拓扑收敛

Hausdorff convergence; almost nonnegative Ricci curvature; Betti number; harmonic 1-form; nilpotency; splitting theorem; positive sectional curvature; gradient curve

基础科学，数学，几何、拓扑Hausdorff收敛；几乎非负Ricci曲率；贝蒂数；调和1-形式；幂零指标；分裂定理；正截面曲率；梯度曲线

Of all such measures endowed with the topology of point-wise convergence on forms a compact convex Hausdorff space.

在上赋予逐点收敛的拓扑就成为紧凸的Hausdorff空间。

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。

In the end of this text gives a description about the compactness of somecertain locally convex topological space with convergence and the completenessproblem.

某种确定的收敛下的局部凸拓扑空间以及凸拓扑下的紧性，完备性问题，在文章的最后给与了阐述。

If the topology is fixed and time-invariant, the consensus value of discrete-time systems also globally asymptotically converges to the convex combination of initial states, which is identical to continuous systems.

如果多智能体网络系统的拓扑结构没有改变，在离散状态下系统的一致平衡点仍收敛于初始状态的凸组合，并且离散状态下系统的一致平衡点与连续状态下系统的一致平衡点相等。

Second, we prove that consensus value of continuous time-invariant systems converges globally asymptotically to the convex combination of initial states, thus, determining the consensus value of the non-balanced topology.

对于多智能体网络连续系统，该系统的一致平衡点最终收敛于初始状态的凸组合，本文最终确定了非平衡拓扑结构的一致平衡点。

Under the locally uniform τ-Opial condition, using product topological net, a new convergence condition of X with locally uniform τ-Opial condition is obtained, and give the ergodic theorem and τ-convergence theorem of the almost-orbits for asympotically nonexpansive typesemigroups in Banach space X are given.

首先给出了局部一致τ-Opial条件的概念，运用乘积拓扑网技巧得到了具有局部一致τ-Opial条件下空间X的新的收敛条件。

Ruck, Hirano and Reich extended Baillon抯 theorem to a uniformly convex Banach space with a Frechet differentiable norm. Hirano-Kido-Takahashi, Oka, Park and Jenong proved the ergodic theorem for commutative semigroups of nonexpansive mappings and asymptotically nonexpansive mappings in the uniformly convex I3anach space with the Frechet differentiable nonn.

aillon的定理被Bruck，Hirano及Reich推广到具Frechet可微范数的一致凸Banach空间中，而当G是一般交换拓扑半群时，Hirano-Kido-Takahashi，Oka，Park及Jeong分别给出了具Frechet可微范数的一致凸Banach空间中非扩张半群及渐近非扩张半群的遍历压缩定理和遍历收敛定理。

For two examples, result testifies that it is feasible to use in nonlinear restriction optimization. Chapter 3 is important part in the paper. Analyze and research BP network, concealed node number of network former frame newly. Give new supplement and advice about How to select study velocity and activation function in BP algorithm.

第3章是论文中最重要的一章，通过实例分析研究了BP网络，对网络模型结构的隐层节点数进行分析和新的探讨；对BP算法中的学习速率和激活函数的选取进行了新的补充和建议；对网络的拓扑结构进行了新的构造；对人工神经网络收敛依据提出了新的判断原则。

A network with different topologic configurations is needed for flatness pattern recognition when strip width is changing, in this case the large learn assignment, slow convergence and local minimal in the network are observed, in order to solve these problems, first, a flatness pattern recognition GA BP network model with only 6 input and 3 output signals has been established based on Legendre orthodoxy polynomial, which is not only simple in structure but also is of clear physical meaning.

针对板宽变化时需要不同拓扑结构的神经网络才能完成板形模式识别任务，网络学习工作量大，网络存在收敛速度慢，易陷入局部极小等结构性能不佳的问题，首次建立了以勒让德正交多项式为基模式的只用 6个输入信号、3个输出信号的板形模式识别 GA- BP网络模型。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。