Mathematical Sciences: Minimal Discrete Energy Problems and Approximation Theory

数学科学：最小离散能量问题和逼近理论

• 批准号: 9501130
• 负责人: Edward Saff
• 金额: $ 17.1万
• 依托单位: University of South Florida
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-05-15 至 1998-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501130&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Minimal; Discrete; Energy

Saff DMS-9501130 The PI's will investigate the optimal and near optimal arrangements of N points on the surface of the unit sphere. Potential theoretic methods will be used to analyze the extremal energy when these points on the sphere interact through a power law potential. They will focus on asymptotic results for this extremal energy and aim at producing algorithms or simple formulas for points on the sphere that yield close-to-optimal energy. This research has connections with the structural analysis of large order carbon fullerenes. Approximation is the defining feature of mathematical analysis. Compact expressions of solutions of problems arising in the physical universe rarely occur. More often, the solutions must be approximated by known quantities which have desirable properties and are easily computed. This research contributes to the dual goals of understanding the special functions of analysis and discovering their approximation properties.

Saff DMS-9501130 PI将研究单位球面上N个点的最佳和接近最佳的布置。势论方法将被用来分析球面上这些点通过幂函数势相互作用时的极值能量。他们将专注于这种极端能量的渐近结果，并致力于为球面上的点产生接近最佳能量的算法或简单公式。这项研究与大阶碳富勒烯的结构分析有关。近似性是数学分析的定义特征。对物理宇宙中出现的问题的解决方案很少有简洁的表达。更常见的情况是，解必须由具有所需性质且易于计算的已知量来近似。这项研究有助于理解分析的特殊功能和发现其近似性质的双重目标。