Abstract:
F. Labourie [arXiv:1212.5015] characterized the Hitchin components for $\operatorname{PSL}(n, \mathbb{R})$ for any $n>1$ by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce the rank $n$ swapping algebra, which is the quotient of the swapping algebra by the $(n+1)\times(n+1)$ determinant relations. The main results are the well-definedness of the rank $n$ swapping algebra and the "cross-ratio" in its fraction algebra. As a consequence, we use the sub fraction algebra of the rank $n$ swapping algebra generated by these "cross-ratios" to characterize the $\operatorname{PSL}(n, \mathbb{R})$ Hitchin component for a fixed $n>1$. We also show the relation between the rank $2$ swapping algebra and the cluster $\mathcal{X}_{\operatorname{PGL}(2,\mathbb{R}),D_k}$-space.

Abstract:
Swapping algebra, introduced by Fran\c{c}ois Labourie, is a commutative Poisson algebra generated by pairs of points of a cyclically ordered set $\mathcal{P}$. In this paper, we induce a Poisson structure on the configuration space $\mathcal{M}_{N,1}$ of $N$ twisted polygons in $\mathbb{RP}^{1}$ by the swapping bracket. Then we relate asymptotically the dual of this Poisson structure to the Virasoro algebra on $\mathcal{M}_{N,1}$. At last, we compare this Poisson structure with another Poisson strcture on $\mathcal{M}_{N,1}$ induced from the affine $\operatorname{SL}(2,\mathbb{R})$ Poisson-Lie group structure, as a result, the two Poisson structure on $\mathcal{M}_{N,1}$ are compatible.

Abstract:
In our previous paper arXiv:math/1411.2796, we introduce the rank $n$ swapping algebra, which is a Poisson algebra associated to an affine variety defined by pair of points on a circle and their determinant relations. In this paper, we show how the rank $n$ swapping algebra is related to a naturally generalized Weil-Petersson form. More precisely, let the rank $n$ swapping multifraction algebra $\mathcal{B}_n(\mathcal{P})$ be the sub fraction algebra of the rank $n$ swapping algebra generated by "cross ratios". Given a generic configuration space $\operatorname{Conf}_{k,n}$ of $k$ flags in $\mathbb{RP}^{n-1}$ and its associated triangulation, we give a Poisson algebra monomorphism from the fraction algebra generated by the Fock-Goncharov coordinates for $\operatorname{Conf}_{k,n}$ into $\mathcal{B}_n(\mathcal{P})$ with respect to the Fock-Goncharov's Poisson bracket and the swapping Poisson bracket. This gives a geometric interpretation of the natural Poisson structure described by Fock and Goncharov in arXiv:math/0311149 via pairs of points on a circle. As a consequence, we reprove that the Poisson structure of Fock-Goncharov does not depend on triangulations.

Abstract:
Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the -norm minimization problem (2011). The advantage of this method is its simplicity and lower storage. In this paper, based on new nonsmooth equations reformulation, we investigate new nonsmooth equations-based algorithms for solving -norm minimization problems. Under mild conditions, we show that the proposed algorithms are globally convergent. The preliminary numerical results demonstrate the effectiveness of the proposed algorithms. 1. Introduction We consider the -norm minimization problem where , , , and is a nonnegative parameter. Throughout the paper, we use and to denote the Euclidean norm and the -norm of vector , respectively. Problem (1.1) has many important practical applications, particularly in compressed sensing (abbreviated as CS) [1] and image restoration [2]. It can also be viewed as a regularization technique to overcome the ill-conditioned, or even singular, nature of matrix , when trying to infer from noiseless observations or from noisy observations , where is the white Gaussian noise of variance [3–5]. The convex optimization problem (1.1) can be cast as a second-order cone programming problem and thus could be solved via interior point methods. However, in many applications, the problem is not only large scale but also involves dense matrix data, which often precludes the use and potential advantage of sophisticated interior point methods. This motivated the search of simpler first-order algorithms for solving (1.1), where the dominant computational effort is a relatively cheap matrix-vector multiplication involving and . In the past few years, several first-order algorithms have been proposed. One of the most popular algorithms falls into the iterative shrinkage/thresholding (IST) class [6, 7]. It was first designed for wavelet-based image deconvolution problems [8] and analyzed subsequently by many authors, see, for example, [9–11]. Figueiredo et al. [12] studied the gradient projection and Barzilai-Borwein method [13] (denoted by GPSR-BB) for solving (1.1). They reformulated problem (1.1) as a box-constrained quadratic program and solved it by a gradient projection and Barzilai-Borwein method. Wright et al. [14] presented sparse reconstruction algorithm (denoted by SPARSA) to solve (1.1). Yun and Toh [15] proposed a block coordinate gradient descent algorithm for solving (1.1). Yang and Zhang [16] investigated alternating direction algorithms for solving (1.1). Quite recently, Xiao et al. [17] developed a nonsmooth equations-based algorithm (called

EVT (electric vehicle terminal) has played an important
role in EV (electric vehicle) operation. Based on research status of vehicle
terminal, EVT brought about in the future should have the following functions:
(1) fundamental functions, including real-time monitoring of batteries,
guidance in station, position guidance of charging/battery-swap infrastructures,
communication with OMS (operation and management system), and so on; (2) advanced
functions, including but not limited to multi-media entertainment, subscribing
and payment for charging/battery-swap, identification, and safety control
during driving. Complete design of new-generation EVT in software structure and
hardware architecture is proposed; a new idea of the application of EVT in EV
industry is put forward.

Abstract:
Organic pollutants coming from various industry processes are harmful to the environment, and semiconductor heterostructure is a promising candidate catalyst for poisonous wastewater treatment in the future. In this study, CuO_{x}/MnO_{2} heterostructures were successfully constructed, using a facile and effective hydrothermal method and chemical both/calcination route, which exhibited higher photocatalytic activity towards the photodegradation of organic contaminants under visible-light driven irradiation. The resulting CuO_{x}/MnO_{2} heterostructures were systematically characterized using various microscopic and spectroscopic techniques. Morphological characterizations show that the CuO_{x} nanoparticles are well anchored on the surface of the MnO_{2} nanowires (NMs). The photocatalytic activity enhancement of the CuO_{x}/MnO_{2} heterostructures (M-4) could be ascribed to the introduction of CuO_{x} on the surface of MnO_{2} NWs and the efficient separation of the electron-hole pairs compared to other CuO_{x}/MnO_{2} heterostructures and pure MnO_{2} NMs. These results show that CuO_{x}/MnO_{2} heterostructures can be a suitable candidate for efficient visible light photocatalysts.

Abstract:
To take advantage of micelle to solvent stacking (MSS) to achieve more sensitivity enhancement with enough selectivity, the application of capillary electrophoretic online sequential concentration based on the MSS was reviewed. MSS has been coupled to sweeping FASS, FASI and normal EKI. Furthermore, multiple stacking by coupling MSS with more than one stacking method has also been reported. It is more sensitive and selective than solely used of one or two stacking methods and is very suitable for complex and trace sample analysis.

Abstract:
Zyxin is a focal adhesion protein that has been implicated in the modulation of cell adhesion and motility, and is hypothesized to be a mechano-sensor in integrin-mediated responses to mechanical force. To test the functional role of zyxin in the mechanotransduction of microvascular smooth muscle cells (VSMC), we utilized atomic force microscopy (AFM) to apply localized pulling forces to VSMC through a fibronectin (FN) focal adhesion induced by a FN-coated bead on cell surface. Application of force with the AFM induced an increase of zyxin accumulation at the site of the FN-bead focal adhesion that accompanied the VSMC contractile response. Whereas, reduction of zyxin expression by using a zyxin-shRNA construct abolished the VSMC contractile response to AFM pulling forces, even though the zyxin-silenced VSMCs displayed increased adhesion to FN in both AFM adhesion assays and cell adhesion assays. The reduced zyxin expression significantly impaired cell spreading and reorganization of the actin cytoskeleton that could indicate a possible underlying reason for the loss of a contractile response to mechanical force. Consistent with these observations, in zyxin-silenced VSMC, we also observed a reduced expression of Rac1, which plays an important role in the actin reorganization in VSMC, but increased thyroid receptor-interacting proteins (TRIP6) and FAK expression, the latter being a major protein that promote cell adhesion. In conclusion, these data support an important enabling role for zyxin in VSMCs ability to mechanically respond to applied force.

Abstract:
We study the dynamical process of disentanglement of two qubits and two qutrits coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. We use the concurrence and negativity to quantify entanglement of two qubits and two qutrits, respectively. Explicit connections between the concurrence (negativity) and the decoherence factors are given for two initial states, the pure maximally entangled state and the mixed Werner state. We find that the concurrence and negativity decay exponentially with fourth power of time in the vicinity of critical point of the environmental system.

Themulti-agenttheory is
introduced and applied in the way to strike the control amount of emergency
control according to stability margin, based on which an emergency control
strategy of the power system is presented. The multi-agent control structure
which is put forward in this article has three layers: system agent, areal
agent and local agents. System agent sends controlling execution signal to the
load-local agent according to the position and the amount of load shedding
upload from areal agent; The areal agent judges whether the power system is
stable by monitoring and analyzing the maximum relative power angle. In the
condition of instability, determines the position of load-shedding, and the
optimal amount of load-shedding according to the stability margin based on the
corrected transient energy function, upload control amount to system agent;
local-generator agent is mainly used for real-time monitoring the power angle
of generator sets and uploading it to the areal agency, local-loads agent
control load by receiving the control signal from system agent. Simulations on
IEEE39 system show that the proposed control strategy improves the system
stability.