Mathematical #Science: Some Elementary Inequalities

班尼特教授的项目主要是寻找 线性变换的p，q -模和下界估计 其矩阵具有非负项。所得 不等式在许多领域都有应用 分析和概率论。 工作层面的数学分析， 对不平等的巧妙操纵。比如说， 有一个著名的不等式断言乘积之和 两个正数序列的平均值不大于 第一个序列的平方和的平方根乘以 第二个类似的表达。这一事实和无数 其他类似的信息构成了 分析的论点是旋转的。班尼特教授的研究 旨在从根本上丰富这些事实。

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.