Nonlocal Flow of Convex Plane Curves and Isoperimetric Inequalities

In the first part of the paper we survey some nonlocal flows of convex plane curves ever studied so far and discuss properties of the flows related to enclosed area and length, especially the isoperimetric ratio and the isoperimetric difference. We also study a new nonlocal flow of convex plane curves and discuss its evolution behavior. In the second part of the paper we discuss necessary and sufficient conditions (in terms of the (mixed) isoperimetric ratio or (mixed) isoperimetric difference) for two convex closed curves to be homothetic or parallel.Comment: 23 page

The technique of inverse Mellin transform for processes occurring in a background magnetic field

We develop the technique of inverse Mellin transform for processes occurring in a background magnetic field. We show by analyticity that the energy (momentum) derivatives of a field theory amplitude at the zero energy (momentum) is equal to the Mellin transform of the absorptive part of the amplitude. By inverting the transform, the absorptive part of the amplitude can be easily calculated. We apply this technique to calculate the photon polarization function in a background magnetic field.Comment: 3 pages, LATEX; talk presented at ICHEP02, Amsterdam, The Netherlands, 24-31 July 200

The Effect of Congressional Sessions on the Stock Market in Emerging Democracy: the Case of Taiwan

Political uncertainty, Congressional effect, Volatility asymmetry, EGARCH-M