33,861 research outputs found
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.
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
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