Mathematical #Science: Some Elementary Inequalities

数学

• 批准号: 8903707
• 负责人: Grahame Bennett
• 金额: $ 4.25万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903707&HistoricalAwards=false
• 关键词: Mathematical; #Science; Some; Elementary; Inequalities

Professor Bennett's project is mainly concerned with finding p,q - norm and lower bound estimates for linear transformations whose matrices have non-negative entries. The resulting inequalities are expected to have applications in numerous areas of analysis and probability theory. Mathematical analysis at the working level is often a matter of the ingenious manipulation of inequalities. For instance, there is a famous inequality asserting that the sum of products of two sequences of positive numbers is not greater than the square root of the sum of squares of the first sequence times the analogous expression for the second. This fact and countless others like it constitute the basic information out of which analytic arguments are spun. The research of Professor Bennett aims at fundamental enrichment of this store of facts.

Bennett教授的项目主要是寻找矩阵具有非负项的线性变换的p，q-范数和下界估计。由此产生的不平等有望在分析和概率论的许多领域中得到应用。工作层面的数学分析往往是巧妙地处理不平等的问题。例如，有一个著名的不等式，断言两个正数序列的乘积和不大于第一个序列的平方和乘以第二个序列的类似表达式的平方根。这一事实和无数类似的事实构成了分析论证所依据的基本信息。班尼特教授的研究旨在从根本上丰富这一事实宝库。