Distortion theorems for normalized biholomorphic quasi-convex mappings

In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball B ⁿ respectively.     

On the Decomposition Theorems for C∗-Algebras

Elliott dimension drop interval algebra is an important class among all C^?-algebras in the classification theory. Especially, they are building stones of AHD algebra and the latter contains all AH algebras with the ideal property of no dimension growth.In this paper, the authors will show two decomposition theorems related to the Elliott dimension drop interval algebra. Their results are key steps in classifying all AH algebras with the ideal property of no dimension growth.     

Uncertainty principles for locally compact quantum groups

In this paper, we prove the Donoho–Stark uncertainty principle for locally compact quantum groups and characterize the minimizer which are bi-shifts of group-like projections. We also prove the Hirschman–Beckner uncertainty principle for compact quantum groups and discrete quantum groups. Furthermore, we show Hardy's uncertainty principle for locally compact quantum groups in terms of bi-shifts of group-like projections.     

Variable sinh-Gaussian solitons in nonlocal nonlinear Schrödinger equation

Based on the nonlocal nonlinear Schrödinger equation that governs phenomenologically the propagation of laser beams in nonlocal nonlinear media, we theoretically investigate the propagation of sinh-Gaussian beams (ShGBs). Mathematical expressions are derived to describe the beam propagation, the intensity distribution, the beam width, and the beam curvature radius of ShGBs. It is found that the propagation behavior of ShGBs is variable and closely related to the parameter of sinh function (PShF). If the PShF is small, the transverse pattern of ShGBs keeps invariant during propagation for a proper input power, which can be regarded as solitons. If the PShF is large, it varies periodically, which is similar to the evolution of temporal higher-order solitons in nonlinear optical fiber. Numerical simulations are carried out to illustrate the typical propagation characteristics.     

Stronger Criteria for Nonseparability in n-Partite Quantum States

We investigate the multipartite entanglement in arbitrary dimensional systems, and separability criteria for nonseparability in n-partite quantum states are derived. Examples such as the generalized noisy-W state and the GHZ basis states mixed with white noise are provided to show that our criteria are independent of and stronger than previously reported ones. Our criteria can also be expressed by the elements of the density matrix, which allows a simple and practical evaluation and computation. The experimental implementation of our criteria is also discussed.     

N2/Ti微空心阴极放电等离子体阴极溅射模拟

采用Monte Carlo方法模拟N2/Ti微空心阴极放电等离子体阴极溅射过程,其中,氮离子(N2+,N+)轰击阴极表面采用PIC/MC模型模拟.计算溅射钛原子的热化过程、钛原子的密度及其平均能量分布.结果表明,沿各方向溅射出的90%金属Ti原子所带的初始能量小于30 eV,其散射角主要分布在30°和60°之间;溅射Ti原子在离微空心阴极壁约0.04 mm处出现热化极大值.     

Full automorphism group of the generalized symplectic graph

Let Fq be a finite field of odd characteristic, m, ν the integers with 1≤m≤ν and Ka 2ν× 2ν nonsingular alternate matrix over Fq. In this paper, the generalized symplectic graph GSp2ν (q, m) relative to K over Fq is introduced. It is the graph with m-dimensional totally isotropic subspaces of the 2ν-dimensional symplectic space F(2ν)q as its vertices and two vertices P and Q are adjacent if and only if the rank of PKQT is 1 and the dimension of P ∩ Q is m-1. It is proved that the full automorphism group of the graph GSp2ν(q, m) is the projective semilinear symplectic group PΣp(2ν, q).     

循环多胞形$C^{3}(6)$的对偶和单形乘积上的小覆盖

计算了循环多胞形$C^{3}(6)$的对偶和单形乘积上(可定向)小覆盖的等变同胚类的个数     

The mechanism of ring-opening polymerization of L-lactide by ICl3 catalysts: Halogen bond catalysis or participating in reactions?

The mechanism of ring-opening polymerization of L-lactide by iodine trichloride (ICl₃) catalyst has been explored by using density functional theory (DFT) calculations and three catalytic pathways were proposed. The first and second pathways belong to the halogen bond catalysis, and the third pathway involves the ICl₃ catalysts participating in reactions. When the carbonyl group was maintained involved in the reaction and activated catalytically by the halogen bond, there are two possible pathways. The first pathway involves only one transition state, and the second pathway requires two transition states. There is another pathway in which ICl₃ directly participates in the reaction, it is named the third pathway. Two different transition states of the four-membered rings are generated successively, the transfer of I─O bonds determined the progress of the reaction. Theoretical calculations in this work provide the most basic understanding of ring-opening polymerization of L-lactide by ICl₃ catalysts. © 2019 Wiley Periodicals, Inc.