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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 朱樺(Huah Chu) | |
| dc.contributor.author | Yi-Ting Chang | en |
| dc.contributor.author | 張憶婷 | zh_TW |
| dc.date.accessioned | 2021-06-13T01:34:41Z | - |
| dc.date.available | 2007-07-26 | |
| dc.date.copyright | 2007-07-26 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-12 | |
| dc.identifier.citation | [1] E.R. Berlekamp, J.C. Conway, and R.K. Guy, Winning Ways, Academic Press, London, (1985), 575-606.
[2] ‥ O. Beyer, The problem of Frobenius in three variables (in Norwegian), Thesis, University of Bergen, Dept. of Mathematics, (1976). [3] H. Bresinsky, Monomial Gorenstein curves in A4 as set theoretical complete intersection, Manuscripta Math. 27 (1979), 353-358. [4] A.L. Dulmage and N.S. Mendelsohn, Gaps in the exponent set of primitive matrices, Illinois J. Math. 8 (1964), 642-656. [5] J. Herzog, Generators and relations of abelian semigroups and semigroup rings, Manuscripta Math. 3 (1970), 175-193. [6] J. Herzog and E. Kunz, DieWerthalbgruppe eines lokalen Rings der dimension 1, Sitzungsberichte der Heidelberger Akademie der Wissenschaften 2 (1971), 27-67. [7] E. Kunz, The value-semigroup of a one-dimensional Gorenstein ring, Proc. Am. Math. Soc. 25 (1970), 748-751. [8] T.H. O’Beirne, Puzzles and Paradoxes, Oxford University Press, New York and London, (1965). [9] J.L. Ram′ırez Alfons′ın, The Diophantine Frobenius Problem, Oxford University Press, New York, (2005). [10] ‥ O.J. R‥odseth, On a linear diophantine problem of Frobenius, J. Reine Angewandte Math. 301 (1978), 171-178. [11] E.S. Selmer, On the linear diophantine Problem of Frobenius, J. Reine Angewandte Math. 293/294(1) (1977), 1-17. [12] E.S. Selmer and ‥ O. Beyer, On the linear diophantine problem of Frobenius in three variables, J. Reine Angewandte Math. 301 (1978), 161-170. [13] J.J. Sylvester, Problem 7382, Educational Times 37 (1884), 26; reprinted in: Mathematical questions with their solution, Educational Times (with additional papers and solutions) 41 (1884), 21. [14] Y. Vitek, Bounds for a linear diophantine problem of Frobenius II, Can. J. Math. 28(6) (1976), 1280-1288. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30077 | - |
| dc.description.abstract | 令 $a,b,c,d$ 為一組獨立的正整數。若一個非負整數可表為 $c_1a+c_2b+c_3c+c_4d$ 的形式，其中 $c_i$ 均為非負整數，則稱它可被 $a,b,c,d$ 表示。
我們將給出在特殊情形中，不能由 $a,b,c,d$ 表出的非負整數個數 $n(a,b,c,d)$，及最大不可表的整數 $g(a,b,c,d)$。最後並討論由 $a,b,c,d$ 生成的半群對稱性。 | zh_TW |
| dc.description.abstract | Let $a,b,c,d$ be independent positive integers.
A nonnegative integer is said to be represented by $a,b,c,d$ if it can be represented as the form $c_1a+c_2b+c_3c+c_4d$, where the $c_i$'s are nonnegative integers. We will find the number $n(a,b,c,d)$ of nonnegative integers cannot be represented by $a,b,c,d$, and the number $g(a,b,c,d)$ which is the largest integer cannot be represented by $a,b,c,d$ in some special cases. Finally we discuss the symmetry property of the semigroup generated by $a,b,c,d$. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T01:34:41Z (GMT). No. of bitstreams: 1 ntu-96-R94221025-1.pdf: 491505 bytes, checksum: ea499fac48653fa328480ce7602eddd9 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | Acknowledgements i
Abstract in Chinese ii Abstract iii Contents iv List of Figures vi 1 Introduction 1 2 Results on Three Elements 5 2.1 R‥odseth’s Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Another Viewpoint on Three Elements Case . . . . . . . . . . . . . . 7 3 Results on Four Elements 15 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 n(a, b, c, d) for m = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 g(a, b, c, d) for m = 1 and n = 1, 2 . . . . . . . . . . . . . . . . . . . . 21 3.4 Symmetry for m = 1 and n = 1 . . . . . . . . . . . . . . . . . . . . . 33 3.5 Almost Arithmetic Sequences . . . . . . . . . . . . . . . . . . . . . . 40 References 45 | |
| dc.language.iso | en | |
| dc.subject | 對稱性 | zh_TW |
| dc.subject | Frobenius問題 | zh_TW |
| dc.subject | 半群 | zh_TW |
| dc.subject | semigroup | en |
| dc.subject | Frobenius problem | en |
| dc.subject | symmetry | en |
| dc.title | 四個元素的 Frobenius 問題與半群的對稱性 | zh_TW |
| dc.title | Frobenius Problem on Four Elements and Symmetry of Semigroups | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 胡守仁(Shou-jen Hu),康明昌(Ming-Chang Kang),陳榮凱(Jung-Kai Chen),陳永秋(Eng-Tjioe Tan) | |
| dc.subject.keyword | Frobenius問題,半群,對稱性, | zh_TW |
| dc.subject.keyword | Frobenius problem,semigroup,symmetry, | en |
| dc.relation.page | 46 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-07-16 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
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| ntu-96-1.pdf Restricted Access | 479.99 kB | Adobe PDF |
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