25,699 research outputs found
Emergent cosmic space in Rastall theory
Padmanabhan's emergent cosmic space proposal is employed to study the Rastall
theory which involves modifying the conservation law of energy-momentum tensor.
As a necessary element for this approach, we firstly propose a modified Komar
energy which reflects the evolution of the energy-momentum itself in the case
of a perfect fluid. After that, an expansion law is invoked to reobtain the
Friedmann equation in this theory.Comment: 8 pages, no figures, published version in CQ
Uniformly expanding vacuum: a possible interpretation of the dark energy
Following the spirit of the equivalence principle, we take a step further to
recognize the free fall of the observer as a method to eliminate causes that
would lead the perceived vacuum to change its original state. Thus, it is
expected that the vacuum should be in a rigid Minkowski state or be uniformly
expanding. By carefully investigating the impact on measurement caused by the
expansion, we clarify the exact meaning of the uniformly expanding vacuum and
find that this proposal may be able to explain the current observations of an
accelerating universe.Comment: 5 pages, accepted by Physics of the Dark Univers
Generalized Hodge dual for torsion in teleparallel gravity
For teleparallel gravity in four dimensions, Lucas and Pereira have shown
that a generalized Hodge dual for torsion tensor can be defined with
coefficients determined by mathematical consistency. In this paper, we
demonstrate that a direct generalization to other dimensions fails and no new
generalized Hodge dual operator could be given. Furthermore, if one enforces
the definition of a generalized Hodge dual to be consistent with the action of
teleparallel gravity in general dimensions, the basic identity for any sensible
Hodge dual would require an \textit{ad hoc} definition for the second Hodge
dual operation which is totally unexpected. Therefore, we conclude that at
least for the torsion tensor, the observation of Lucas and Pereira only applies
to four dimensions.Comment: 12 pages, corrected typos, rearranged reference
Learning Pixel-Distribution Prior with Wider Convolution for Image Denoising
In this work, we explore an innovative strategy for image denoising by using
convolutional neural networks (CNN) to learn pixel-distribution from noisy
data. By increasing CNN's width with large reception fields and more channels
in each layer, CNNs can reveal the ability to learn pixel-distribution, which
is a prior existing in many different types of noise. The key to our approach
is a discovery that wider CNNs tends to learn the pixel-distribution features,
which provides the probability of that inference-mapping primarily relies on
the priors instead of deeper CNNs with more stacked nonlinear layers. We
evaluate our work: Wide inference Networks (WIN) on additive white Gaussian
noise (AWGN) and demonstrate that by learning the pixel-distribution in images,
WIN-based network consistently achieves significantly better performance than
current state-of-the-art deep CNN-based methods in both quantitative and visual
evaluations. \textit{Code and models are available at
\url{https://github.com/cswin/WIN}}
Wide Inference Network for Image Denoising via Learning Pixel-distribution Prior
We explore an innovative strategy for image denoising by using convolutional
neural networks (CNN) to learn similar pixel-distribution features from noisy
images. Many types of image noise follow a certain pixel-distribution in
common, such as additive white Gaussian noise (AWGN). By increasing CNN's width
with larger reception fields and more channels in each layer, CNNs can reveal
the ability to extract more accurate pixel-distribution features. The key to
our approach is a discovery that wider CNNs with more convolutions tend to
learn the similar pixel-distribution features, which reveals a new strategy to
solve low-level vision problems effectively that the inference mapping
primarily relies on the priors behind the noise property instead of deeper CNNs
with more stacked nonlinear layers. We evaluate our work, Wide inference
Networks (WIN), on AWGN and demonstrate that by learning pixel-distribution
features from images, WIN-based network consistently achieves significantly
better performance than current state-of-the-art deep CNN-based methods in both
quantitative and visual evaluations. \textit{Code and models are available at
\url{https://github.com/cswin/WIN}}.Comment: There is a code issue that makes our work may be regarded as entirely
out the way of the correct research direction. Therefore, we add the
correction into abstract to answer the questions being often asked. Besides.
we hope the most talent you may try to think about how to map the particular
matrix to generative ones. Then, you may have a significant innovation
publishe
On the unsplittable minimal zero-sum sequences over finite cyclic groups of prime order
Let be a prime and let be a cyclic group of order . Let
be a minimal zero-sum sequence with elements over , i.e., the sum of
elements in is zero, but no proper nontrivial subsequence of has sum
zero. We call is unsplittable, if there do not exist in and such that and is also a minimal zero-sum sequence.
In this paper we show that if is an unsplittable minimal zero-sum sequence
of length , then
or
. Furthermore, if is a
minimal zero-sum sequence with , then \ind(S) \leq 2.Comment: 11 page
gravity from holographic Ricci dark energy model with new boundary conditions
Commonly used boundary conditions in reconstructing gravity from
holographic Ricci dark energy model (RDE) are found to cause some problem, we
therefore propose new boundary conditions in this paper. By reconstructing
gravity from the RDE with these new boundary conditions, we show that
the new ones are better than the present commonly used ones since they can give
the physically expected information, which is lost when the commonly used ones
are taken in the reconstruction, of the resulting theory. Thus, the new
boundary conditions proposed here are more suitable for the reconstruction of
gravity.Comment: 10 page
Exponential Decay for Lions-Feireisl's Weak Solutions to the Barotropic Compressible Navier-Stokes Equations in 3D Bounded Domains
For barotropic compressible Navier-Stokes equations in three-dimensional (3D)
bounded domains, we prove that any finite energy weak solution obtained by
Lions [Mathematical topics in fluid mechanics, Vol. 2. Compressible
models(1998)] and Feireisl-Novotn\'{y}-Petzeltov\'{a} [J. Math. Fluid Mech.
3(2001), 358-392] decays exponentially to the equilibrium state. This result is
established by both using the extra integrability of the density due to Lions
and constructing a suitable Lyapunov functional just under the framework of
Lions-Feireisl's weak solutions.Comment: 16 page
Positive radial solutions for coupled Schr\"{o}dinger system with critical exponent in
We study the following coupled Schr\"odinger system \ds -\Delta
u+u=u^{2^*-1}+\be u^{\frac{2^*}{2}-1}v^{\frac{2^*}{2}}+\la_1u^{\al-1}, &x\in
\R^N, \ds -\Delta v+v=v^{2^*-1}+\be
u^{\frac{2^*}{2}}v^{\frac{2^*}{2}-1}+\la_2v^{r-1}, &x\in \R^N, u,v > 0, &x\in
\R^N, where N\geq 5, \la_1,\la_2>0,\be\neq 0, 2<\al,r<2^*,2^*\triangleq
\frac{2N}{N-2}. Note that the nonlinearity and the coupling terms are both
critical. Using the Mountain Pass Theorem, Ekeland's variational principle and
Nehari mainfold, we show that this critical system has a positive radial
solution for positive \be and some negative \be respectively.Comment: 22 pages. arXiv admin note: text overlap with arXiv:1209.2522 by
other authors. text overlap with arXiv:1209.2522 by other author
Test for a Mean Vector with Fixed or Divergent Dimension
It has been a long history in testing whether a mean vector with a fixed
dimension has a specified value. Some well-known tests include the Hotelling
-test and the empirical likelihood ratio test proposed by Owen [Biometrika
75 (1988) 237-249; Ann. Statist. 18 (1990) 90-120]. Recently, Hotelling
-test has been modified to work for a high-dimensional mean, and the
empirical likelihood method for a mean has been shown to be valid when the
dimension of the mean vector goes to infinity. However, the asymptotic
distributions of these tests depend on whether the dimension of the mean vector
is fixed or goes to infinity. In this paper, we propose to split the sample
into two parts and then to apply the empirical likelihood method to two
equations instead of d equations, where d is the dimension of the underlying
random vector. The asymptotic distribution of the new test is independent of
the dimension of the mean vector. A simulation study shows that the new test
has a very stable size with respect to the dimension of the mean vector, and is
much more powerful than the modified Hotelling -test.Comment: Published in at http://dx.doi.org/10.1214/13-STS425 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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