On nonuniform exponential stability for skew-evolution semiflows on Banach spaces

The paper considers some concepts of nonuniform asymptotic stability for skew-evolution semiflows on Banach spaces. The obtained results clarify differences between the uniform and nonuniform cases. Some examples are included to illustrate the results.Comment: 11 page

Equivalent Definitions for Uniform Exponential Trichotomy of Evolution Operators in Banach Spaces

The aim of this paper is to give necessary and sufficient conditions for the uniform exponential trichotomy property of nonlinear evolution operators in Banach spaces. The obtained results are generalizations for infinite-dimensional case of some well-known results of Elaydi and Hajek on exponential trichotomy of differential systems

Phase Space Factors for Double-Beta Decays

Double-beta decay is presently a very studied process both theoretically and experimentally due to its potential to provide valuable information about important, but still unknown issues related to the neutrino properties and conservation of some symmetries. In the theoretical study of the double-beta decay two key quantities entering the half-life formulas are important, namely the phase space factors embedding the influence of the Coulomb field of the daughter nucleus on the emitted electrons/positrons, and the nuclear matrix elements embedding the nuclear structure effects of the nuclei participating in the decay. Accurate calculation of both of them are needed for good predictions of the double-beta decay half-lives and transitions still unmeasured, and for constraining various beyond Standard Model parameters associated with mechanisms that may contribute to the neutrinoless double-beta decay modes. During time much attention has been paid to the nuclear matrix elements that were considered to bring the largest uncertainties in the computation of the double-beta decay half-lives, while the phase space factors were considered until the recent past to be computed with enough precision. However, newer computation of the phase space factors performed with more precise methods revealed relevant deviations from their values reported previously, especially for heavier nuclei and for positron emitting and electron capture decay modes. In this paper we review the progress made in the computation of the phase space factors for double beta decay. We begin with the non-relativistic approaches, continue with the relativistic approaches which use approximate electron/positron wave functions, and end up with recent, more precise, computations of the phase space factors where exact electron wave functions are obtained from the resolution of a Dirac equation in a Coulomb-type potential and with inclusion of finite nuclear size and screening effects. We report an up-dated and complete list of the phase space factors (PSF) for the following DBD modes: β−β−, β+β+, ECβ+, and ECEC and for transitions to final ground and first excited 2+ and 0+ states of the daughter nuclei. We also make a comparison between different values of the phase space factors found in literature and discuss the differences between these results