Mathematical Sciences: Problems in Analysis, Probability, and Finite Mathematics

数学科学：分析、概率和有限数学问题

• 批准号: 9106223
• 负责人: Steven Krantz
• 金额: $ 6万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-04-01 至 1993-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9106223&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Analysis; Probability

Six undergraduates will receive support from this Research Experiences for Undergraduates award. They will work under the direction of several faculty advisors all of whom have strong research programs under way. This program continues a successful program of undergraduate research at Washington University. It will be augmented during the next two years by a series of visits by leading mathematical researchers. The environment for this activity is particularly fecund at Washington University which has produced many of the top finalists and leading teams in the Putnam examinations over the past ten years. Included among the many topics which will be available for student projects is the study of the phi-transform. This concept is a very recent variation of the wavelet transform allowing one to decompose general functions into sums of simple terms. It has interesting computational characteristics which allow for simple but important questions to be undertaken early without need for extensive theoretical training. Work will also be done on the boundary behavior of conformal mappings and harmonic measure. This work will fit well into the development of students who have recently completed an undergraduate complex variables course. Another area of interest includes problems arising in the theory of several complex variables. Here, researchers can construct numerical models for automorphism groups and perform calculations of invariants associated with boundary differential invariants. The work only requires basic algebra and an understanding of symbol manipulation programs. In the process, students will develop concrete understanding of geometric structures and the analysis related to them. A more applied program developing mathematical models of molecular evolution will also be available. Students will consider questions concerning the distribution of nucleotides in the coding regions of individuals chosen from a random-mating population. Connections with algorithms for estimating phylogenies of creatures whose traits are known in the present will be investigated.

六名本科生将获得这项研究的支持 本科生经验奖。 他们将在 几位导师的指导，他们都有很强的 研究项目正在进行中。 该计划继续取得成功 在华盛顿大学的本科研究计划。 它 在未来两年里， 由顶尖的数学研究人员 环境对于这一点 活动在华盛顿大学特别多产， 产生了许多顶级决赛选手和领先的团队， 普特南考试在过去的十年。 包括在将提供给 学生项目是对φ变换的研究。 这个概念 是小波变换的一个非常新的变体，允许 将一般函数分解为简单项的和。 它 具有有趣的计算特性， 一些简单但重要的问题需要尽早解决， 需要广泛的理论培训。 工作也将完成 关于共形映射与调和函数的边界性态 measure. 这项工作将很好地适应发展， 最近完成本科综合课程的学生 变量课程 另一个令人感兴趣的领域包括 多复变量理论 在这里，研究人员可以 构造自同构群的数值模型， 边界微分不变量的计算 不变量 这项工作只需要基本的代数和 理解符号操作程序。 在这个过程中， 学生将发展几何的具体理解 结构及其相关分析。 一个更实用的程序开发的数学模型， 分子进化也将可用。 学生将 考虑有关核苷酸分布的问题 从随机交配中选择的个体的编码区 人口与估算算法的联系 目前已知特征的生物的遗传学 将被调查。