Inverse Nodal Problems in Two Dimensions (Mathematics)

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，或者特征函数的零点，而解是微分算子的系数。利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。互动活动包括教授有界域逆谱理论的高级本科或研究生一年级课程，鼓励和建议女性数学学生，并赞助一位来访的女数学家的研讨会报告。该项目进一步推进了VPW计划的目标，即(1)为女性提供在工程和NSF支持的科学学科中发展职业的机会；(2)通过为在工业、政府和学术机构工作的女性科学家和工程师提供更大的知名度，鼓励女性在科学和工程领域追求职业。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。

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.