Single and multiple averages along subsequences

沿子序列的单个和多个平均值

• 批准号: 0801316
• 负责人: Mate Wierdl
• 金额: $ 13.17万
• 依托单位: University of Memphis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-06-15 至 2012-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0801316&HistoricalAwards=false
• 关键词: Single; multiple; averages; along; subsequences

This proposal's main purpose is to investigate an area of mathematics which grew out of the science of interpreting data of large number of measurements. The basic problem is this: under normal circumstances, when people have to make repeated measurements of some data to draw statistical conclusions, they try to make the measurements at regular intervals, like once every second. The existing theories usually assume that the measurements are taken _exactly_ at every second. In reality, measurements are made at every second only approximately. The proposal's investigations are aimed to look at these possible random perturbations, and try to develop tools to help interpret the obtained data. One of the main motivation for these investigations is the fact that random perturbations may result in a completely different set of data from those one could obtain under the ideal circumstances. As it may be guessed, many of the problems we face are difficult, and to solve these problems we resort to tools used in several different branches of mathematics.

这项建议的主要目的是调查一个数学领域，该领域源于解释大量测量数据的科学。基本的问题是：在正常情况下，当人们必须对一些数据进行重复测量才能得出统计结论时，他们会尝试定期进行测量，比如每秒一次。现有的理论通常假设测量准确地在每一秒进行。在现实中，每一秒的测量只是大约进行的。该提案的调查旨在研究这些可能的随机扰动，并试图开发工具来帮助解释所获得的数据。进行这些调查的主要动机之一是，随机扰动可能会导致一组与理想情况下完全不同的数据。正如人们可能猜测的那样，我们面临的许多问题都是困难的，为了解决这些问题，我们求助于数学的几个不同分支中使用的工具。