拓扑收敛

Next,it proves that if E is a barrelled space and F〓 is a locally convex space,Kis all the compact operators of L,then the weak operator topology and the uniformly operator topology have the same sub-series convergence series in Kif and only if 〓 contains no copyof 〓.

其次又得到，若E是桶型空间，〓是局部凸空间，那么紧算子空间K中弱算子拓扑与一致算子拓扑具有相同子级数收敛的充要条件是〓不拓扑同胚地包含〓。

However,in this paper,it is first introduced sequential convergence C and L*- space which is a vector space giving some relation:xmCx between sequences and points in it,then the bounded set is defined in vector space.

设C为一序列收敛关系，T是由C确定的拓扑，B是由C确定的有界集族，则有B=BT(C，并进一步从L*-空间构造了包囿拓扑向量空间。

It investigates mainly the dualinvariant of λ- multiplier convergent series, the full invariant ofλ-multiplier convergent series, the λ- multiplier convergent series in spaceswith a basis, the compact sets in the infinite matrix topological algebras, thecharacteristics of have the same compact sets in different topologies,the weak sequentially completeness of , the characteristics ofSchur-matrices, the characteristics of p- uniform Toeplitz matrices and theEberlein-Smulian theorem in the locally convex spaces, etc.

主要研究了〓数乘收敛级数的对偶不变性，〓数乘收敛级数的全程不变性，有基空间中的〓数乘收敛级数，无穷矩阵拓扑代数〓中的紧集，〓在不同拓扑下具有相同紧集的刻划，〓的弱序列完备性，Schur—矩阵的刻划，p-一致Toeplitz矩阵的刻划以及局部凸空间上的Eberlein—Smulian定理等。

First, the digraph is used to represent the topology of multi-agent systems, and then, a first-order integrator model and a consensus convergence criterion of systems are established.

首先提出了能使用有向图表示的多智能体网络系统的拓扑结构，并根据该拓扑结构建立了网络系统的1阶数学模型和提出了多智能体网络系统一致收敛准则。

We introduce the uniform Hausdorff metric H on the space 〓 offuzzy complex numbers and investigate the topological structure of 〓.We show the completeness of 〓 and study on 〓 limits of thesequence of fuzzy complex numbers,metrical and leverwise convergence,and relation between metrical convergence and leverwise convergence.Weprove the equivalence theorem of metrical convergence and leverwiseconvergence on 〓.

在模糊复数空间〓上引进一致Hausdorff度量H，讨论了模糊复数空间的拓扑结构，证明了的完备性，并在完备的模糊复数度量空间上研究了模糊复数列的极限、度量收敛和水平收敛，讨论了度量收敛与水平收敛之间的关系，在上证明了度量收敛与水平收敛的等价性定理。

In light of the convergence theorem obtained in Chapter 2, a result on topology preservation of 2-dimensional SOM algorithm with continuous inputs is given. In Chapter 4, an equivalence relation on n dimensional Euclidean space, called equi-action relation, is introduced and a number of properties on this relation are studied.

指出了已有的有关SOM算法拓扑保序定义的缺陷，并在此基础上，给出了一个具有连续输入的二维SOM算法的拓扑保序新定义；利用第二章中的收敛性定理，我们进而获得了一个具有连续输入的二维SOM算法的拓扑保序性定理。

To examine the topological space theory by nonstandard analysis, the nonstandard characteristics of ideals convergence is given in the enlargement model.

为了用非标准分析方法进一步研究拓扑空间，在扩大模型下，对理想收敛的基本理论进行了非标准刻画：设X是拓扑空间，I是X中的理想，I收敛于点x，当且仅当v v 。

A sensitivity analysis of adjoint method is presented to analyze the topology optimization problems. Meanwhile, the globally convergent version of the method of moving asymptotes is used in the optimization algorithm.

提出了适用于微型柔性机构多目标拓扑优化设计的伴随矩阵敏度分析方法，并将广义收敛移动渐进算法用于多目标多约束微型柔性机构拓扑优化问题的求解。

The above problems are studied in this thesis. First, the implicit NND scheme with mix flux splitting method proposed by Zhang Hanxin that is first order accurate in time and second order in space is modified. The modified scheme keeps the characteristics of fast convergence and is second order accurate both in time and space. It can be capable of simulating the unsteacly flow. Second, the topological method founded by Zhang Hanxin is improved to study the characteristics of vortex near the singular point on its axis and the cross streamlines on the longitudinal section passing the vortex axis. On the basis of topological results, a program which visualises numerical results is made out. It can help us analyse the characteristics of vortex motion.

本文对上述问题做了研究：第一，在数值模拟方面，借助于张涵信提出的NND算法和混合通量法，我们将他建立的时间为一阶、空间为二阶精度的快速隐式算法推广为时间和空间均为二阶精度的算法，这样做保留了原格式收敛快的特点，而且能适用于真实的非定常流态的计算；第二，将张涵信的拓扑分析方法加以推广，研究了涡轴附近及破裂点邻域内流场的空间特征，并以这些拓扑分析结果为指导，研制了一套显示计算结果的软件，这一软件能很好地帮助我们分析流场的计算结果和旋涡演变的特征。

In this paper, a new kind of T2 axiom called strong T2 separation in topological systems is introduced. Characterizations of T2 separation by net convergences and by filter convergences are given.

提出拓扑系统的一种新的T2分离性－强T2分离性，给出了T2拓扑系统的网式收敛刻画和强T2拓扑系统的滤子式收敛刻画。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷