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Author give a direct prove of the generic continuity of semicontinuous real-valued function which is defined on topological space.

最后给出了定义在拓扑空间上的半连续实值函数通有连续性的一个直接证明。

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.

在巴拿赫空间理论中，Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一，分隔性定理是Hahn-Banach定理的重要应用，本文利用"超平面"的方法，改进了一个分隔性定理的证明；另外，本文利用邻域的"平移"方法，给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。

Compared with the discrete distribution, we defined a comparison function for continuous distribution, and pointed out the relationship between the discrete distribution and continuous distribution.

仿照离散分布，定义了连续分布的比较函数，并沟通了离散和连续分布的伴随关系。

At last for a continuous map defined on a compact metric space, the strong-e-chain, strong-chain-transitive component are introduced and some existing results are improved.

最后对定义在紧致度量空间上的一个连续映射，引入了强-∈-链，强链传递分支的概念，改进了一些已有的结论。

Class I areas shall be defined as areas in continuous view of the operator.

一级区域为经常可被检测者看到的区域。

A sufficient and necessary condition about a linear weak* densely defined operator is the generator of a contraction weak continuous operator semigroup on X* is given.

叮叫且川人蛋A川＊三5，人＞o 第三章从另一角度出发，利用定义在X"上的耗散算子刻画弱"连续算子半群的生成元。

In first part,The Theory and Simulation on Reconstruction Algorithms,webuild a well-defined mathematical model for OCT,on which we prove more than 10theorems,analyze and answer a series of significant questions about OCTreconstruction,from existence, uniqueness,continuousness,stability to sampling,resolution,ill-posedness and accuracy.

在上篇重建算法的理论与实践中，我们将OCT抽象为基于n维Radon变换的数学模型，从而分析、讨论、回答了从存在性、唯一性、连续性、稳定件到采样条件、分辨能力以及病态特件和重建精度等一系列在理论和了OCT的重建理论体系。

Proof standard should be a kind of legal request defined that main bodies who is burden with proof try to reach when they prove the controvert facts with evidences and expound their own opinions.

总之，我们探讨的证明标准应该仅涉及狭义的证明和具体的具有可操作性的标准。

Two features of these operations are apparent immediately: firstly, a large number of users must be able to operate at the same time without interfering with each other, and secondly, the distances over which the system must provide communication need not in general be great, since much of the system's operation will be either within the confines of a conurbation or along well-defined major vehicle trunk routes or railway lines.

这些部门的两个特征立刻就明显了：第一，很多的使用者必须能够在没有干扰彼此的情况下同时操作，第二，系统所能提供交流的距离大体上不需要太长，因为许多系统的操作是在大都市的边界里面或沿着明确限定的主要车辆主干路径或铁路线。

The relationship between the topology and convegence of networks is approached and the reason causing overtraining and overfitting is analysed. Then the redundant weights and nodes in the network are defined by using improved activity function and a new algorithm called the BPNSO for determining the network structure for any application is proposed, which use dual optimization objective function combining the mean squre error of the network output with network complexity penalty function.

文章对网络拓扑结构与网络收敛性和稳定性的关系进行了探讨，分析了网络出现Overtraining或Overfitting的原因和解决的目标，提出了神经网络结构优化的策略，改进了活化函数，定义了冗余权值和冗余节点的概念，为辨识和删除冗余权值和冗余节点，提出采用优化目标函数中增加网络复杂度罚函数的双重优化目标函数，并对罚因子提出了基于学习误差和权值的自适应动态调整公式，论文定义了这种BP网络结构优化方法为BPNSO，并给出了完整的计算流程。

You can snipe the second and third union leaders from this position.

您可以鹬第二和第三工会领袖从这一立场出发。

Aiming at the currently shortage of XML streams quality detecting, this paper proposes a new forecasting method of XML streams quality by least squares support vector machines, which is used the method of XML keys' vector matrix as windows, and vector product wavelet transform to multilevel decompose and refactor the XML streams series, that can fulfill real-time checking demand of XML quality, and ensure constraint, consist- ency and integrality. For even more adapting net load, it proposes a control strategy by weight and adaptive adjustment to ensure XML streams quality.

针对当前XML数据流质量检测存在的不足，提出构建XML键的矢量矩阵作为窗口，利用矢量积小波变换多级分解与重构XML数据流，再结合最小二乘支持向量机对XML数据流质量进行预测的一种方法，满足XML数据流质量重构时实时检测的要求，保证XML数据的约束性、一致性与完整性；为了更好的适应网络负载，采取加权与自适应窗口调整等调度策略充分保证XML数据流的质量检测。