UUM Electronic Theses and Dissertation
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Generalized Triad Design Algorithms

Saa, Tareq Mohammad Abu (2012) Generalized Triad Design Algorithms. PhD. thesis, Universiti Utara Malaysia.

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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

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