查询词典 compact convergence

The text applies the covering theory to the study and discussion of the relative compact, the relative countably compact and the relative Lindelff compact.

运用覆盖理论，对相对紧、相对可数紧和相对Lindelff紧进行研究和讨论，给出了它们之间的一些关系，并且结合相对分离性，获得某些传递等性质。

By using the partition theorem of unity, a continuous selection theorem for a multimap from a compact Hausdorff topological space to a finitely continuous topological spaces (simply, FC-spaces) without any convexity structure was obtained, and from which and Tychonoff fixed point theorem, a collectively fixed point theorem for a family of multimaps on the product space of compact FC-spaces and several collectively fixed point theorems for a family of multimaps on the product space of non-compact FC-spaces were given.

利用单位分解定理得到从紧的Hausdorff拓扑空间到没有任何凸结构的有限连续拓扑空间的集值映射的连续选择定理，并从该结果和Tychonoff不动点定理，得到紧的FC-空间的乘积空间上映射族的集族不动点定理和若干个非紧的FC-空间的乘积空间上的映射族的集族不动点定理，对文献中的相应结果进行了改进和一般化。

Furthermore, the first-order optimality condition and its equivalent reformulations for generalized semi-infinite max-min programming with a non-compact set are presented using the lower-Hadamard directional derivative and subdifferential.2. Chapter 3 studies the gradient-type methods for unconstrained optimization problems. Section 1 proposes a new class of three-term memory gradient methods. The global convergence property of the method is established. Furthermore, in order to improve the convergence property of the method, a new class of memory gradient projection methods is presented with the property that the whole sequence of iterates converges to a solution to the problem under the conditions such as pseudo-convexity and continuous differentiability of objective function. In section 2, two new classes of methods, called gradient-type method with perturbations and hybrid projection method with perturbations, are proposed. In these methods, non-monotone line search technique is employed, which makes them easily executed in computer.

第3章研究了无约束优化问题的梯度型算法，第1节提出了一类新的三项记忆梯度算法，讨论了算法的全局收敛性，进一步提出了一类新的具有更好收敛性质的记忆梯度投影算法，并证明了该算法在函数伪凸的情况下具有整体收敛性，第2节在非单调步长搜索下提出了带扰动项的梯度型算法及其混合投影算法，这两类算法的一个重要特征就是步长采用线搜索确定而不象许多文献中那样要求步长趋于零，这样更容易在计算机上实现，在较弱的条件下证明了这些算法的全局收敛性，数值算例表明了算法的有效性。

Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space.

Tan和Xu已经证明了建立在一致凸Banach空间紧凸子集上的渐进非扩张映射的Ishikawa迭代序列的收敛原理，随之，刘齐侯又阐述了Banach空间上渐进准非扩张映射T的具误差的Ishikawa迭代序列收敛于T的不动点的充分必要条件；之后，Xu和Noor也证明了定义在一致凸Banach空间某非空有界闭凸子集上的渐进非扩张映射的三步迭代序列的收敛原理。

It carries out absolute convergence test, club convergence test and conditional convergence test on the provincial productivity incorporating all the three environmental pollutants and incorporating no environmental pollutants respectively.

研究发现，省级TFP指数存在发散趋势，省级技术效率指数表现出了收敛趋势，省级技术进步指数没有表现出收敛趋势。

Cauchy convergence criteria is proved the convergence and spread the basic method and through this method also launched many simple method, thus the important position of cauchy criterion, this kind of method is obvious superiority of the characteristics of itself, through to judge whether to prove the convergence, and this will bring convenience to the standards for the following summary, and probes into some of the relationship between them.

柯西收敛准则是证明收敛与发散的基本方法，并且通过此种方法还推出了非常多简单的方法，由此可见柯西准则的重要地位，此种方法的优越性也是显而易见的，就是通过本身的特征来判断是不是收敛，这就给证明带来了方便，本文将这几种准则作了以下总结，并且探讨了它们之间的一些关系。

Our results show that not only the club convergence has been obviously exhibited, that is, the output per capita congregates within the east, middle and west districts respectively; but also the conditional convergence has been identified, that is, given the same level of human capital, market openness and other factors the economic provinces have demonstrated a certain growth convergence.

本文认为中国地区间的经济增长，不仅存在着显著的"俱乐部收敛"特征，即按东中西划分的区域内部人均产出具有明显的聚集现象；而且存在着条件收敛的特征，即在具有相同的人力资本、市场开放度等结构特征的经济地区间存在着一定的增长收敛趋势。

However, Hacking convincingly argues that the theorem of convergence of opinions is not about the convergence of a posterior probability Pre, but about the convergence of a conditional probability Pr.

然而，哈金有说服力地表明，意见收敛定理证明的是条件概率Pr的收敛，而不是验后概率Pre的收敛。

Our results show thatnot only the club convergence has been obviously exhibited,that is ,the outputper capita congregates within the east,middle and west districts respectively;but also the conditional convergence has been identified,that is ,given the samelevel of human capital,market openness and other factors the economic provinceshave demonstrated a certain growth convergence.

本文认为中国地区间的经济增长，不仅存在着显著的"俱乐部收敛"特征，即按东中西划分的区域内部人均产出具有明显的聚集现象；而且存在着条件收敛的特征，即在具有相同的人力资本、市场开放度等结构特征的经济地区间存在着一定的增长收敛趋势。

We investigate the convergence, cut-convergence and almost everywhere cut-convergence of sequences of fuzzy numbers.

并给出了这种模糊映射在一有向线段上积分在获取统计数字方面的一个应用实例。

He tendered his resignation to the Prime Minister.

他向首相递了辞呈。不适合

International economy and trade,Nanking 210044

国际经济与贸易，南京 210044