Mathematical Sciences: Some Elementary Inequalities

数学分析的基础是 真实的数字系统，这反过来又取决于 完整性和极限的概念。 的理论和 真实的数的实践、估计和近似是一门 基本概念，对所有形式的科学和 工程师的奋进。 有几个著名的不等式 那些有柯西、施瓦茨、闵可夫斯基和 例如，保持器--很久以前就被发现了， 这是一般不等式理论的基础。 这是一个 当发现一个新的不平等时， 对于这样一个事件肯定预示着重要的， 以前未被怀疑或无法获得的应用程序。 班尼特教授有令人羡慕的荣誉， 最近发现了一些新的基本不等式。他们 导致解决了一些悬而未决的问题， 优势理论。 此外，这项工作使 班尼特教授的猜想更加有力 他的不等式的扩展，这反过来又会打开新的 在非常基础的学科，如函数的研究方向， 理论，算子理论，特征值分布，正交 矩阵理论和矩阵理论。 班尼特教授将继续 这个独特而重要的研究项目

The foundation upon which mathematical analysis rests is the real number system, which in turn depends upon the concept of completeness and limits. Both in theory and practice, estimation and approximation of real numbers is a fundamental concept, crucial to all forms of scientific and engineering endeavor. There are a few famous inequalities -- those that bear the names Cauchy, Schwarz, Minkowski, and Holder, for example -- that were discovered long ago, and which are basic to the general theory of inequalities. It is a rare and important event when a new inequality is discovered, for such an occurence surely foreshadows important and previously unsuspected or unobtainable applications. Professor Bennett has the enviable distinction of having recently discovered some new fundamental inequalities. They have led to solution of a number of outstanding problems in the theory of majorization. Moreover, this work has allowed Professor Bennett to conjecture still more powerful extensions of his inequalities, which in turn would open new research directions in very basic subjects such as function theory, operator theory, eigenvalue distribution, orthogonal series, and matrix theory. Professor Bennett will continue this unique and important research program.