25,069 research outputs found
A covariant Lagrangian for stable nonsingular bounce
The nonsingular bounce models usually suffer from the ghost or gradient
instabilities, as has been proved recently. In this paper, we propose a
covariant effective theory for stable nonsingular bounce, which has the
quadratic order of the second order derivative of the field but the
background set only by . With it, we explicitly construct a fully
stable nonsingular bounce model for the ekpyrotic scenario.Comment: 12 pages, 6 figures; published in JHEP; an Appendix and references
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The -rainbow index of random graphs
A tree in an edge colored graph is said to be a rainbow tree if no two edges
on the tree share the same color. Given two positive integers , with
, the \emph{-rainbow index} of is the
minimum number of colors needed in an edge-coloring of such that for any
set of vertices of , there exist internally disjoint rainbow
trees connecting . This concept was introduced by Chartrand et. al., and
there have been very few related results about it. In this paper, We establish
a sharp threshold function for and
respectively, where and are
the usually defined random graphs.Comment: 7 pages. arXiv admin note: substantial text overlap with
arXiv:1212.6845, arXiv:1310.278
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