各式樣方法在等角直線叢;Various Methods on Equiangular Lines

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/79278

Title:	各式樣方法在等角直線叢;Various Methods on Equiangular Lines
Authors:	俞韋亘
Contributors:	國立中央大學數學系
Keywords:	等角直線叢;半正定規劃;equiangular lines;semidefinite programming
Date:	2019-02-21
Issue Date:	2019-02-21 15:08:03 (UTC+8)
Publisher:	科技部
Abstract:	本計畫的目標是獲取在等角直線叢問題上的新穎結果。等角直線叢就是一堆線集使得兩兩之間的夾角都是同一個角度。關於這類問題在1948年就已經開始被漢傑提斯所研究。在這，我們關心的是n維歐式空間中最大的等角直線叢是多少? 最大的等角直線叢的分類問題也還知道得很少。我們想要嘗試各式各樣的方法來探討這個問題。例如用半正定規劃，賽德爾矩陣的分析，多項式方法，瑞姆斯理論還有對有界半徑的禁止子圖方法。 ;The goals of this project are to achieve new results in the equiangular line problems. A set of lines in Euclidean space is called equiangular if any pair of lines forms the same angle. The study of equiangular lines has long history in discrete geometry area. It is started in 1948 by Hanntjes. We address the problems to determine maximum size of equiangular lines. The classification of maximum equiangular lines are open for most of dimensions. We like to use several different methods to study the extremal equiangular lines problems. For instance, we like to try semidefinite programming method, analysis of Seidel matrices, polynomial methods, Ramsey Theory and forbidden subgraphs of bounded spectral radius.
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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