizilerinden oluşan kuaterniyonlar da birçok araştırmacı tarafından ilginç bulunmuştur. Bu tip diziler kuaterniyon dizileri olarak adlandırılır. Çalışılan bu dizilerin bileşenlerinin karakteristik polinomları genellikle ikinci derecedendir. Bu tezde ilk olarak karakteristik polinomunun derecesi üç olan Tribonacci ve Tribonacci-Lucas kuaterniyon dizileri üzerinde çalışılmış ve bazı özdeşlikler elde edilmiştir. Sonrasında karakteristik polinomlarının derecesi iki olan dizilerin kuantum genelleştirilmesi verilerek elde edilen dizilerle de kuantum kuaterniyon dizileri elde edilmiştir. Ayrıca kuantum kuaterniyon polinomları tanımlanmış ve çeşitli özellikleri incelenmiştir. Bazı özel kuaterniyon dizileri için de zaman evolüsyonu ve dönme uygulamaları verilmiştir. Son olarak ise bazı yeni iki değişkenli kuadratik kuaterniyon polinom denklemleri için Horadam kuaterniyon köklerinin kapsamlı bir analizi sunulmuştur.
Quaternions are fundamental objects of various parts of mathematics. They have applications in both theoretical and applied mathematics. Quaternions whose components are from special number sequences were also found interesting by many authors. These types of sequences are called as quaternion sequences. The characteristic polynomials of the components of these studied sequences are generally second order. In this thesis firstly Tribonacci and Tribonacci-Lucas quaternion sequences whose characteristic polynomials are third order were studied and some identities were obtained. Next, quantum quaternion sequences were obtained by the quantum generalization of the sequences whose characteristic polynomials are second degree. Also quantum quaternion polynomials were defined and several properties were investigated. Time evolution and rotation applications were given for some special quaternion sequences. Finally, a comprehensive analysis of Horadam quaternion roots for some new bivariate quadratic quaternion polynomial equations was presented.
Quaternions are fundamental objects of various parts of mathematics. They have applications in both theoretical and applied mathematics. Quaternions whose components are from special number sequences were also found interesting by many authors. These types of sequences are called as quaternion sequences. The characteristic polynomials of the components of these studied sequences are generally second order. In this thesis firstly Tribonacci and Tribonacci-Lucas quaternion sequences whose characteristic polynomials are third order were studied and some identities were obtained. Next, quantum quaternion sequences were obtained by the quantum generalization of the sequences whose characteristic polynomials are second degree. Also quantum quaternion polynomials were defined and several properties were investigated. Time evolution and rotation applications were given for some special quaternion sequences. Finally, a comprehensive analysis of Horadam quaternion roots for some new bivariate quadratic quaternion polynomial equations was presented.
Açıklama
Anahtar Kelimeler
Matematik, Mathematics, , , , , , ,
