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

NSF/CBMS 数学科学区域会议，使用谱数据解决反问题，2001 年 12 月 14-18 日

• 批准号: 0085884
• 负责人: Roger Knobel
• 金额: $ 2.97万
• 依托单位: The University of Texas Rio Grande Valley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-01-01 至 2001-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0085884&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

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.

NSF/CBMS关于使用光谱数据解决逆问题的区域会议将在德克萨斯大学泛美分校举行。会议将于十二月十四日至十八日举行。Rensselaer Polytechnic Institute的福特基金会数学教授Joyce McLaughlin教授将作为会议首席讲师提供十场讲座。讲座将提供关于使用光谱数据解决逆问题的独立和全面的阐述。在这些问题中，使用间接测量来确定对象的材料属性。 对于要提出的一组问题，数据包括固有频率和选定的振型测量。这些讲座将介绍解决这些问题的最新方法，并给出数学和实验的见解，数据如何取决于要恢复的材料属性。这些讲座的主旨是二维问题，简要介绍和一维问题的见解。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，并显示选定振型数据的几何特性。在某些情况下，光谱数据在其他情况下被利用，应用数学家和科学家将提供一些额外的讲座，解决相关的逆问题。