Discontinuous Almost Automorphic Functions and Almost Automorphic Solutions of Differential Equations with Piecewise Constant Argument

In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties are used to prove the almost automorphicity of bounded solutions of a system of differential equations with piecewise constant argument. Due to the strong discrete character of these equations, the existence of a unique discrete almost automorphic solution of a non-autonomous almost automorphic difference system is obtained, for which conditions of exponential dichotomy and discrete Bi-almost automorphicity are fundamental

Polarization observables in elastic electron deuteron scattering including parity and time reversal violating contributions

The general formalism for polarization observables in elastic electron deuteron scattering is extended to incorporate parity and time reversal violating contributions. Parity violating effects arise from the interference of $\gamma$ and $Z$ exchange as well as from the hadronic sector via a small parity violating component in the deuteron. In addition we have allowed for time reversal invariance violating contributions in the hadronic sector. Formal expressions for the additional structure functions are derived, and their decomposition into the various multipole contributions are given explicitly.Comment: 34 pages Revte

Perturbative BF-Yang-Mills theory on noncommutative R^4

A U(1) BF-Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is presented and in this formulation the U(1) Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is seen as a deformation of the pure BF theory. Quantization using BRST symmetry formalism is discussed and Feynman rules are given. Computations at one-loop order have been performed and their renormalization studied. It is shown that the U(1) BFYM on noncommutative ${\mathbb{R}}^4$ is asymptotically free and its UV-behaviour in the computation of the $\beta$-function is like the usual SU(N) commutative BFYM and Yang Mills theories.Comment: 15 pages, 4 figures, latex, version to appear in NP

Dynamical Heterogeneities Below the Glass Transition

We present molecular dynamics simulations of a binary Lennard-Jones mixture at temperatures below the kinetic glass transition. The ``mobility'' of a particle is characterized by the amplitude of its fluctuation around its average position. The 5% particles with the largest/smallest mean amplitude are thus defined as the relatively most mobile/immobile particles. We investigate for these 5% particles their spatial distribution and find them to be distributed very heterogeneously in that mobile as well as immobile particles form clusters. The reason for this dynamic heterogeneity is traced back to the fact that mobile/immobile particles are surrounded by fewer/more neighbors which form an effectively wider/narrower cage. The dependence of our results on the length of the simulation run indicates that individual particles have a characteristic mobility time scale, which can be approximated via the non-Gaussian parameter.Comment: revtex, 10 pages, 20 postscript figure

Very light CP-odd scalar in the Two-Higgs-Doublet Model

We show that a general two-Higgs-doublet model (THDM) with a very light CP-odd scalar (A) can be compatible with the rho parameter, Br(b --> s\gamma), R_b, A_b, (g-2) of muon, Br(Upsilon --> A gamma), and the direct search via the Yukawa process at LEP. For its mass around 0.2 GeV, the muon (g-2) and Br(Upsilon --> A \gamma) data require tan(beta) to be about 1. Consequently, A can behave like a fermiophobic CP-odd scalar and predominantly decay into a photon pair ("gamma gamma"), which registers in detectors of high energy collider experiments as a single photon signature when the momentum of A is large. We compute the partial decay width of Z --> A A A and the production rate of f \bar{f} --> Z A A --> Z +"gamma gamma", f^' {\bar f} --> W^{\pm} A A --> W^\pm + "gamma gamma" and f \bar f --> H^+ H^- --> W^+ W^- A A --> W^+ W^- + "gamma gamma" at high energy colliders such as LEP, Tevatron, LHC, and future Linear Colliders. Other production mechanisms of a light A, such as gg --> h --> AA --> "gamma gamma", are also discussed.Comment: Some improvementes, references updated, 3 new figures, one new appendix, abstract and conclusions unchaged. Version to appear in Physical Review