Mathematical Sciences: Some Elementary Inequalities

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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.