Surprising Geometric Phenomena in High Dimensional Convexity Theory

Geometrization of Probability

The framework of the subject we will discuss in this survey involves very high dimensional spaces (normed spaces, convex bodies) and accompanying asymptotic (by increasing dimension) phenomena. The starting point of this direction was the open problems of Geometric Functional Analysis (in the ’60s and ’70s). This development naturally led to the Asymptotic Theory of Finite Dimensional spaces (i...

Bézier nets, convexity and subdivision on higher-dimensional simplices

The Effect of Antenna Movement and Material Properties on Electromagnetically Induced Transparency in a Two-Dimensional Metamaterials

Increasing development of nano-technology in optics and photonics by using modern methods of light control in waveguide devices and requiring miniaturization and electromagnetic devices such as antennas, transmission and storage as well as improvement in the electromagnetic tool, have led researchers to use the phenomenon of electromagnetically induced transparency (EIT) and similar phenomena i...

Geometric Plurisubharmonicity and Convexity - an Introduction

This is an essay on potential theory for geometric plurisubharmonic functions. It begins with a given closed subset Gl of the Grassmann bundle G(p, TX) of tangent p-planes to a riemannian manifold X . This determines a nonlinear partial differential equation which is convex but never uniformly elliptic (p < dimX). A surprising number of results in complex analysis carry over to this more genera...

SOME PROPERTIES FOR FUZZY CHANCE CONSTRAINED PROGRAMMING

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...