The Exact Solutions of Some (2 + 1)-Dimensional Integrable Systems

The equivalence of three (2 1)-dimensional soliton equations is proved, and the quite generalsolutionswitha some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, many specialtypes of the localized excitations like the solitoff solitons, multi-dromion solutions, lump, and multi-ring soliton solutionsare obtained.     

高压电场作用下乙醇-水溶液体系变化红外光谱分析

本文报道了用红外光谱分析电磁场作用下乙醇 水溶液体系变化情况。分析结果表明 :当乙醇溶液受到 2 0kV·cm- 1 的交变电磁场处理 (5 0Hz)时 ,分子之间的氢键缔合先增大后减少 ;高乙醇含量溶液受到同样强度电场较长时间处理时 ,有乙醇发生氧化反应 ,从红外谱中可看到νCO 峰及ν(OH) (H2 O) 峰的出现 ;经处理后的溶液自然放置 7天再测定 ,其红外谱图基本保持不变。文中对各出现变化的峰进行了分析 ,并对其机理进行了推导     

高校思想政治工作的困境及其对策

思想政治工作被视为一切工作的“生命线”，其地位和作用不言而喻。然而，就目前高校学生思想政治教育工作而言，受到国际，国内的政治，经济环境的影响，以及高校学生思想政治教育工作本身的诸多困扰，使高校的学生思想政治教育工作面临着严峻的挑战。如何研究新情况，形成新认识，开辟新境界，解决新问题巳是不可回避的课题。     

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.     

Finitely additive integration and local integration with respect to upper integrals

Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the q_l-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as q_l-integrable f with q(|f|) < ∞, and of q_l-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most finitely additive integration theories.     

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.