U.S.-U.K. Collaborative Research: Exponentiation and O-Minimal Expansions of R

美国-英国合作研究：R 的求幂和 O 最小展开式

基本信息

批准号：
9224546
负责人：
David Marker
金额：
$ 1.62万
依托单位：
University of Illinois at Chicago
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1993
资助国家：
美国
起止时间：
1993-08-15 至 1998-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9224546&HistoricalAwards=false
关键词：
U.S.U.K.Collaborative Research Exponentiation

项目摘要

9224546 Marker This three-year award for U.S.-United Kingdom cooperative research in mathematics involves David E. Marker, C. Ward Henson, Lou van den Dries of the Chicago and Urbana-Champaign campuses of the University of Illinois respectively, and Angus Macintyre, Alex Wilkie, Kobi Peterzil of Oxford University's Mathematics Institute. The objectives of the research is to apply complex analytical methods to model theory in exponentiation and O- minimal expansions of R. Model theoretical results obtained so fair show that subsets of R definable exponentiation behave in many ways like semialgebraic and subanalytic subsets. The investigators will study finer definability and growth rate questions of R and extend their results to natural expansions allowing further analytical structure. This collaboration takes advantage of the complementary expertise of the Oxford and University of Illinois research groups. Both have worked extensively on model theory and analysis interface, exponentiation, and study of complex function defined in exponential terms. Since exponentially defined semialgebraic and subanalytic sets arise naturally in many mathematical and engineering fields, this research will advance understanding of their uses in real algebraic and real analytic geometry, dynamical systems, control theory, statistics and robotics. ***

9224546 Marker 这项为期三年的美英数学合作研究奖涉及伊利诺伊大学芝加哥分校和厄巴纳-香槟分校的 David E. Marker、C. Ward Henson、Lou van den Dries 以及 Angus Macintyre，牛津大学数学研究所的 Alex Wilkie 和 Kobi Peterzil。研究的目标是将复杂的分析方法应用于 R 的求幂和 O 最小展开的模型理论。如此公平地获得的模型理论结果表明，R 可定义求幂的子集在许多方面表现得像半代数和亚解析子集。研究人员将研究 R 的更精细的可定义性和增长率问题，并将其结果扩展到自然扩展，从而允许进一步的分析结构。此次合作利用了牛津大学和伊利诺伊大学研究小组的互补专业知识。两人都在模型理论和分析接口、指数以及以指数项定义的复杂函数的研究方面进行了广泛的研究。由于指数定义的半代数和亚解析集在许多数学和工程领域中自然出现，因此这项研究将增进对它们在实代数和实解析几何、动力系统、控制理论、统计学和机器人学中的应用的理解。 ***