Saa, Tareq Mohammad Abu (2012) Generalized Triad Design Algorithms. PhD. thesis, Universiti Utara Malaysia.
Tareq_Mohammad_Abu_Saa.pdf
Restricted to Registered users only
Download (3MB) | Request a copy
Abstract
This thesis mainly focuses on the development of a triad design on v objects, TD(v), which is a way of arranging distinct triples on v objects with some properties. Previous studies on TD(v) reported its existence when v≡1 or 5 (mod 6) and TD(7) was developed by using a brute-force method. In this study, generalized and new algorithms for developing TD(v) for any v = 6n + 1 or v = 6n + 5 were developed. In general, the first part of the thesis develops two new techniques to solve the problems above. In addition, new constructions for the starter of a compatible factorization on v objects, a SCF(v), and new algorithms for a CF(v) was developed. The second part of the thesis develops three new techniques for building algorithms of the TD(v), TD(v) = CF(v) where is the completion of the CF(v). Furthermore, a starter triad design, STD(v) = SCF(v) and many remarkable theorems were proved. Additionally, a new technique for STD(v) algorithms, known as the “Generalized Interval Method - GIM” was constructed, by analyzing the pattern of the triples in the STD(v) using the intervals number and the components of triples. This technique, finally listed TD(6n + 1) and TD(6n + 5) by repeated addition of 1 (mod v) from the STD(v).
Item Type: | Thesis (PhD.) |
---|---|
Supervisor : | Ibrahim, Haslinda |
Item ID: | 2976 |
Uncontrolled Keywords: | Compatible factorization, Triad design, Starter of compatible factorization, Starter of triad design |
Subjects: | Q Science > QA Mathematics |
Divisions: | Awang Had Salleh Graduate School of Arts & Sciences |
Date Deposited: | 20 Sep 2012 06:18 |
Last Modified: | 27 Apr 2016 07:31 |
Department: | Awang Had Salleh Graduate School of Arts and Sciences |
Name: | Ibrahim, Haslinda |
URI: | https://etd.uum.edu.my/id/eprint/2976 |