Sequences generated by polynomials over integral domain
Master of Science (Mathematics), 2019
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Prince of Songkla University
2024
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th-psu.2016-194582024-06-07T06:22:09Z Sequences generated by polynomials over integral domain Veasna Kim Supawadee Prugsapitak Faculty of Science (Mathemetics and Statistics) คณะวิทยาศาสตร์ ภาควิชาคณิตศาสตร์และสถิติ Sequences (Mathematics) Master of Science (Mathematics), 2019 In the first part of this dissertation, let D be an integral domain. For sequences ā = (a1, a2,, an) and I = (i1, 2,..., in) in D" with distinct i,, call ā a (D", I)-polynomial sequence if there exists f(x) € D[x] such that f(i;) = a; foe all 1 ≤ j ≤n. Criteria for a sequence to be a (D", I)-polynomial sequence are established, and explicit structures of D/P, are determined. In the second part of this dissertation, let f(x) € Z[x], call Aff(x) = f(x + 1) − f(x) a difference polynomial of f(x). Let c = (c1, c2,..., Cn-1) in Zn-1. If there exists f(x) € Z[x] such that AF ƒ (i) = c; for all 1 ≤ i ≤ n − 1, then we call c, a difference polynomial sequence of length n - 1. Denote by AP, the set of all difference polynomial sequences. Criteria for a difference polynomial sequences are established, and explicit structures of Zn-1/AP and P-1/AP are determined. In the third part of this dissertation, let D be an integral domain, I = (i1, i2,..., in) Є D" with i; it if j k and A = (( a, a,..., a1), (a2, a, a,)... (aaa)) where a, a,..., a1, a2, az a22,..., an, an,..., ar are elements in D. If there exists f(x) in D[x] such that f(m) (i) = a for all 1 ≤ j ≤ n and 0 < m <r, where f(m) (i;) = a denotes the m(th) derivative of f(x) evaluated at the point i;, call a differential polynomial sequence of length n and order (71, 72,...,n) with respect to I. Criteria for a sequence to be a differential polynomial sequence of length n and order (r1, T2,...,n) with respect to I. We also investigate the case where r; = k for all j and (n, k) = (1, k), (2, 1), (3, 1) and (2, 2). Royal Scholarship under Her Royal Highness Princess Maha Chakri Sirindhorn Ed- ucation Project to the Kingdom of Cambodia, the Commission on Higher Education, Thailand 2024-06-07T06:22:09Z 2024-06-07T06:22:09Z 2019 Thesis http://kb.psu.ac.th/psukb/handle/2016/19458 en Attribution-NonCommercial-NoDerivs 3.0 Thailand http://creativecommons.org/licenses/by-nc-nd/3.0/th/ application/pdf Prince of Songkla University |
| institution |
Prince of Songkhla University |
| building |
Khunying Long Athakravi Sunthorn Learning Resources Center |
| continent |
Asia |
| country |
Thailand Thailand |
| content_provider |
Khunying Long Athakravi Sunthorn Learning Resources Center |
| collection |
PSU Knowledge Bank |
| language |
English |
| topic |
Sequences (Mathematics) |
| spellingShingle |
Sequences (Mathematics) Veasna Kim Sequences generated by polynomials over integral domain |
| description |
Master of Science (Mathematics), 2019 |
| author2 |
Supawadee Prugsapitak |
| author_facet |
Supawadee Prugsapitak Veasna Kim |
| format |
Theses and Dissertations |
| author |
Veasna Kim |
| author_sort |
Veasna Kim |
| title |
Sequences generated by polynomials over integral domain |
| title_short |
Sequences generated by polynomials over integral domain |
| title_full |
Sequences generated by polynomials over integral domain |
| title_fullStr |
Sequences generated by polynomials over integral domain |
| title_full_unstemmed |
Sequences generated by polynomials over integral domain |
| title_sort |
sequences generated by polynomials over integral domain |
| publisher |
Prince of Songkla University |
| publishDate |
2024 |
| url |
http://kb.psu.ac.th/psukb/handle/2016/19458 |
| _version_ |
1802995675247411200 |