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博士将在两个维度上开发针对结节逆问题的算法。 在这类新的反问题中，数据是淋巴结位置或本征函数的零，而解决方案是差分运算符的系数。 二级二级运算符的一维逆淋巴结问题已经使用偶像值的渐近形式进行了仔细研究，并且用于淋巴结位置的渐近形式。 在二维中，算法将基于使用变分原理得出的公式。 互动活动包括教授有关有限领域的逆光谱理论的高级本科或第一年的研究生级课程，鼓励和建议女性数学学生，并赞助来访的女性数学家的研讨会演讲。 该项目进一步推进了VPW计划的目标，该计划是（1）为妇女提供机会，以提高其在工程学和NSF支持的科学学科和（2）来鼓励妇女从事科学和工程学的职业，通过为在工业，政府政府和学术机构中雇用的女性科学家提供更高的知名度，从而为妇女从事科学和工程学的职业。 通过鼓励妇女参与科学，这是对国家未来科学活力的宝贵投资。