ABSTRACT. The notion of symmetrization, also known as Davenport’s reflection principle, is well known in the area of the discrepancy theory and quasiMonte Carlo (QMC) integration. In this paper we consider applying a symmetrization technique to a certain class of QMC point sets called digital nets over Zb. Although symmetrization has been recognized as a geometric technique in the multi-dimensi...

Univariate symmetrization technique has many good properties. In this paper, we adopt the high-dimensional viewpoint, and propose a new symmetrization procedure in arbitrary (convex) polytopes of R with central symmetry. Moreover, the obtained results are used to extend to the arbitrary centrally symmetric polytopes the well-known Hermite-Hadamard inequality for convex functions.

The symmetrization method of Gale, Kuhn and Tucker for matrix games is extended for bimatrix games. It is shown that the equilibria of a bimatrix game and its symmetrization correspond two by two. A similar result is found with respect to quasi-strong, regular and perfect equilibria.

Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev inequalities. Our methods are very general and can be easily adapted to more general contexts.

We have performed first-principles calculations to investigate the behavior of the hydrogen bond in δ-AlOOH under pressure. The highest OH-stretching A1 and B2 mode frequencies decrease under pressure leading to hydrogen bond symmetrization. After hydrogen bond symmetrization, the corresponding frequencies gradually increase. This softening and subsequent hardening of the OH bonds is a good spe...

Shortly before his death in 1995, Kenneth B. Schwartz, a cancer patient at Massachusetts General Hospital (MGH), founded The Kenneth B. Schwartz Center at MGH. The Schwartz Center is a nonprofit organization dedicated to supporting and advancing compassionate health care delivery that provides hope to the patient and support to caregivers, and encourages the healing process. The Center sponsors...