| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 林軒宇 | zh_TW |
| DC.creator | Xuan-Yu Lin | en_US |
| dc.date.accessioned | 2020-10-20T07:39:07Z | |
| dc.date.available | 2020-10-20T07:39:07Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=107221013 | |
| 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 | 在此論文中，首先先介紹二距離集合的定義，以及相關的文獻探討。之後介紹二個計算最大二距離集合個數的方法，線性規劃和半正定規劃。以及列出在 3 和 4 維中，若固定兩個內積值，去找此集合上界為整數的構造，與計算這些構造的最小能量是否為現在找出來的最小的解。然後用線性規劃證明當內積值為 −1、0，最大二距離集合的上限為 2n。最後列出 3 維中，特殊角的構造和 3 維二距離集合個數為 5 個點和 6 個點的所有構造。 | zh_TW |
| dc.description.abstract | In this thesis, we first introduce the definition of the two-distance set and the related literature discussion. Second, two methods for calculating the maximum two-distance set
are introduced, graph representation, linear programming and semidefinite programming method. Third, we try to find the structures if the upper bound of such two-distance set are integer, and check whether it is an energy minimization configuration. Fourth, when the inner product values are −1 and 0, using linear programming to prove that, the maximum two-distance set is 2n. Finally, the constructions of two-distance set of the special angles and the cardinality of two-distance set with 5 points and 6 points are listed in 3-dimensions. | en_US |
| DC.subject | 二距離集合 | zh_TW |
| DC.subject | 球面二距離集合 | zh_TW |
| DC.subject | Two-distance set | en_US |
| DC.subject | Spherical two-distance set | en_US |
| DC.title | 歐式空間二距離集合之探討 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | A study of two-distance set in Euclidean space | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |