| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 葉政叡 | zh_TW |
| DC.creator | Cheng-Jui Yeh | en_US |
| dc.date.accessioned | 2023-7-20T07:39:07Z | |
| dc.date.available | 2023-7-20T07:39:07Z | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=110221021 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.abstract | 考慮空間中過原點的若干條直線，若任兩條直線間所形成的夾角只有一種角度，我們稱該集合為等角直線叢。這樣的構造可以由空間中單位球面上的有限點集合（即球面碼）來描述。球面上的離散幾何極值問題有著相當悠久的歷史，知名的問題有吻球數問題、球面上最密堆積問題及能量最小化問題等。在這篇文章中，我們複習目前用來解以上問題的主流方法，即Delsarte的線性規劃及Bachoc-Vallentin的半正定規劃等最佳化方法，並考慮後者的對偶問題來重現歐式空間中維度介於$23$與$60$間且角度為acos(1/5)的等角直線叢的上界。 | zh_TW |
| dc.description.abstract | Equiangular lines is a set of lines through the origin in the space with a single angle between any two of them. It can be identified as a finite set of points on the sphere which is known as spherical code. The search for extreme structures of spherical codes satisfying certain conditions has a long history in discrete geometry, such as the kissing number problem, Tammes′ problem, and energy minimizing problem. In this paper, we review two effective methods for dealing with those long-standing questions, namely, Delsarte′s linear programming and Bachoc-Vallentin′s semidefinite programming, and use the dual form of the latter to reproduce the bound on equiangular lines of angle acos(1/5) in R^n where 22<n<61. | en_US |
| DC.subject | 球面碼 | zh_TW |
| DC.subject | 距離集合 | zh_TW |
| DC.subject | 等角直線叢 | zh_TW |
| DC.subject | 半正定規劃 | zh_TW |
| DC.subject | spherical codes | en_US |
| DC.subject | s-distance sets | en_US |
| DC.subject | equiangular lines | en_US |
| DC.subject | semidefinite programming | en_US |
| DC.title | 多項式方法於等角直線叢上的半正定規劃上界 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | Polynomial Method in Semidefinite Programming Bounds for Equiangular Lines | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |