Mathematical Sciences: Overconstrained Mechanisms and Complex Algebraic Geometry

数学科学：过度约束机制和复杂代数几何

• 批准号: 9302021
• 负责人: Andrew Sommese
• 金额: $ 6万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302021&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Overconstrained; Mechanisms; Complex

This award supports the research of Professor A. Sommese to work on the applications of algebraic geometry to numerical analysis and problems in linkages. In particular problems arising from the theory of over-constrained mechanisms. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields, but it has applications to many areas of engineering as well. The research supported in the present proposal shows the importance of this once purely theoretical area for robotics and manufacturing.

该奖项支持 A. Sommese 教授的研究，致力于代数几何在数值分析和连杆问题中的应用。 特别是过度约束机制理论引起的问题。 这项研究属于代数几何领域，它是现代数学最古老的部分之一，但在过去十年里蓬勃发展，解决了几个世纪以来一直存在的问题。最初，它处理由最简单的方程（即多项式）在平面上定义的图形。如今，该领域不仅使用代数方法，还使用分析和拓扑方法，相反，它广泛应用于这些领域，而且也应用于许多工程领域。 本提案支持的研究表明了这个曾经纯粹的理论领域对于机器人和制造的重要性。