Mathematical Sciences: Harmonic Analysis Algorithms

六名学生将被选中参加这项研究 本科生项目的经验。 7名教师 从事五个研究项目将向学生介绍 各种可能的方向， 能量 其中包括phi-transform的工作， 调和分析法将一般函数分解为 简单的条款。 它混合了时间和频率的考虑， 以强大而微妙的方式提供抵消。 特别 涉及电磁散射、心电图的示例 分析和NMR成像将被研究。 关于陈-莫泽- 多复变理论中的田中不变量 由于计算不变量的困难而受到阻碍。 现在可以让学生参与符号的使用 操纵算法来进行估计和创建数值 模型来研究这些重要的数学结构。 学生还可以研究分子的数学模型。 进化，（编码中核苷酸的分布） 从随机交配群体中选择的个体的区域）; 关于构建磁共振成像的新高分辨率方法 原始MR扫描仪数据的共振图像;傅立叶分析 在局部域上;在组合数论上， 特别是素数分布的随机性。 将努力鼓励学生发展他们的 以可替代的形式工作或作为高级荣誉的基础 论文

Six students will be chosen to participate in this Research Experiences for Undergraduates project. Seven faculty members engaged in five research programs will introduce the students to a variety of possible directions on which to focus their energies. They include work on the phi-transform, a new tool in harmonic analysis for decomposing general functions as sums of simple terms. It mixes time and frequency considerations, providing cancellation in powerful and subtle ways. Particular examples involving electromagnetic scattering, electrocardiogram analysis and NMR imaging will be studied. Work on Chern-Moser- Tanaka invariants in the theory of several complex variables has been hampered by the difficulty in calculating the invariants. Now it is possible to involve students in the use of symbol manipulation algorithms to make estimates and create numerical models to study these important mathematical structures. Students may also work on mathematical models of molecular evolution, (the distribution of nucleotides in the coding regions of individuals chosen from a random-mating population); on new high resolution methods for constructing magnetic resonance images from raw MR scanner data; on Fourier analysis over local fields; and on combinatorial number theory, specifically, on the randomness of the distribution of primes. Efforts will be made to encourage students to develop their work into publishable form or as the basis for senior honors theses.