Inverse Nodal Problems in Two Dimensions (Mathematics)

McLaughlin博士将开发逆节点问题的算法， 二维的 在这类新的反问题中，数据是 节点位置，或本征函数的零点，解为 微分算子中的系数 一维逆节点 二阶算子的问题已经仔细研究，使用 特征值的渐近形式和节点的渐近形式 岗位 在两个维度上，算法将基于公式 这是用变分原理推导出来的。 互动活动包括教授高级本科生或 一年级研究生水平课程的逆谱理论， 有界域，鼓励和建议女数学学生， 并赞助一位来访的女士 数学家 本项目进一步促进了VPW计划的目标，即（1） 为妇女提供机会， 工程和NSF支持的科学学科和（2） 鼓励妇女从事科学和工程职业， 提高女科学家和女工程师的知名度 受雇于工业、政府和学术机构。 通过 鼓励妇女参与科学，这是一个宝贵的 投资于国家未来的科学活力。

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.