Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations

In this paper, we are concerned with the partial regularity of the suitable weak solutions to the fractional MHD equations in $\mathbb{R}^{n}$ for $n=2,\,3$. In comparison with the work of the 3D fractional Navier-Stokes equations obtained by Tang and Yu in [24, Commun. Math. Phys. 334: 1455--1482, 2015], our results include their endpoint case $\alpha=3/4$ and the external force belongs to more general parabolic Morrey space. Moreover, we prove some interior regularity criteria just via the scaled mixed norm of the velocity for the suitable weak solutions to the fractional MHD equations.Comment: 33 page

Containment Control of Linear Multi-Agent Systems with Multiple Leaders of Bounded Inputs Using Distributed Continuous Controllers

This paper considers the containment control problem for multi-agent systems with general linear dynamics and multiple leaders whose control inputs are possibly nonzero and time varying. Based on the relative states of neighboring agents, a distributed static continuous controller is designed, under which the containment error is uniformly ultimately bounded and the upper bound of the containment error can be made arbitrarily small, if the subgraph associated with the followers is undirected and for each follower there exists at least one leader that has a directed path to that follower. It is noted that the design of the static controller requires the knowledge of the eigenvalues of the Laplacian matrix and the upper bounds of the leaders' control inputs. In order to remove these requirements, a distributed adaptive continuous controller is further proposed, which can be designed and implemented by each follower in a fully distributed fashion. Extensions to the case where only local output information is available are discussed.Comment: 16 pages, 4 figures. arXiv admin note: text overlap with arXiv:1312.737

A new Coherent-Entangled state generated by an asymmetric beam splitter and its applications

A new kind of tripartite non-symmetric coordinate coherent-entangled state (TNCCES) $| \beta,\gamma,x >$ is proposed which exhibits the properties of both coherence and entanglement and makes up a new quantum mechanical representation.We investigate some properties of TNCCES such as completeness and orthogonality which prove it is just a tripartite complete continuous coordinate base. A protocol for generating TNCCES is proposed using asymmetric beam splitter. And in application of TNCCES, we find its corresponding Wigner operator and carry out its marginal distribution form; further a new tripartite entangled squeezed operator is also presented. The multipartite CES and its generation are also disussed

Anisotropic thermal expansion and thermomechanic properties of monolayer β\beta-Te

Recently, $\beta$-Te (atomically 2D tellurium) with rectangular crystal structure has been synthesized successfully on highly oriented pyrolytic graphite substrates by using molecular beam epitaxy. It has been found possessing remarkable properties such as ultralow lattice thermal conductivity and high thermoelectric efficiency. Based on the first-principles calculations, we study the thermal expansion and thermomechanic properties of the experimental phase monolayer $\beta$-Te, using quasiharmonic approach. It is found $\beta$-Te shows large positive thermal expansion at elevated temperature, while the linear thermal expansion coefficient is negative along a direction at very low temperature. The linear thermal expansion coefficient along b direction is 4.9*10$^{-5}$ K$^{-1}$ at 500 K, which is considerably large in 2D materials. $\beta$-Te exhibits strong in-plane anisotropy, including thermal expansion, 2D elastic moduli and Poisson's ratios. However, the elastic moduli, Poisson's ratios and the in-plane anisotropy are weakened with increasing temperature, and the variations are dominated by the generalized mode Gr\"{u}neisen parameters.Comment: 25 pages, 7 figures, 14 formula

Remarks on the singular set of suitable weak solutions to the 3D Navier-Stokes equations

In this paper, let $\mathcal{S}$ denote the possible interior singular set of suitable weak solutions of the 3D Navier-Stokes equations. We improve the known upper box-counting dimension of this set from $360/277(\approx1.300)$ in [24] to $975/758(\approx1.286)$. It is also shown that $\Lambda(\mathcal{S},r(\log(e/r))^{\sigma})=0(0\leq\sigma<27/113)$, which extends the previous corresponding results concerning the improvement of the classical Caffarelli-Kohn-Nirenberg theorem by a logarithmic factor in Choe and Lewis [3, J. Funct. Anal., 175: 348-369, 2000] and in Choe and Yang et al. [4, Comm. Math. Phys, 336: 171-198, 2015]. The proof is inspired by a new $\varepsilon$-regularity criterion proved by Guevara and Phuc in [7, Calc. Var. 56:68, 2017].Comment: In this version, Theorem 1.3 and its proof are revised. The reason for the modification of Theorem 1.3 is to answer a issue proposed by the reviewer. An author is adde

Neural networks for stock price prediction

Due to the extremely volatile nature of financial markets, it is commonly accepted that stock price prediction is a task full of challenge. However in order to make profits or understand the essence of equity market, numerous market participants or researchers try to forecast stock price using various statistical, econometric or even neural network models. In this work, we survey and compare the predictive power of five neural network models, namely, back propagation (BP) neural network, radial basis function (RBF) neural network, general regression neural network (GRNN), support vector machine regression (SVMR), least squares support vector machine regresssion (LS-SVMR). We apply the five models to make price prediction of three individual stocks, namely, Bank of China, Vanke A and Kweichou Moutai. Adopting mean square error and average absolute percentage error as criteria, we find BP neural network consistently and robustly outperforms the other four models.Comment: 13 pages, 3 figures, 4 table

Blur Robust Optical Flow using Motion Channel

It is hard to estimate optical flow given a realworld video sequence with camera shake and other motion blur. In this paper, we first investigate the blur parameterization for video footage using near linear motion elements. we then combine a commercial 3D pose sensor with an RGB camera, in order to film video footage of interest together with the camera motion. We illustrates that this additional camera motion/trajectory channel can be embedded into a hybrid framework by interleaving an iterative blind deconvolution and warping based optical flow scheme. Our method yields improved accuracy within three other state-of-the-art baselines given our proposed ground truth blurry sequences; and several other realworld sequences filmed by our imaging system.Comment: Preprint of our paper accepted by Neurocomputin

Tests for CPT sum rule and U-spin violation in Time-dependent CP violation of Bs0→K+K−B^0_s \to K^+ K^- and Bd0→π+π−B^0_d \to \pi^+ \pi^-

Recent LHCb data for time-dependent CP violation in $B_d^0 \to \pi^+\pi^-$ and $B^0_s\to K^+K^-$ show deviations from theoretical predictions. Besides their central values for $\mathcal C_{K^+K^-}$, $\mathcal S_{K^+K^-}$ and $\mathcal A^{\Delta \Gamma}_{K^+K^-}$ violate quantum mechanic CPT invariant sum rule (CPT sum rule) prediction of $|\mathcal C_{K^+K^-}|^2 + |\mathcal S_{K^+K^-}| ^2 + |\mathcal A^{\Delta \Gamma}_{K^+K^-}|^2 = 1$ (LHCb data imply the sum to be $0.67\pm 0.20$.), their values for $\mathcal C_{K^+ K^-}= 0.24\pm 0.06\pm {0.02}$ and $\mathcal C_{\pi^+ \pi^-} = - 0.24\pm 0.07\pm 0.01$ also show large violation of SU(3) or its U-spin sub-group symmetry (SU(3)/U) relation $\mathcal C_{K^+ K^-} /\mathcal C_{\pi^- \pi^+} = - \mathcal B(B_d^0 \to \pi^- \pi^+)\tau_{B^0_s}/\mathcal B(B^0_s \to K^+ K^-)\tau_{B_d^0}$ (LHCb data imply the ratio of left-side to right-side to be $4.67\pm 1.88$.) . The LHCb results need to be further confirmed to be taken seriously. We suggest to use time-dependent CP violation in $B_s\to K^0\bar K^0, \pi^+\pi^-, \pi^0\pi^0$ to further test the CPT sum rule. Assuming that the sum rule holds, we propose that violation of the SU(3)/U relation may indicate a large FSI phase difference in the $\pi^+\pi^-$ and $K^+K^-$ re-scattering. We suggest several other U-spin pairs of $B\to PP$ decays to further test SU(3)/U relations.Comment: 12 pages, 1 figure; ACP of $B^0_d \to \pi^+ \pi^-$ updated to the latest HFAG average, figures slightly changed, a few comments and refs adde

A High-contrast Imaging Algorithm: Optimized Image Rotation and Subtraction

Image Rotation and Subtraction (IRS) is a high-contrast imaging technique which can be used to suppress the speckles noise and facilitate the direct detection of exoplanets. IRS is different from Angular Differential Imaging (ADI), in which it will subtract a copy of the image with 180 degrees rotated around its PSF center, rather than the subtraction of the median of all of the PSF images. Since the planet itself will be rotated to the other side of the PSF, IRS does not suffer from planet self-subtraction. In this paper, we have introduced an optimization algorithm to IRS (OIRS), which can provide an extra contrast gain at small angular separations. The performance of OIRS has been demonstrated with ADI data. We then made a comparison of the signal to noise ratio (S/N) achieved by algorithms of locally optimized combination of images (LOCI) and OIRS. Finally we found that OIRS algorithm can deliver a better S/N for small angular separations.Comment: 18 pages, 8 eps figures, 1 table, accepted for publication in The Astrophysical Journalon on Jan. 10th, 201