无K1,r图中的哈密顿圈（英文）

本文借助对图的本质独立集和图的部分平方图的独立集的研究，对于K1,r图中哈密顿圈的存在性给出了八个充分条件。我们将利用T－插点技术对这八个充分条件给出统一的证明，本文的结果从本质上改进了C－Q.Zhang于1988年利用次形条件给出的k-连通无爪图是哈密顿图的次型充分条件，同时。G.Chen和R.H.Schelp在1995年利用次型条件给出的关于k-连通无K1，4图是哈密顿图的充分条件也被我们的结果改进并推广到无K1,r图。     

On Characterizations of Proper Efficiency for Nonconvex Multiobjective Optimization

In this paper, nonconvex multiobjective optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one scalar optimization problem and the existence of an exact penalty function of a scalar constrained program, respectively. One of the characterizations is applied to derive necessary conditions for a properly efficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints.     

Duffing方程的唯三周期解问题

考虑Duffing方程x+g(x,t)=h(t),在g(x,t)满足简单的凸凹性条件。以及g＇(x,t)跨越第一共振点时,本文指出,当强迫振动项h(t)充分小时,所讨论的Duffing方程的2π周期解恰有三个.     

Integral-Type Darboux Transformations for the mKdV Hierarchy with Self-Consistent Sources

We present integral-type Darboux transformation for the mKdV hierarchy and for the mKdV hierarchy withself-consistent sources. In contrast with the normal Darboux transformation, the integral-type Darboux transformationscan offer non-auto-Backlund transformation between two (2n 1)-th mKdV equations with self-consistent sources withdifferent degrees. This kind of Darboux transformation enables us to construct the N-soliton solution for the mKdVhierarchy with self-consistent sources. We also propose the formulas for the m times repeated integral-type Darbouxtransformations for both mKdV hierarchy and mKdV hierarchy with self-consistent sources.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅱ

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations.     

有界连通区域上Dirichlet空间及其算子

本文主要讨论了有界连通区域Dirichlet空间上Toeplitz算子的Fredholm性质,计算了符号在C1中的Toeplitz算子的本性谱和Fredholm指标．     

Asymptotic Behavior on a Competition Model Arising from an Unstirred Chemostat

This paper is concerned with the unstirred chemostat model with two-species and one non-reproducingresource.The global attractivity of the positive steady-state solutions of the original system is established.Moreover,the effects of the growth rate on the unique positive equilibrium of the single population model arestudied.     

Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.     

OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.