Inverse Nodal Problems in Two Dimensions (Mathematics)

二维逆节点问题（数学）

• 批准号: 8902967
• 负责人: Joyce McLaughlin
• 金额: $ 6.25万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-01-01 至 1991-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902967&HistoricalAwards=false
• 关键词: Inverse; Nodal; Problems; Two; Dimensions

Dr. McLaughlin will develop algorithms for inverse nodal problems in two dimensions. In this new class of inverse problems the data is nodal positions, or zeroes of eigenfunctions, and the solutions are coefficients in differential operators. One dimensional inverse nodal problems for second order operators have been carefully studied using asymptotic forms for eigenvalues and asymptotic forms for nodal positions. In two dimensions the algorithm will be based on formulas which have been derived using variational principles. Interactive activities include teaching an advanced undergraduate or first year graduate level course on inverse spectral theory for bounded domains, encouraging and advising women mathematics students, and sponsoring a seminar presentation by a visiting woman mathematician. This project furthers VPW program objectives which are (1) to provide opportunities for women to advance their careers in engineering and in the disciplines of science supported by NSF and (2) to encourage women to pursue careers in science and engineering by providing greater visibility for women scientists and engineers employed in industry, government, and academic institutions. By encouraging the participation of women in science, it is a valuable investment in the Nation's future scientific vitality.

McLaughlin 博士将开发二维逆节点问题的算法。 在这类新的反问题中，数据是节点位置或特征函数的零点，解是微分算子中的系数。 使用特征值的渐近形式和节点位置的渐近形式仔细研究了二阶算子的一维逆节点问题。 在二维中，算法将基于使用变分原理导出的公式。 互动活动包括教授本科生或一年级研究生关于有界域逆谱理论的高级课程，鼓励和建议女数学学生，以及赞助一位访问女数学家的研讨会演讲。 该项目进一步推进了 VPW 计划的目标，即 (1) 为女性提供在 NSF 支持的工程和科学学科领域推进职业生涯的机会，以及 (2) 通过提高女性在科学和工程领域的知名度，鼓励女性从事科学和工程领域的职业生涯。受雇于工业、政府和学术机构的女科学家和工程师。 通过鼓励女性参与科学，这是对国家未来科学活力的宝贵投资。