Generalized Triad Design Algorithms
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 s...
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| Format: | Thesis |
| Language: | en |
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2012
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| Online Access: | https://etd.uum.edu.my/2976/1/Tareq_Mohammad_Abu_Saa.pdf https://etd.uum.edu.my/2976/ |
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| _version_ | 1833436030649237504 |
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| author | Saa, Tareq Mohammad Abu |
| author_facet | Saa, Tareq Mohammad Abu |
| author_sort | Saa, Tareq Mohammad Abu |
| building | UUM Library |
| collection | Institutional Repository |
| content_provider | Universiti Utara Malaysia |
| content_source | UUM Electronic Theses |
| continent | Asia |
| country | Malaysia |
| description | 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). |
| format | Thesis |
| id | my.uum.etd-2976 |
| institution | Universiti Utara Malaysia |
| language | en |
| publishDate | 2012 |
| record_format | eprints |
| spelling | my.uum.etd-29762016-04-27T07:31:52Z https://etd.uum.edu.my/2976/ Generalized Triad Design Algorithms Saa, Tareq Mohammad Abu QA Mathematics 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). 2012 Thesis NonPeerReviewed application/pdf en https://etd.uum.edu.my/2976/1/Tareq_Mohammad_Abu_Saa.pdf Saa, Tareq Mohammad Abu (2012) Generalized Triad Design Algorithms. PhD. thesis, Universiti Utara Malaysia. |
| spellingShingle | QA Mathematics Saa, Tareq Mohammad Abu Generalized Triad Design Algorithms |
| title | Generalized Triad Design Algorithms |
| title_full | Generalized Triad Design Algorithms |
| title_fullStr | Generalized Triad Design Algorithms |
| title_full_unstemmed | Generalized Triad Design Algorithms |
| title_short | Generalized Triad Design Algorithms |
| title_sort | generalized triad design algorithms |
| topic | QA Mathematics |
| url | https://etd.uum.edu.my/2976/1/Tareq_Mohammad_Abu_Saa.pdf https://etd.uum.edu.my/2976/ |
| url_provider | http://etd.uum.edu.my/ |