Extensions of q-Chu-Vandermonde's identity

In this paper, we apply q-exponential operator to get some general q-Chu-Vandermonde's identities.     

THE NESTED TOTAL LEAST SQUARES PROBLEM:FORMULATION,SOLUTIONS AND PERTURBATION ANALYSIS

In this paper, we propose the nested totoal least squatres problem (NTLS), which is an extension of the equality constrained least squares problem (LSE). The formulation of the NTLS problem is given and the solution set of the NTLS problem is obtained. The least squares residuals and the minimal norm correction matrices of the NTLS solution are provided and a perturbation analysis of the NTLS solutions is given.     

一类全纯函数的正规性

研究了具有一定性质的全纯函数．设F是平面上区域D内的全纯函数族．如果对于任意的f∈F 都有 其中C为常数且f(0)≠0,则F正规．     

On the Painlevé integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schrödinger equations

It is proven that generalized coupled higher-order nonlinear Schrödinger equations possess the Painlevé property for two particular choices of parameters, using the Weiss–Tabor–Carnevale method and Kruskal’s simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests.     

一种新颖的表面光波导型原子(或分子)分束器

提出了一种采用二元π位相板与柱面透镜组合而构成表面光波导型原子（或分子）分束器及其Mach-Zehnder干涉仪与X-分束器列阵的新方案，介绍了本方案的物理思想与基本原理，导出了光强分布、强度梯度、分束距离和分束路径的宽度与光学系统参数间的解析关系，并分析和讨论了本方案的潜在应用及其可行性. 研究表明，本方案设计新颖、光路简单，便于与其他元件组合构成具有表面微结构的集成原子（或分子）光学元器件及其全光型原子（或分子）芯片. 关键词： 原子（或分子）光波导 原子（或分子）分束器 原子（或分子）芯片 二元π位相板     

CODIMENSION 3 BIFURCATIONS OFHOMOCLINIC ORBITS WITH ORBITFLIPS AND INCLINATION FLIPS

The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is non-principal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold periodic orbit and three-fold periodic orbit are also obtained.     

基于吴方法的孤波自动求解软件包及其应用

基于非线性代数方程组的吴特征列方法,在计算机代数系统Maple上实现了非线性微分方程孤波解的自动求解,编制了一个小型实用的软件包。作为应用,考虑了一个一般的五阶模型方程,利用该软件包获得了此方程新的孤波解以及孤子解存在的条件。