Bäcklund transformation,infinite conservation laws and periodic wave solutions to a generalized (2+1)-dimensional Boussinesq equation

Under investigation in this paper is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the water wave interaction. By using Bell polynomials, a lucid and systematic approach is proposed to systematically study the integrability of the equation, including its bilinear representation, soliton solutions, periodic wave solutions, Bäcklund transformation and Lax pairs, respectively. Furthermore, by virtue of its Lax equations, the infinite conservation laws of the equation are also derived with the recursion formulas. Finally, the asymptotic behavior of periodic wave solutions is shown with a limiting procedure.     

Energy band alignment of 2D/3D MoS2/4H-SiC heterostructure modulated by multiple interfacial interactions

The interfacial properties of MoS₂/4H-SiC heterostructures were studied by combining first-principles calculations and X-ray photoelectron spectroscopy. Experimental (theoretical) valence band offsets (VBOs) increase from 1.49 (1.46) to 2.19 (2.36) eV with increasing MoS₂ monolayer (1L) up to 4 layers (4L). A strong interlayer interaction was revealed at 1L MoS₂/SiC interface. Fermi level pinning and totally surface passivation were realized for 4H-SiC (0001) surface. About 0.96e per unit cell transferring forms an electric field from SiC to MoS₂. Then, 1L MoS₂/SiC interface exhibits type I band alignment with the asymmetric conduction band offset (CBO) and VBO. For 2L and 4L MoS₂/SiC, Fermi level was just pinning at the lower MoS₂ 1L. The interaction keeps weak vdW interaction between upper and lower MoS₂ layers. They exhibit the type II band alignments and the enlarged CBOs and VBOs, which is attributed to weak vdW interaction and strong interlayer orbital coupling in the multilayer MoS₂. High efficiency of charge separation will emerge due to the asymmetric band alignment and built-in electric field for all the MoS₂/SiC interfaces. The multiple interfacial interactions provide a new modulated perspective for the next-generation electronics and optoelectronics based on the 2D/3D semiconductors heterojunctions.     

量子环上粒子体系的计算

对于量子环上带电粒子体系,组成本征函数的基矢数及哈密顿矩阵元素数都极大,数值计算量庞大.本文介绍在处理此问题时按轨道总角动量分类从基矢集中选择子基矢集的方法和技巧.应用计算机进行数值计算时,此方法比以往节省90%以上的时间.     

格值上下文无关文法的范式

给出了格值上下文无关文法（LCFG）,Chomsky范式文法,Greibach范式文法的定义.证明了对任意的LCFG存在与之等价的Chomsky范式文法;给出了对任意的LCFG,存在与之等价的Greibach范式文法的条件.文中结论表明了LCFG的特性与其取值格的代数性质密切相关.     

具脉冲效应和Beddington-DeAnglis功能反应时滞周期捕食系统

研究一类具有脉冲效应和Beddington-DeAnglis功能反应的时滞周期捕食系统,给出系统持续生存和周期解存在的条件.证明了在无时滞情况下,周期解是全局稳定的.     

Effect of electric field on the spectrum and the persistent current of a quantum ring with two electrons （II） additional effect of a charged impurity

This paper studies the effect of a charged impurity together with or without an external homogeneous electric field on a quantum ring threaded by a magnetic field B and containing two electrons. The potential caused by the impurity has been plotted which is helpful to the understanding of the electronic structures inside the ring. The deep valley appearing in the potential curve is the source of localization, which affects seriously the Aharonov-Bohm oscillation （ABO） of the energy and persistent current. It also causes the fluctuation of the total orbital angular momentum L of the pair of electrons. It is found that the appearance of the impurity reduces the domain of the fractional ABO. During the increase of B, the domain of the integral ABO may appear earlier when B is even quite small. The transition from the localized states to extended states has also been studied. Furthermore, it has deduced a set of related formulae for a transformation, by which an impurity with a charge ep placed at an arbitrary point Rp is equivalent to an impurity with a revised charge ep placed at the X-axis with a revised radial distance Rp. This transformation facilitates the calculation and make the analysis of the physical result clearer.     

Removable edges in a spanning tree of a k-connected graph

An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G O e denotes the graph obtained from G by the following way： deleting e to get G - e, and for any end vertex of e with degree k - 1 in G - e, say x, deleting x, and then adding edges between any pair of non-adjacent vertices in NG-e （x）. The existence of removable edges of k-connected graphs and some properties of k-connected graphs have been investigated. In the present paper, we investigate the distribution of removable edges on a spanning tree of a k-connected graph （k ≥ 4）.     

Perturbation methods in semilinear elliptic problems involving critical hardy-sobolev exponent

In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation method in critical point theory.     

On uniform convexity of Banach spaces

This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.     

Representation of measures of noncompactness and its applications related to an initial value problem in Banach spaces

Science China Mathematics - This paper is devoted to studying the representation of measures of non-generalized compactness, in particular, measures of noncompactness, of non-weak compactness and...