| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 謝欣妤 | zh_TW |
| DC.creator | Hsin-Yu Heish | en_US |
| dc.date.accessioned | 2023-12-29T07:39:07Z | |
| dc.date.available | 2023-12-29T07:39:07Z | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=110221024 | |
| 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 | 本論文將會整理離散幾何中一個有趣的領域: 等角直線組（equiangular lines)的歷史演進與發展。以1973年 Lemmens-Seidel 的文章為主體，並加入後續的進展，例如 Barg-Yu 證明了24維度之後的半正定規劃的上界，Lin-Yu 對Neumann定理的推廣, Greaves et al 對於14和16維度決定最大條數的結果。我們整理這些相關文獻，把等角直線組的故事與發展說明得更完整，並且詳細寫下相關的例子或構造。本文以Lemmens-Seidel第四節和第五節為重，第四節說明柱(pillar)是甚麼和相關定理證明，第五節討論當角度固定在arccos(1/5)時，會說明上下界會如何變化。 | zh_TW |
| dc.description.abstract | This paper dives into an intriguing realm of discrete geometry: the historical evolution and development of equiangular lines. It primarily builds upon the 1973 Lemmens-Seidel paper, incorporating subsequent advancements. For instance, Barg-Yu proved upper bounds for semidefinite programming beyond 24 dimensions, Lin-Yu extended Neumann′s theorem, and Greaves et al revealed results on determining the maximum number of lines in 14 and 16 dimensions. We′ll organize these relevant works, providing a more comprehensive narrative of the equiangular lines′ story and development, while delving into specific examples or constructions. The focus of this paper lies in Lemmens-Seidel′s fourth and fifth sections, the fourth section what a ＂pillar＂ is and proves associated theorems, while the fifth section how upper and lower bounds shift when the angle is fixed at arccos(1/5). | en_US |
| DC.subject | 等角直線 | zh_TW |
| DC.subject | Equiangular Lines | en_US |
| DC.title | 等角直線叢的研究 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | A Study on 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 |