Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves

By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained.Comment: 31 pages; revise

Quenched Invariance Principle for a Reflecting Diffusion in a Continuum Percolation Cluster

We consider a continuum percolation built over stationary ergodic point processes. Assuming that the occupied region has a unique unbounded cluster and the cluster satisfies volume regularity and isoperimetric condition, we prove a quenched invariance principle for reflecting diffusions on the cluster.Comment: 26 page

Local Central Limit Theorem for Reflecting Diffusions in a Continuum Percolation Cluster

Reflecting diffusions on continuum percolation clusters are considered. Assuming that the occupied region has a unique unbounded cluster and the cluster satisfies geometrical conditions such as volume regularity, isoperimetric conditions, and a hole size condition, we prove a quenched local central limit theorem for reflecting diffusions on the cluster.Comment: 37 page

CP,T and/or CPT Violations in the K0-K0bar System --Implications of the KTeV,NA48 and CPLEAR Results

Possible violation of CP, T and/or CPT symmetries in the \ko-\kob system is studied from a phenomenological point of view. For this purpose, we first introduce parameters which represent violation of these symmetries in mixing parameters and decay amplitudes in a convenient and well-defined way and, treating these parameters as small, derive formulas which relate them to the experimentally measured quantities. We then perform numerical analyses, with the aid of the Bell-Steinberger relation, to derive constraints to these symmetry-violating parameters, firstly paying particular attention to the results reported by KTeV Collaboration and NA48 Collaboration, and then with the results reported by CPLEAR Collaboration as well taken into account. A case study, in which either CPT symmetry or T symmetry is assumed, is also carried out. It is demonstrated that CP and T symmetries are violated definitively at the level of 10^{-4} in $2\pi$ decays and presumably at the level of 10^{-3} in the \ko-\kob mixing, and that the Bell-Steinberger relation helps us to establish CP and T violations being definitively present in the \ko-\kob mixing and to test CPT symmetry to a level of 10^{-4} ~ 10^{-5}.Comment: 21 pages, 1 figure

A geometric degree formula for A-discriminants and Euler obstructions of toric varieties

AbstractWe give explicit formulas for the dimensions and the degrees of A-discriminant varieties introduced by Gelfand, Kapranov and Zelevinsky. Our formulas can be applied also to the case where the A-discriminant varieties are higher-codimensional and their degrees are described by the geometry of the configurations A. Moreover combinatorial formulas for the Euler obstructions of general (not necessarily normal) toric varieties will be also given