广义Vandermonde行列式的计算公式

给出两类广义Vandermonde行列式的计算公式以及各类广义Vandermonde行列式的计算方法.     

Conditional Fredholm determinant for the S-periodic orbits in Hamiltonian systems

For S being a symplectic orthogonal matrix on R2n, the S-periodic orbits in Hamiltonian systems are a solution which satisfies x(0)=Sx(T) for some period T. This paper is devoted to establishing the theory of conditional Fredholm determinant in studying the S-periodic orbits in Hamiltonian systems. First, we study the property of the conditional Fredholm determinant, such as the Fréchet differentiability, the splittingness for the cyclic type symmetric solutions. Also, we generalize the Hill formula originally gotten by Hill and Poincaré. More precisely, let M be the monodromy matrix of the S-periodic orbits, then we get the formula relating the characteristic polynomial of the matrix SM and the conditional Fredhom determinant. Moreover, we study the relation of the conditional Fredholm determinant and the relative Morse index. Applications to the problem of linear stability for the S-periodic orbits are given.     

范德蒙行列式的新证明及其应用

首先给出范德蒙行列式的一个新的证明,与以前的证明相比,本文给出的证明更具有通用性．其次介绍范德蒙行列式在n阶行列式计算和在向量组线性相关性证明中的两个应用．     

Basis Property of Chains of Eigenfunctions for Certain Boundary-Value Problems

Mathematical Notes -     

TRIGONOMETRIC SU(N) GAUDIN MODEL

In this paper, we obtain the eigenstates and the eigenvalues of the Hamiltonians of the trigonometric SU(N) Gaudin model based on the quasi-classical limit of the trigonometric SU(N) chain with the periodic boundary condition. By using the quantum inverse scattering method, we also obtain the eigenvalues of the generating function of the trigonometric SU(N) Gaudin model.     

国际资本结构动态决定因素的实证研究——基于制造业上市公司的面板数据

选取12个国家地区制造业上市公司2004-2008年的公司特征数据和国家宏观经济指标,研究国际间资本结构动态决定的宏观与微观因素的协整作用关系.主要发现有:一是发达国家对于现代资本结构理论假设条件和关系诠释比发展中国家更为贴近,发展中国家公司特征因素与目标资本结构的关系异象根源于特定经济制度背景;二是克服截面数据POOL回归分析法忽视国别差异因素的缺陷,通过国别哑变量和沃尔德F统计量检验得出,不同国家的公司资本结构微观特征决定因素存在定量上的差异;三是选用能够克服异方差问题的国别哑变量系数标准化为权重的加权最小二乘法回归表明,国家宏观经济法律因素直接或者通过公司特征指标间接作用于国际资本结构决策.     

Discrete three-dimensional three wave interaction equation with self-consistent sources

A discrete three-dimensional three wave interaction equation with self-consistent sources is constructed using the source generation procedure. The algebraic structure of the resulting fully discrete system is clarified by presenting its discrete Gram-type determinant solution. It is shown that the discrete three-dimensional three wave interaction equation with self-consistent sources has a continuum limit into the three-dimensional three wave interaction equation with self-consistent sources.     

The Wronskian technique for nonlinear evolution equations

The investigation of the exact traveling wave solutions to the nonlinear evolution equations plays an important role in the study of nonlinear physical phenomena. To understand the mechanisms of those physical phenomena, it is necessary to explore their solutions and properties. The Wronskian technique is a powerful tool to construct multi-soliton solutions for many nonlinear evolution equations possessing Hirota bilinear forms. In the process of utilizing the Wronskian technique,the main difficulty lies in the construction of a system of linear differential conditions, which is not unique. In this paper,we give a universal method to construct a system of linear differential conditions.     

Multisoliton solutions in terms of double Wronskian determinant for a generalized variable-coefficient nonlinear Schrödinger equation from plasma physics, arterial mechanics, fluid dynamics and optical communications

In this paper, the multisoliton solutions in terms of double Wronskian determinant are presented for a generalized variable-coefficient nonlinear Schrödinger equation, which appears in space and laboratory plasmas, arterial mechanics, fluid dynamics, optical communications and so on. By means of the particularly nice properties of Wronskian determinant, the solutions are testified through direct substitution into the bilinear equations. Furthermore, it can be proved that the bilinear Bäcklund transformation transforms between (N − 1)- and N-soliton solutions.     

New double Wronskian solutions of the AKNS equation

Soliton solutions, rational solutions, Matveev solutions, complexitons and interaction solutions of the AKNS equation are derived through a matrix method for constructing double Wronskian entries. The latter three solutions are novel. Moreover, rational solutions of the nonlinear Schrodinger equation are obtained by reduction.