序列空间

In general,the convergent sequence and bounded set are concepts only in topological spaces.

收敛序列和有界集一般是拓扑空间中的概念，文章首先引入序列收敛C和L-空间(给出某种序列收敛关系的向量空间)，然后在其中定义有界集。

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。

The result is generalized to a sequence of Banach spaces.

由此得出：Banach空间X上n次积分C-半群序列S强收敛于Banach空间X上n次积分C-半群S的充分条件是其生成元序列A强收敛于A，并将这一结论推广到一般的Banach空间序列上。

It is one of the important characters of the grey system theory to utilize grey generation modeling. The basis structures of generating space in AGO and in IAGO are respectively obtained by the mathematical research of r-AGO series and r-IAGO series. The results are the following: the coherent and direct expression of the generating basis vector in AGO and r-AGO, the relation expression between two r-AGO series and two r-IAGO series, the relation among generating basis vector, generating series and moving operator.

利用灰色生成建模是灰色系统理论的重要特点之一，通过对r次生成序列（包含r-AGO序列和r-IAGO序列）的数学研究，得到了AGO生成空间和IAGO生成空间的基本结构：AGO和r-AGO生成基向量的统一的直观表达式、任意两个r-AGO序列间与任意两个r-IAGO序列间的关系式、生成基向量生成序列与移动算子间的关系。

On the characterizations of spaces by the infinite matrix methods,let E be a topo-logical vector space,if for each 〓 and 〓,there is a sequence 〓 in A suchthat 〓.Then E is said to be a sequential topological vector space.

在无穷矩阵方法对空间的刻划方面，设E是一个拓扑向量空间，若对每个〓一定存在A中序列〓使得〓，那么称E是一个序列型拓扑向量空间。

In chapter 2, we prove that sn—first countable spaces are preserved by the finite subsequence-covering mappings.By this result, we prove that the finite subsequence-covering, quotient mappings preserve g—metrizable spaces, also prove that the finite subsequence-covering, closed mappings preserve sn—metrizable spaces, g-metrizable spaces, metrizable spaces, point-countable bases.

在第二章中，我们主要证明了有限子序列覆盖映射保持sn-第一可数空间，作为它的应用，又证明了有限子序列覆盖、商映射保持g-第一可数空间，也证明了有限子序列覆盖闭映射保持sn-度量空间，g-度量空间，度量空间，点可数基。

A hybrid model of short-term load forecasting based on chaotic theory, correlation and neural networks is presented in this paper. Firstly, reconstruct attractors in phase spaces using chaotic theory, Secondly fit the attractor's evolvement using BP neural networks, because selecting neural network's input training data using Euclid distance and correlation, improve neural network's associative memory and ratiocinative ability, can better fit the attractor's evolvement.

提出一种将混沌理论、关联度和神经网络相结合的短期负荷预测模型，首先利用混沌理论重构负荷时间序列的相空间吸引子，然后用BP 神经网络来拟合空间吸引子的演化，由于使用空间欧氏距离和关联度联合来选取神经网络的训练样本，这样就提高了神经网络对负荷序列混沌特性的联想和泛化推理能力，能够更好的拟合吸引子的演化。

Firstly, reconstruct attractors in phase spaces using chaotic theory,Secondly fit the attractor s evolvement using BP neural networks, because selecting neural network s input training data using Euclid distance and correlation, improve neural network s associative memory and ratiocinative ability, can better fit the attractor s evolvement.

提出一种将混沌理论、关联度和神经网络相结合的短期负荷预测模型，首先利用混沌理论重构负荷时间序列的相空间吸引子，然后用BP神经网络来拟合空间吸引子的演化，由于使用空间欧氏距离和关联度联合来选取神经网络的训练样本，这样就提高了神经网络对负荷序列混沌特性的联想和泛化推理能力，能够更好的拟合吸引子的演化。

The phase space reconstruction theory of chaotic dynamic system, in combination of the non-linear reflecting and pan-capacity of neural network, can be used to establish the prediction model; and a kind of new prediction method is suggested to realize the complete tracing of phase point evolution process and to predict "the price nails", whereby improving the prediction accurateness and effectively solving the problem of negative prediction, with the satisfactory results obtained.

采用混沌理论预测系统边际电价针对我国电力市场电价变化特点，利用电价和负荷时间序列的混沌特性，重构准确的电价序列相空间，通过跟踪相空间相邻相点的演化趋势，建立基于快速BP网络的电价预测模型，对我国川渝电网电价进行预测，取得良好效果利用混沌动力系统的相空间重构理论，结合神经网络的非线性映射和泛化能力建立预测模型，提出一种新的预测方法实现了相点演化过程的全局跟踪，对"价格钉"进行预测，提高了预测精度，有效解决了负预测问题，得到满意的结果。

Due to the nonlinear and nonstationary of river water turbidity, a novel intelligent forecasting model based on phase space reconstruction and RBF neural network is proposed. Firstly, the embedding dimension is chosen by using the false nearest neighbor method. And the time delay can be obtained with the mutual information. The phase space is reconstructed from the time series with the embedding dimension and the time delay got. The reconstructed time array is used as the input signal of RBF neural network.

首先将现场取得的数据进行预处理，建立所需时间序列样本；再利用虚假邻域法确定最小嵌入维数，根据互信息法计算确定浊度时间序列的最佳延迟时间；接着根据取得的嵌入维数和延迟时间对江水浊度时间序列数据进行相空间重构；利用重构相空间后的时间阵列，作为建立预报模型所需的浊度样本阵列，用RBF神经网络建立预报模型；利用该模型对江水浊度进行预报。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。