Quantum anomalous Hall effect and related topological electronic states

Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically doped topological insulator (TI) completed a quantum Hall trio—quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that the intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time-reversal symmetry (TRS) broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as TIs and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.     

Crystal Morphology of High-Pressure Crystallized Bisphenol-A Polycarbonate

High-pressure crystallized bisphenol-A polycarbonate (BAPC) samples were investigated using wide-angle X-ray diffraction (WAXD), differential scanning calorimetry (DSC), and scanning electron microscopy (SEM). The results showed that BAPC chain-extended crystals with c-axis thickness around 2.0 μm were developed through the melt crystallization. Furthermore, a high-crystallinity BAPC sample with a wide variety of microstructures was obtained by a stepwise double-heat treatment at high pressure. In the sample, individual spherulites can be easily exposed and isolated with selective etching, which results in open porous microspheres. These spheres provide the possibility to study the spherulite structure in three dimensions. The open porous microspheres may have functional applications, such as catalyst support and for other surface active materials.     

Theoretical study of LiCl− and LiBr− molecular ions

The molecular structures and spectroscopic constants of the ground electronic states of LiCl^? and LiBr^? are investigated with the coupled-cluster method. To improve the accuracy of our calculations, we have employed the extrapolation schemes as well as corrections of the core–valence correlation and scalar relativistic effect. The equilibrium parameters, potential energy curves, force constants, vibrational energy levels and spectroscopic parameters of both molecular ions are derived, in which those of LiBr^? are reported for the first time. The electron affinities and vertical detachment energies of neutral and anionic LiCl and LiBr are also evaluated.     

Second-Order Smoothing Objective Penalty Function for Constrained Optimization Problems

In this article, a novel objective penalty function as well as its second-order smoothing is introduced for constrained optimization problems (COP). It is shown that an optimal solution to the second-order smoothing objective penalty optimization problem is an optimal solution to the original optimization problem under some mild conditions. Based on the second-order smoothing objective penalty function, an algorithm that has better convergence is introduced. Numerical examples illustrate that this algorithm is efficient in solving COP.     

On the rigidity theorems for lagrangian translating solitons in pseudo-Euclidean space I

Let f be a smooth strictly convex solution of
defined on a domain Ω C R^n, where ai, bi and c are constants. Then the graph Mvf of △f is a spacelike translating soliton for mean curvature flow in pseudo-Euclidean space with the translating vector（al, a2, . ., an; bz, b2, , bn）. In this paper, we will use alCfine technique to show a Berustein Theorem： if the graph Mvf is complete, then f（x） must be a quadratic polynomial and Mvf is an ailine n-plane.     

Asymptotic error expansions for hypersingular integrals

This paper presents quadrature formulae for hypersingular integrals $\int_a^b\frac{g(x)}{|x-t|^{1+\alpha }}\mathrm{d}x$ , where a?<?t?<?b and 0?<?α?≤?1. The asymptotic error estimates obtained by Euler–Maclaurin expansions show that, if g(x) is 2m times differentiable on [a,b], the order of convergence is O(h ^2μ ) for α?=?1 and O(h ^2μ???α ) for 0?<?α?<?1, where μ is a positive integer determined by the integrand. The advantages of these formulae are as follows: (1) using the formulae to evaluate hypersingular integrals is straightforward without need of calculating any weight; (2) the quadratures only involve g(x), but not its derivatives, which implies these formulae can be easily applied for solving corresponding hypersingular boundary integral equations in that g(x) is unknown; (3) more precise quadratures can be obtained by the Richardson extrapolation. Numerical experiments in this paper verify the theoretical analysis.     

Two Equivalent Properties of \mathcal{Z}_3-Connectivity

The concept of group connectivity was introduced by Jaeger et al. (J Comb Theory Ser B 56:165–182, 1992) for the study of integer flows. The concept of all generalized Tutte-orientations was introduced by Barát and Thomassen (J Graph Theory 52:135–146, 2006) for the study of claw-decompositions of graphs. In this paper, we establish the equivalence of the following 3 properties: a graph is $\mathcal{Z}_3$ -connected, a graph admits all generalized Tutte-orientations and a graph is 3-flow contractible. We also give some applications of this result.     

Experimental validation of domain-level gradient-based and hierarchical PCE-based routing and control in heterogeneous optical networks

A domain-level gradient-based routing （DLR） algorithm for heterogeneous optical networks with syn- chronous digital hierarchy and optical transport network domains is proposed and experimentally vali- dated. This algorithm classifies domains into groups with incremental levels on the basis of domain-level partitioning, and guides paths level by level along a gradient on the basis of interdomain routing tree evolution. The proposed algorithm is implemented in the hierarchical path computation element-based control architecture for connection provisioning. Testbeds with commercial and emulated nodes are es- tablished to verify the feasibility and performance of the algorithm. Experimental and emulation results show that DLR effectively performs in terms of network blocking probability, real time characteristics, and scalability.