NSF/CBMS Regional Conference in the Mathematical Sciences, Using Spectral Data to Solve Inverse Problems, December 14-18, 2001

美国国家科学基金会/CBMS利用光谱数据解决逆问题区域会议将在德克萨斯大学泛美分校举行。会议日期为2001年12月14日至18日。伦斯勒理工学院福特基金会数学教授Joyce McLaughlin教授将作为会议首席讲师提供10场讲座。讲座将提供一个独立的和全面的阐述，使用光谱数据来解决逆问题。在这些问题中，间接测量被用来确定物体的材料性质。对于要提出的一组问题，数据由固有频率和选定的模态振型测量组成。这些讲座将介绍解决这些问题的最新方法，并从数学和实验两方面深入了解数据如何依赖于要恢复的材料特性。这些讲座的主要内容是二维问题，对一维问题有一个简短的介绍和见解。演示实验将包括展示振动系统在固有频率下的响应，显示响应随材料特性变化的变化，以及显示所选模态振型数据的几何特性。应用数学家和科学家将提供一些额外的讲座，讨论相关的逆问题，在某些情况下，光谱数据将在其他环境中使用。

An NSF/CBMS Regional Conference on Using Spectral Data to Solve Inverse Problems will be held at the University of Texas - Pan American. The dates for the conference are December 14-18, 2001. Professor Joyce McLaughlin, the Ford Foundation Professor of Mathematics at Rensselaer Polytechnic Institute, will provide ten lectures as the conference Principal Lecturer.The lectures will provide a self-contained and comprehensive exposition on the use of spectral data to solve inverse problems. In these problems, indirect measurements are used to determine material properties of objects. For the set of problems to be presented, the data consists of natural frequencies and selected mode shape measurements. These lectures will present the newest methods for solving these problems, and give both mathematical and experimental insight into how the data depends on the material properties to be recovered. The main thrust for these lectures is for two-dimensional problems, with a brief introduction and insight given for one-dimensional problems. Demonstration experiments will be included to exhibit the response of vibrating systems at natural frequencies, to show the change in the response as material properties change, and to show geometric properties of selected mode shape data. A select number ofadditional lectures will be provided by applied mathematicians and scientists addressing related inverse problems, in some cases where spectral data is utilized in other contexts.