非线性参数规划问题$\varepsilon$-最优解集集值映射的连续性

对非线性参数规划问题$\varepsilon$-最优解集集值映射的连续性条件进行了研究.首先在可行集集值映射局部有界且正则的条件下,讨论了非线性参数规划问题最优值函数的连续性,然后针对$\varepsilon$-最优解集集值映射的结构特征并利用此结果和集值分析理论,给出了非线性参数规划问题$\varepsilon$-最优解集集值映射连续的一个充分条件.     

一类非单调二阶锥互补问题解集的非空性与有界性

本文在二阶锥上引入一类新的映射,称之为笛卡尔P_*(κ)映射,它是单调映射的推广.文中讨论涉及这类映射的二阶锥互补问题的解的存在性和解集的有界性.主要结论为:如果所考虑的互补问题是严格可行的,那么它的解集是非空有界的.     

几个不动点定理及其应用

得到凝聚映象的几个新的不动点定理 ,并用到一类非线性积分方程的非零解、正解和解的性状的研究上得出了新的结果 .     

Painlevé–Kuratowski stability of approximate efficient solutions for perturbed semi-infinite vector optimization problems

This paper is concerned with the stability of semi-infinite vector optimization problems (SIVOP) under functional perturbations of both objective functions and constraint sets. First, we establish the Berge-lower semicontinuity and Painlevé–Kuratowski convergence of the constraint set mapping. Then, using the obtained results, we obtain sufficient conditions of Painlevé–Kuratowski stability for approximate efficient solution mapping and approximate weakly efficient solution mapping to the (SIVOP). Furthermore, an application to the traffic network equilibrium problems is also given.     

一类非线性双曲型发展方程的孤子解

研究了一类非线性发展方程.首先在无扰动情形下,利用待定函数和泛函同伦映射方法得到了非扰动发展方程的孤子精确解和扰动方程的任意次近似行波孤子解.接着引入一个同伦映射,并选取初始近似函数,再用同伦映射理论,依次求出非线性双曲型发展扰动方程孤子解的各次近似解析解.再利用摄动理论举例说明了用该方法得到的近似解析解的有效性和各次近似解的近似度.最后,简述了用同伦映射方法得到的近似解的意义,指出了用上述方法得到的各次近似解具有便于求解、精度高等优点.     

Constraint qualifications for constrained Lipschitz optimization problems and applications to a MPCC

Three constraint qualifications (the weak generalized Robinson constraint qualification, the bounded constraint qualification, and the generalized Abadie constraint qualification), which are weaker than the generalized Robinson constraint qualification (GRCQ) given by Yen (1997) [1], are introduced for constrained Lipschitz optimization problems. Relationships between those constraint qualifications and the calmness of the solution mapping are investigated. It is demonstrated that the weak generalized Robinson constraint qualification and the bounded constraint qualification are easily verifiable sufficient conditions for the calmness of the solution mapping, whereas the proposed generalized Abadie constraint qualification, described in terms of graphical derivatives in variational analysis, is weaker than the calmness of the solution mapping. Finally, those constraint qualifications are written for a mathematical program with complementarity constraints (MPCC), and new constraint qualifications ensuring the C-stationary point condition of a MPCC are obtained.     

锥拟凸集值映射多目标优化的解集的连通性

在一般拓扑向量空间中,本文引进了一类锥进凸（锥严格拟凸）集值映射。并在目标映射是锥拟凸（锥严格拟凸）和上半连续的条件下,利用Minkowski泛函,证明了弱有效解（有效解）集是连通的。文[9]中的结论是本文所得结果大目标映射为单值和拓扑空间为格的情况下的特例。     

A general iterative scheme for k-strictly pseudo-contractive mappings and optimization problems

In this paper, we introduce a new general iterative scheme for finding fixed points of a strictly pseudo-contractive mapping and then prove that the sequence generated by the proposed iterative scheme converges strongly to a fixed point of the mapping, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator. Additional results of the main result are also obtained.     

计算机求解渐开线齿轮齿廓的保角映射函数

平面弹性理论的复变函数保角映射解法可以求得齿轮的应力和位移的精确解.而相应于各种不同参数的轮齿齿廓的保角映射函数的求得却是比较困难的.以往均采用试算法,这是费时且昂贵的.作者编制了求解保角映射函数的计算机程序,并通过大量的计算证明这一程序是成功的,所取得的映射函数是精确的.从而解决了保角映射法求解渐开线齿轮应力和位移应用于实际工程计算的主要障碍.     

A hybrid proximal point algorithm for finding minimizers and fixed points in CAT(0) spaces

We introduce a hybrid proximal point algorithm and establish its strong convergence to a common solution of a proximal point of a lower semi-continuous mapping and a fixed point of a demicontractive mapping in the framework of a CAT(0) space. As applications of our new result, we solve variational inequality problems for these mappings on a Hilbert space. Illustrative example is given to validate theoretical result obtained herein.     

Steady vortical flow around a finite plate

An explicit solution for a layer of fluid with constant vorticitysurrounding a thin plate of finite length is obtained usingelementary conformal mapping methods. In the limit of largeplate length the behaviour of the solution near the ends ofthe plate tends to that of the previously known solution fora semi-infinite plate. Contour dynamics is used to investigatethe stability of the steady solutions.     

Banach空间中广义混合平衡问题,变分不等式问题和不动点问题的混杂投影方法

在Banach空间中,一个新的混杂投影迭代程序被引入来逼近广义混合平衡问题解集,变分不等式问题解集和一个相对弱非扩张映射的不动点集的公共元．所得结果改进和推广了最近一些文献的相应结果．     

一类曲面映射类的分解

设S为至少有一个穿孔点α的Riemann曲面.对于曲线α■S,可以定义关于α■S的Dehn twist t_α.设H是S的映射类群的子群,H中的元素保持α不动,并且投影为S=S∪{α}上平凡的映射类变换.定义t_α是关于α■S的Dehn twist.本文考虑关于X(S上的映射类变换)的方程(t_α■θ)~n■X=圮,其中θ∈H是任意给定的.由于(t_αoθ)~n和t_α~n都投影为关于简单闭曲线■的Dehn twist t_■.所以上述方程在H中的解是存在的.对充分大的n,我们给出上述方程有形如X=θ~(n)的解的充要条件.此外,对任给的θ∈H,刻画了子空间H′■H,这里方程的解X=X_n最终要属于H′.最后,考虑简单映射类变换的某些复合映射,并给出了相应的刻画:它们在沿S上的某些简单曲线做剖分后所得的穿孔pant上是不可约的.     

一类大气尘埃等离子体扩散模型研究

研究了一类大气非线性尘埃等离子体扩散方程初值问题.首先在无扰动情形下,利用Fourier变换方法得到了尘埃等离子体扩散方程初值问题的精确解,接着引入一个同伦映射,并选取初始近似函数,再用同伦映射理论,依次求出了非线性尘埃等离子体扰动初值问题的各次近似解析解.并引用不动点理论,指出了近似解析解的有效性和各次近似解的近似度,通过举例, 用模拟曲线和表格作了近似对照.最后,简述了用同伦映射方法得到的近似解的物理意义.简叙了用上述方法得到的各次近似解具有便于求解、精度高等优点.     

Existence and uniqueness of solution for quasi-equilibrium problems and fixed point problems on complete metric spaces with applications

In this paper, we presented new and important existence theorems of solution for quasi-equilibrium problems, and we show the uniqueness of its solution which is also a fixed point of some mapping. We also show that this unique solution can be obtained by Picard’s iteration method. We also get new minimax theorem, and existence theorems for common solution of fixed point and optimization problem on complete metric spaces. Our results are different from any existence theorems for quasi-equilibrium problems and minimax theorems in the literatures.     

Global existence and blow-up of solutions of nonlocal diffusion problems with free boundaries

In this paper, we investigate some nonlocal diffusion problems with free boundaries. We first give the existence and uniqueness of local solution by the ODE basic theory and the contraction mapping principle. Then we provide a complete classification for the global existence and finite time blow-up of solutions. Moreover, estimates of blow-up rate and blow-up time are also obtained for the blow-up solution.     

Anti-periodic solution for delayed cellular neural networks with impulsive effects

In this paper, we discuss anti-periodic solution for delayed cellular neural networks with impulsive effects. By means of contraction mapping principle and Krasnoselski’s fixed point theorem, we obtain the existence of anti-periodic solution for neural networks. By establishing a new impulsive differential inequality, using Lyapunov functions and inequality techniques, some new results for exponential stability of anti-periodic solution are obtained. Meanwhile, an example and numerical simulations are given to show that impulses may change the exponentially stable behavior of anti-periodic solution.     

A sharper decay rate for a viscoelastic wave equation with power nonlinearity

We consider a viscoelastic wave equation with power nonlinearity. First, we construct a local solution by the Faedo-Galerkin approximation scheme and contraction mapping theorem. Next, we continue the local solution to the global one by a priori estimates obtained from a decreasing energy. Finally, we discuss the decay rate of the global solution by assuming that the kernel function is convex.     

Lipschitzian stability of parametric variational inequalities over perturbed polyhedral convex sets

In this paper we investigate the Lipschitz-like property of the solution mapping of parametric variational inequalities over perturbed polyhedral convex sets. By establishing some lower and upper estimates for the coderivatives of the solution mapping, among other things, we prove that the solution mapping could not be Lipschitz-like around points where the positive linear independence condition is invalid. Our analysis is based heavily on the Mordukhovich criterion (Mordukhovich in Variational Analysis and Generalized Differentiation. vol. I: Basic Theory, vol. II: Applications. Springer, Berlin, 2006) of the Lipschitz-like property for set-valued mappings between Banach spaces and recent advances in variational analysis. The obtained result complements the corresponding ones of Nam (Nonlinear Anal 73:2271–2282, 2010) and Qui (Nonlinear Anal 74:1674–1689, 2011).     

不动点理论与里卡提方程两个正周期解的存在性

利用压缩映射原理,得到里卡提方程一个正周期解的存在性;利用变量变换方法,将里卡提方程转化为伯努利方程.根据伯努利方程的周期解和变量变换,得到里卡提方程的另一个周期解.并讨论了两个正周期解的稳定性,一个周期解在某个区间上是吸引的,另一个周期解在R上是不稳定的.