12,246 research outputs found
Statefinder hierarchy exploration of the extended Ricci dark energy
We apply the statefinder hierarchy plus the fractional growth parameter to
explore the extended Ricci dark energy (ERDE) model, in which there are two
independent coefficients and . By adjusting them, we plot
evolution trajectories of some typical parameters, including Hubble expansion
rate , deceleration parameter , the third and fourth order hierarchy
and and fractional growth parameter ,
respectively, as well as several combinations of them. For the case of variable
and constant , in the low-redshift region the evolution
trajectories of are in high degeneracy and that of separate somewhat.
However, the CDM model is confounded with ERDE in both of these two
cases. and , especially the former, perform much better.
They can differentiate well only varieties of cases within ERDE except
CDM in the low-redshift region. For high-redshift region, combinations
can break the degeneracy. Both of
and have the ability to
discriminate ERDE with from CDM, of which the degeneracy
cannot be broken by all the before-mentioned parameters. For the case of
variable and constant , and can
only discriminate ERDE from CDM. Nothing but pairs
and can discriminate not only
within ERDE but also ERDE from CDM. Finally we find that
is surprisingly a better choice to discriminate within ERDE itself, and ERDE
from CDM as well, rather than .Comment: 8 pages, 14 figures; published versio
Measuring the degree of unitarity for any quantum process
Quantum processes can be divided into two categories: unitary and non-unitary
ones. For a given quantum process, we can define a \textit{degree of the
unitarity (DU)} of this process to be the fidelity between it and its closest
unitary one. The DU, as an intrinsic property of a given quantum process, is
able to quantify the distance between the process and the group of unitary
ones, and is closely related to the noise of this quantum process. We derive
analytical results of DU for qubit unital channels, and obtain the lower and
upper bounds in general. The lower bound is tight for most of quantum
processes, and is particularly tight when the corresponding DU is sufficiently
large. The upper bound is found to be an indicator for the tightness of the
lower bound. Moreover, we study the distribution of DU in random quantum
processes with different environments. In particular, The relationship between
the DU of any quantum process and the non-markovian behavior of it is also
addressed.Comment: 7 pages, 2 figure
Serrin Type Criterion for the Three-Dimensional Viscous Compressible Flows
We extend the well-known Serrin's blowup criterion for the three-dimensional
(3D) incompressible Navier-Stokes equations to the 3D viscous compressible
cases. It is shown that for the Cauchy problem of the 3D compressible
Navier-Stokes system in the whole space, the strong or smooth solution exists
globally if the velocity satisfies the Serrin's condition and either the
supernorm of the density or the -norm of the divergence of
the velocity is bounded. Furthermore, in the case that either the shear
viscosity coefficient is suitably large or there is no vacuum, the Serrin's
condition on the velocity can be removed in this criteria.Comment: 16 page
Semi-Supervised Sparse Coding
Sparse coding approximates the data sample as a sparse linear combination of
some basic codewords and uses the sparse codes as new presentations. In this
paper, we investigate learning discriminative sparse codes by sparse coding in
a semi-supervised manner, where only a few training samples are labeled. By
using the manifold structure spanned by the data set of both labeled and
unlabeled samples and the constraints provided by the labels of the labeled
samples, we learn the variable class labels for all the samples. Furthermore,
to improve the discriminative ability of the learned sparse codes, we assume
that the class labels could be predicted from the sparse codes directly using a
linear classifier. By solving the codebook, sparse codes, class labels and
classifier parameters simultaneously in a unified objective function, we
develop a semi-supervised sparse coding algorithm. Experiments on two
real-world pattern recognition problems demonstrate the advantage of the
proposed methods over supervised sparse coding methods on partially labeled
data sets
Global Well-Posedness of Classical Solutions with Large Oscillations and Vacuum to the Three-Dimensional Isentropic Compressible Navier-Stokes Equations
We establish the global existence and uniqueness of classical solutions to
the Cauchy problem for the isentropic compressible Navier-Stokes equations in
three spatial dimensions with smooth initial data which are of small energy but
possibly large oscillations with constant state as far field which could be
either vacuum or non-vacuum. The initial density is allowed to vanish and the
spatial measure of the set of vacuum can be arbitrarily large, in particular,
the initial density can even have compact support. These results generalize
previous results on classical solutions for initial densities being strictly
away from vacuum, and are the first for global classical solutions which may
have large oscillations and can contain vacuum states.Comment: 30 page
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