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

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

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

Starch function in ornamental tobacco floral nectary development

Morphological changes of floral nectary gland and subcellular transition of floral nectary cells of ornamental tobacco LxS8 were exclusively investigated in this study. Enlargement of the floral nectary gland of ornamental tobacco LxS8 that occurs during development is accompanied by a major accumulation of Periodic Acid-Schiff\u27s staining (PAS-staining) starch grains in nectary amyloplasts. Quantification of starch purified from the nectary at various stages of development showed little starch at an early developmental stage, soon thereafter the amount of starch increased dramatically, reaching a peak approximately 24 hours prior to anthesis. After this time, the amount of starch declined dramatically until the flower reached anthesis, suggesting that the accumulated starch was converted to sugars (sucrose, glucose, and fructose) for nectar production that occurs prior to anthesis. A Transmission Electron Microscopy (TEM) study of plastid development further verified that ornamental tobacco nectaries accumulate large amounts of starch during floral development and hydrolyze that starch prior to anthesis. Compositional and structural analyses of nectary starch showed that amylose content and degree of amylopectin branching varied during nectary development. The average chain length in amylopectin was relatively short at early developmental stages, reached maximal length towards the end of nectary development, and was reduced again at anthesis, consistent with the synthesis of an increasingly complex form of starch up to middle stages of nectary development, followed by decreases in starch complexity and amount due to starch degradation in the mature nectary.;Tobacco floral nectaries undergo changes in form and function. As nectaries change from green to orange, a new pigment is expressed. Analysis demonstrated that it is beta-carotene. Plastids undergo dramatic changes. Early in nectary development, they divide and by stage 9 (S9) they are engorged with starch. About S9, nectaries shift from quiescent anabolism to active catabolism resulting in starch breakdown and production of nectar sugars. Starch is replaced by osmiophilic bodies, which contain needle-like carotenoid crystals. Between S9 and S12, amyloplasts are converted to chromoplasts. Changes in carotenoids and ascorbate were assayed and are expressed at low levels early in development; however, following S9 metabolic shift, syntheses of beta-carotene and ascorbate greatly increase in advance of expression of nectar redox cycle. We propose that biosynthesis of these antioxidants is governed by availability of substrate molecules that arise from starch breakdown. These processes and events may be amenable to molecular manipulation to provide a better system for insect attraction, cross pollination, and hybridization.;Thirty-nine different nectary-expressed cDNAs from the nectaries of ornamental tobacco plants that encode 14 different starch metabolic enzymes, 7 different mevalonate metabolic enzymes, 7 different MEP metabolic enzymes, 8 different beta-carotene metabolic enzymes, and 3 different ascorbate metabolic enzymes were identified from ornamental tobacco LxS8. The translated protein sequences were used to identify gene functionality by comparison with well characterized protein sequences from Arabidopsis, maize and solanaceous species. Subsequently RT-PCR or real-time RT-PCR were used to evaluate gene expression throughout nectary development. This analysis revealed that starch metabolism was highly regulated at transcriptional level in ornamental tobacco floral nectary. Three different classes of starch metabolic gene expression pattern appeared. Most starch anabolic genes, including starch synthase 1 (SS1), starch synthase 3 (SS3) and granule-bound starch synthase (GBSS), were expressed early in nectary development (Stage 2 and Stage 6), and the expression was significantly down-regulated after Stage 9. In contrast, the starch catabolic genes, including branching enzyme 1 (BE1), isoamylase 1 (ISA1), alpha-amylase (AMY), beta-amylase (BMY), were not highly expressed at early stages, but were significantly induced by Stage 9 of nectary development. A third class of gene expression that included R1, phosphorylase (PHO), and starch branching enzyme 2 (SBE2) were expressed through nectary development. Immnunodetection shows that ADP-glucose pyrophosphorylase (AGPase) small subunit and sucrose synthase (SuSy) were highly expressed at early stages. Enzyme activity analysis of AGPase also shows that enzyme activity was higher at early stages. Transcript analysis for carotenoid and ascorbate biosynthetic pathways showed that these genes are significantly expressed at S6, prior to the S9 metabolic shift. Thus, formation of antioxidants beta-carotene and ascorbate after the metabolic shift is independent of transcriptional regulation.;We also evaluated the transport of radiolabeled sugars nectar. Consistency in the amounts and ratios of radiolabeled sugars in nectar indicates that the transported photosynthate sugars were subject to metabolic constraints in the nectary tissue prior to their incorporation into nectar. The velocity of radiolabeled sugars accumulated in nectar illustrates that transported photosynthate contributes to the later nectar production. A series of transgenic plants had been generated. The genetic evidence verified that starch regulates the timing and amount of floral nectar

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

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

Emergence of cooperation induced by preferential learning

The evolutionary Prisoner's Dilemma Game (PDG) and the Snowdrift Game (SG) with preferential learning mechanism are studied in the Barab\'asi-Albert network. Simulation results demonstrate that the preferential learning of individuals remarkably promotes the cooperative behavior for both two games over a wide range of payoffs. To understand the effect of preferential learning on the evolution of the systems, we investigate the time series of the cooperator density for different preferential strength and payoffs. It is found that in some specific cases two games both show the $1/f$-scaling behaviors, which indicate the existence of long range correlation. We also figure out that when the large degree nodes have high probability to be selected, the PDG displays a punctuated equilibrium-type behavior. On the contrary, the SG exhibits a sudden increase feature. These temporary instable behaviors are ascribed to the strategy shift of the large degree nodes.Comment: 10 pages, 5 figure

Dynamical Coarse Graining of Large Scale-Free Boolean networks

We present a renormalization-grouplike method performed in the state space for detecting the dynamical behaviors of large scale-free Boolean networks, especially for the chaotic regime as well as the edge of chaos. Numerical simulations with different coarse-graining level show that the state space networks of scale-free Boolean networks follow universal power-law distributions of in and out strength, in and out degree, as well as weight. These interesting results indicate scale-free Boolean networks still possess self-organized mechanism near the edge of chaos in the chaotic regime. The number of state nodes as a function of biased parameter for distinct coarse-graining level also demonstrates that the power-law behaviors are not the artifact of coarse-graining procedure. Our work may also shed some light on the investigation of brain dynamics.Comment: 5 pages, 6 figure