Mathematical Sciences: The Differential Geometry of PartialDifferential Equations

数学科学：偏微分方程的微分几何

• 批准号: 9505125
• 负责人: Robert Bryant
• 金额: $ 13.5万
• 依托单位: Duke University
• 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: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505125&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Geometry; PartialDifferential

9505125 Bryant The proposed research lies in the area of exterior differential systems. The proposer seeks to classify systems of various types which admit non-trivial conservation laws, and to develop effective algorithms for computing integrable extensions of a given system. The proposer also wishes to understand the geometric invariants of a control system and to investigate control algorithms. The main tools to be used are Cartan's method of equivalence and Cartan-Kahler theory. Exterior differential systems generalize systems of partial differential equations; their study is heavily geometric and heavily computational at the same time. Control theory is used extensively in such areas as manufacturing and robotics; the proposed research may help to create more efficient design algorithms based upon a deeper understanding of the geometric invariants involved.

9505125布莱恩特提出的研究在于外部差异系统领域。提议者试图对各种类型的系统进行分类，这些系统接受非平凡的保护法，并开发有效的算法来计算给定系统的可集成扩展。提议者还希望了解控制系统的几何不变，并研究控制算法。要使用的主要工具是卡坦的等价方法和cartan-kahler理论。 外部微分系统概括了部分微分方程的系统；他们的研究是严重的几何形状，并且同时进行了大量计算。控制理论在制造和机器人技术等领域广泛使用；拟议的研究可能有助于基于对所涉及的几何不变剂的更深入的了解，从而创建了更有效的设计算法。