45,786 research outputs found
Dyonic (A)dS Black Holes in Einstein-Born-Infeld Theory in Diverse Dimensions
We study Einstein-Born-Infeld gravity and construct the dyonic (A)dS planar
black holes in general even dimensions, that carry both the electric charge and
magnetic fluxes along the planar space. In four dimensions, the solution can be
constructed with also spherical and hyperbolic topologies. We study the black
hole thermodynamics and obtain the first law. We also classify the singularity
structure.Comment: Latex, 21 pages, typos corrected and references adde
Godel Metrics with Chronology Protection in Horndeski Gravities
G\"odel universe, one of the most interesting exact solutions predicted by
General Relativity, describes a homogeneous rotating universe containing naked
closed time-like curves (CTCs). It was shown that such CTCs are the consequence
of the null energy condition in General Relativity. In this paper, we show that
the G\"odel-type metrics with chronology protection can emerge in
Einstein-Horndeski gravity. We construct such exact solutions also in
Einstein-Horndeski-Maxwell and Einstein-Horndeski-Proca theories.Comment: Latex, 11 pages, references adde
Arbitrary phase rotation of the marked state can not be used for Grover's quantum search algorithm
A misunderstanding that an arbitrary phase rotation of the marked state
together with the inversion about average operation in Grover's search
algorithm can be used to construct a (less efficient) quantum search algorithm
is cleared. The rotation of the phase of the marked state is not only the
choice for efficiency, but also vital in Grover's quantum search algorithm. The
results also show that Grover's quantum search algorithm is robust.Comment: 5 pages, 5 figure
Diamond-free Families
Given a finite poset P, we consider the largest size La(n,P) of a family of
subsets of that contains no subposet P. This problem has
been studied intensively in recent years, and it is conjectured that exists for general posets P,
and, moreover, it is an integer. For let \D_k denote the -diamond
poset . We study the average number of times a random
full chain meets a -free family, called the Lubell function, and use it for
P=\D_k to determine \pi(\D_k) for infinitely many values . A stubborn
open problem is to show that \pi(\D_2)=2; here we make progress by proving
\pi(\D_2)\le 2 3/11 (if it exists).Comment: 16 page
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