Computational Equipment for Approximation Theory, Control Theory, Graph Theory

近似论、控制论、图论的计算设备

• 批准号: 0215442
• 负责人: Douglas Hardin
• 金额: $ 4万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-15 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0215442&HistoricalAwards=false
• 关键词: Computational; Equipment; Approximation; Theory; Control

NSF Proposal DMS-0215442PIs: Hardin, Ellingham, Horn, Saff, and Schumaker ABSTRACTComputational Equipment for Approximation Theory, ControlTheory, and Graph TheoryThe Department of Mathematics at Vanderbilt University willpurchase computer equipment dedicated to supporting researchin the mathematical sciences. The equipment will be used forseveral research projects, as follows. Professor Ellinghamwill investigate conjectures in graph theory involvingsurface embeddings, traversability, and independent sets.Professor Hardin will construct and develop applicationsof local orthogonal bases. Professor Horn will investigatethe controllability of linked elastic structurres usingnumerical methods. Professors Hardin and Saff willinvestigate discrete minimum energy problems on the sphere.Professors Saff and Schumaker will research the theory andapplications of splines, especially on the sphere.Professor Ellingham's research involves graphs, which aremathematical models of networks. Communication,transportation and other networks are often modeled usingtechniques from graph theory. Professor Hardin's researchinvolves wavelets, which are an important tool forcompressing images, sounds, and other real-world information.They may be applied to problems in fitting equations to datapoints in any area of science, or processing images, forexample from medical scanning equipment. Professor Horn'sresearch involves control theory, which allows computationof how forces should be applied to a complicated system toachieve a desired outcome. There are applications to manyreal-world structures such as trusses, robot arms, solarpanels, and suspension bridges. The work by ProfessorsHardin and Saff involves the best way to place points ona sphere so that the sphere is covered as uniformly aspossible. This problem has applications in many fields,including the structure of viruses, crystallography,structure of molecules, and electrostatics. The researchby Professors Saff and Schumaker involves trying to provideaccurate but easily computable representations of quantitieson the surface of a sphere. For example, these technique maybe used to construct an accurate model of the Earth'sgravitational field.

NSF 提案 DMS-0215442PI：Hardin、Ellingham、Horn、Saff 和 Schumaker 摘要用于近似理论、控制理论和图论的计算设备范德比尔特大学数学系将购买专用于支持数学科学研究的计算机设备。该设备将用于以下几个研究项目。 Ellingham 教授将研究图论中涉及表面嵌入、可遍历性和独立集的猜想。Hardin 教授将构建和开发局部正交基的应用。霍恩教授将使用数值方法研究连接弹性结构的可控性。 Hardin和Saff教授将研究球体上的离散最小能量问题。Saff和Schumaker教授将研究样条的理论和应用，特别是在球体上。Ellingham教授的研究涉及图，即网络的数学模型。通信、交通和其他网络通常使用图论技术进行建模。 哈丁教授的研究涉及小波，它是压缩图像、声音和其他现实世界信息的重要工具。它们可以应用于任何科学领域的数据点拟合方程的问题，或处理图像，例如来自医学扫描设备的图像。霍恩教授的研究涉及控制理论，它可以计算如何将力施加到复杂的系统上以实现期望的结果。 它适用于许多现实世界的结构，例如桁架、机器人臂、太阳能电池板和吊桥。 Hardin 和 Saff 教授的工作涉及在球体上放置点的最佳方法，以便尽可能均匀地覆盖球体。这个问题在许多领域都有应用，包括病毒结构、晶体学、分子结构和静电学。 萨夫和舒梅克教授的研究涉及试图提供球体表面上的量的准确但易于计算的表示。例如，这些技术可以用来构建地球引力场的精确模型。