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In this paper, we investigate the persistence of lower dimensional invariant tori of symplectic mappings.

首先，我们研究了辛映射椭圆型低维不变环面。

Secondly, we investigate the hyperbolic lower dimensional invariant tori of symplectic mappings.

其次，我们研究了辛映射双曲型低维不变环面。

By applying existence theorems of maximal elements for a family of GB-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces.

通过应用G-凸空间的乘积空间内一族GB-优化映象的极大元的存在定理，在G-凸空间的非紧设置下证明了某些重合点定理，Fan-Browder型不动点定理和极小极大不等式组的解的存在性定理。

Computer-simulation results related to the TNN model substantiate that the timing neural network could handle well the inverse-interpolation problems of one-to-one and multiple-to-one mappings. Keywords: neural networks, weights direct determination, inverse problems, timing neural network

基于前面提出的网络模型，本文进一步提出一种增加时序控制条件的神经网络，即时序神经网络模型，并给出理论推导和进行仿真验证，结果表明该时序神经网络能够成功解决一一映射及非一一映射反插值问题。

We introduce a set of real functions H, and use to it to give a fixed point theorem of tother type for complex mappings on complete metric spaces, which improves and generalizes the corresponding results on compact metric spaces or under the condition of weakening compactness obtained by Fisher, Telci and Xu Xiao-li, respectively.

利用引入的实函数类H，在完备度量空间上给出了复合映射的另一种类型的不动点定理，改进并推广了Fisher、Telci和徐晓立等在紧致度量空间上或在弱化紧性条件下得到的相应结果。

In part Ⅲ, we mainly investigate the tractability of nonlinear generalized system F =0 and the stability problem of its solution, where 〓 is smooth mappings.

第三部分，主要是研究非线性广义系统F=0的可解性及其零解的稳定性问题，其中〓是光滑映射。

In this paper, the problem of an iterative sequence approximation a common fixed point for nonexpansive non-self mappings is studied in real uniformly convex Banach space, then we obtain a strongly convergence theorem.

在实一致凸Banach空间中，讨论了关于非扩张非自映射序列逼近公共不动点的问题，获得了一个强收敛定理，改进和推广了现有文献的一些相应结果。

The objective of Chapter 2 is to give the weak convergence theorem of S ={T1 :t E G of asymptotically nonexpansive mappings in a uniformly convex Banach space without assuming that X has a Frechet differentiable norm.

本文第二章在G仅要求是一个定向网，X为不具有范数Frechet可微条件的一致凸Banach空间的情况下，给出了一族渐近非扩张映射的弱收敛定理。

This chapter is dedicated to the study of the properties of close-to-convex univalent harmonic mappings.

在这一章中，我们主要研究了单叶调和映照的近于凸子族，首先给出了近于凸单叶调和映照与正实部解析函数之间的一个关系。

By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.

应用局部凸H－空间内具有闭零调值的上半连续集值映象的Fan－Glicksberg型不动点定理和极大化定理，对无限最优化总理2和约束对策问题在没有线性结构的局部凸H－空间内证明了解的某些新的存在定理，这些定理改进和推广了最近文献中的许多重要结果。

I want to be a big fish in a small pond.

我要做一条在小池塘里的大鱼。

While the software functioned well, we did not feel the same about their customer support!

虽然该软件运行良好，我们没有同样的感觉他们的客户支持！