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 $p > 155$ be a prime and let $G$ be a cyclic group of order $p$. Let $S$ be a minimal zero-sum sequence with elements over $G$, i.e., the sum of elements in $S$ is zero, but no proper nontrivial subsequence of $S$ has sum zero. We call $S$ is unsplittable, if there do not exist $g$ in $S$ and $x,y \in G$ such that $g=x+y$ and $Sg^{-1}xy$ is also a minimal zero-sum sequence. In this paper we show that if $S$ is an unsplittable minimal zero-sum sequence of length $|S|= \frac{p-1}{2}$, then $S=g^{\frac{p-11}{2}}(\frac{p+3}{2}g)^4(\frac{p-1}{2}g)$ or $g^{\frac{p-7}{2}}(\frac{p+5}{2}g)^2(\frac{p-3}{2}g)$. Furthermore, if $S$ is a minimal zero-sum sequence with $|S| \ge \frac{p-1}{2}$, then \ind(S) \leq 2.Comment: 11 page

f(T)f(T) gravity from holographic Ricci dark energy model with new boundary conditions

Commonly used boundary conditions in reconstructing $f(T)$ 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 $f(T)$ 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 $f(T)$ theory. Thus, the new boundary conditions proposed here are more suitable for the reconstruction of $f(T)$ 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 RN (N≥5)\R^N\,(N\geq5)

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 $T^2$-test and the empirical likelihood ratio test proposed by Owen [Biometrika 75 (1988) 237-249; Ann. Statist. 18 (1990) 90-120]. Recently, Hotelling $T^2$-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 $T^2$-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