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

The cosmological constant as an eigenvalue of the Hamiltonian constraint in Horava-Lifshits theory

In the framework of Horava-Lifshitz theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. The explicit calculation is performed with the help of a variational procedure with trial wave functionals of the Gaussian type. We analyze both the case with the detailed balanced condition and the case without it. In the case without the detailed balance, we find the existence of an eigenvalue depending on the set of coupling constants (g2,g3) and (g4,g5,g6), respectively, and on the physical scale.Comment: RevTeX,11 Pages, Substantial Improvements. References added. To appear in Phys.Rev.

Hopanoid lipids may facilitate aerobic nitrogen fixation in the ocean.

Cyanobacterial diazotrophs are considered to be the most important source of fixed N2 in the open ocean. Biological N2 fixation is catalyzed by the extremely O2-sensitive nitrogenase enzyme. In cyanobacteria without specialized N2-fixing cells (heterocysts), mechanisms such as decoupling photosynthesis from N2 fixation in space or time are involved in protecting nitrogenase from the intracellular O2 evolved by photosynthesis. However, it is not known how cyanobacterial cells limit O2 diffusion across their membranes to protect nitrogenase in ambient O2-saturated surface ocean waters. Here, we explored all known genomes of the major marine cyanobacterial lineages for the presence of hopanoid synthesis genes, since hopanoids are a class of lipids that might act as an O2 diffusion barrier. We found that, whereas all non-heterocyst-forming cyanobacterial diazotrophs had hopanoid synthesis genes, none of the marine Synechococcus, Prochlorococcus (non-N2-fixing), and marine heterocyst-forming (N2-fixing) cyanobacteria did. Finally, we conclude that hopanoid-enriched membranes are a conserved trait in non-heterocyst-forming cyanobacterial diazotrophs that might lower the permeability to extracellular O2 This membrane property coupled with high respiration rates to decrease intracellular O2 concentration may therefore explain how non-heterocyst-forming cyanobacterial diazotrophs can fix N2 in the fully oxic surface ocean