U.S.-Australia Cooperative Research: Trigonometric Sums andTheir Applications to Engineering Problems

美澳合作研究：三角和及其在工程问题中的应用

• 批准号: 9015137
• 负责人: James Byrnes
• 金额: $ 2.86万
• 依托单位: University of Massachusetts Boston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-03-15 至 1994-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9015137&HistoricalAwards=false
• 关键词: U.S.; Australia; Cooperative; Research; Trigonometric

This award will support collaborative research between Dr. James Byrnes of the University of Massachusetts at Boston and Dr. Gavin Brown of the University of New South Wales. The research is to advance theoretical understanding of the properties of trigonometic sums with restricted coefficients, and to explore the application of these results to important engineering problems. A primary focus of the project is to resolve the question of how close to constant the modulus of a polynomial can be along a curve, typically the unit circle, in which case, the polynominal is a finite trigonometric sum. This question is important both to theoretical mathematical analysis because of the fundamental nature of polynominals, and to engineering because of the applicability of the work to the problem of minimizing peak to average ratios of power in transmitter design. The project represents excellent collaboration between the U.S. and Australian researchers in that both are at the point of expanding their parallel expertise in classical mathe- matical analysis to the solution of engineering problems, important to both countries. This is significant fundamental work in an important area of mathematical research, as well as having the potential for solving major engineering problems.

该奖项将支持波士顿马萨诸塞大学的詹姆斯·伯恩斯博士和新南威尔士大学的加文·布朗博士之间的合作研究。本研究的目的是加深对限制系数三角和性质的理论理解，并探索这些结果在重要工程问题中的应用。该项目的一个主要焦点是解决多项式的模沿曲线(通常是单位圆)可以多接近于常数的问题，在这种情况下，多项式是有限的三角和。由于多项式的基本性质，这个问题对于理论数学分析是重要的，对于工程也是重要的，因为这项工作适用于发射机设计中最小化峰值与平均功率比的问题。该项目代表了美国和澳大利亚研究人员之间的出色合作，因为双方都在将他们在经典数学分析方面的并行专业知识扩展到对两国都重要的工程问题的解决上。这是一个重要的数学研究领域的重要基础工作，也具有解决重大工程问题的潜力。