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

NSF/CBMS关于使用光谱数据解决反问题的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系教授Joyce McLaughlin教授将以会议主讲人的身份主讲十场讲座，讲解如何利用光谱数据解决反问题。在这些问题中，间接测量被用来确定物体的材料属性。对于将要提出的这组问题，数据由固有频率和选定的振型测量组成。这些讲座将介绍解决这些问题的最新方法，并提供关于数据如何依赖于要恢复的材料属性的数学和实验方面的见解。这些讲座的主旨是二维问题，并对一维问题进行了简要的介绍和见解。将包括演示实验，以展示振动系统在自然频率下的响应，显示响应随材料特性变化的变化，并显示所选振型数据的几何特性。应用数学家和科学家将提供一些精选的额外讲座，解决相关的逆问题，在某些情况下，光谱数据在其他情况下被利用。

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.