逼近地

If we hope to use a sequence of finite objects to approximate infinite objects, then we should know what kinds of infinite objects are approximable and how to approximate them effectively.

无穷形式对象可逼近的充分条件为了研究哪一类无穷对象可以逼近以及如何有效地逼近它们，我们用过程模式作为无穷对象上的计算的模型，用以刻画接受无穷输入、生成无穷输出的无穷对象上的计算。

Several strong results on neural network approximation capability obtained in this dissertation are important in the approximation theory and applications of neural networks.

本文系统地研究了多层神经网络的非线性逼近能力，给出了多层网络可一致逼近有限维空间R〓紧集上的连续函数、无穷维函数空间紧集上的连续泛函和连续算子以及布尔函数的理论证明。

Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in differential mid-value are summarized.

对函数逼近论中等距节点和差分理论进行了研究，揭示了差分、差商与导数之间的联系；将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中，简明地推导出Lagrange差分中值定理等4个定理，并在此基础上对"中间点"的渐近性进行了研究，得出了一系列"中间点"的渐近性的结果，概括了有关文献对微分中值公式的"中间点"的渐近性的讨论；给出的引理改进了函数逼近论的证明方法，精简了函数逼近论中的一些内容。

In the fourth chapter, firstly it introduces the Boolean functions algebraic expressions of the 2-value clock-controlled stop-and-go generator and Gunther generator. It reveals the balanced property of the two kinds of Boolean functions, and studies the Walsh cycle spectrum and the autocorrelation function. It also obtains the coincidence rate of their output sequences with affine sum of some bits of input sequences, and analyzes their ability of resisting the best affine approximation cryptanalysis and differential cryptanalysis. Secondly, we properly present a new definition of the Best Affine Approximation, namely BAA on the Boolean vector functions, followed by the spectral characteristic of such defined BAA attacks through using the decomposition formula of the union distribution for random variables. A lower bound of such BAA attacks is proposed. Finally, we also study the spectral characteristic of the second kind of nonlinearity of Boolean vector functions, followed by a higher bound of such nonlinearity. Furthermore, the limited relationship between the second kind of nonlinearity of Boolean vector functions and the linear structure of the linear combination of every component is analyzed.

在第四章中，首先给出了2值密钥流"停走生成器"和"衮特生成器"中实际存在的布尔函数的代数表示，揭示了这两类布尔函数的平衡性，随后研究了它们的Walsh循环谱和自相关函数等，得到了它们的输出序列与输入序列中的某些bit的仿射项的符合率，分析了它们抵抗最佳仿射逼近攻击和差分攻击的能力；其次，我们合理地给出了布尔向量函数最佳仿射逼近的新定义，利用布尔随机变量联合分布的分解式考察了相应的谱特征，并给出了布尔向量函数与其最佳仿射逼近的符合率的一个下界；最后，我们还考察了布尔向量函数第二类非线性度的谱特征，给出了布尔向量函数第二类非线性度的一个上界，并揭示了布尔向量函数第二类非线性度与其各个分量的线性和的线性结构之间存在的制约关系。

Research emphasis is put on thefollowing aspects:First,study of multiwavelet basis(e.g.periodic vector,interpolation vector,multi-dimensional vector)suitable for different practical demands.Second,from perspective of operatorapproximation order,study of normal function approximation operator,contrast and comparison ofwavelet operator and multiwavelet operator and their respective applicable fields.And further,onbasis of the above,exploration of approaches of multiwavelet analysis application in function spacetheoretical research,and higher-lever,more convenient approaches for multi-function spaceapproximation theoretical research.Third,by fully employing unique features of multiwavelet,research action of multiwavelet analysis in the construction of L〓space non-conditionalbasis.Fourth,research such as transient signal analysis,image edge extraction,datacompression,fractal signal analysis.

其一，研究适宜于不同实际问题需要的向量小波基（如周期向量小波、插值向量小波、高维向量小波等）；其二，从算子逼近阶的角度研究一般函数逼近算子、小波算子和向量小波算子的异同点以及较优适用领域；在此基础上，探索将向量小波分析应用于函数空间理论研究的途径，寻找更高层次、更便捷地研究多元函数空间逼近理论的方法；其三，充分利用向量小波所独具的完美性质，探索在〓空间〓无条件基的构造中，向量小波分析的价值；其四，对向量小波适用的信号瞬态分析、图像边缘分析、数据压缩保真、分形信号分析等领域应给予特别的重视。

This article makes use of the approximation property of Laguerre orthogonal function series to present a Laguerre function approxima te model of linear dynamic systems.The model eliminates the need for assumption of the plant order and the time delay and approaches unknown systems via estimat ing the Laguerre coefficients on-line.

蒋中摘要：利用Laguerre正交函数序列对空间函数的良好逼近特性，建立了线性动态系统的Laguerre函数近似模型，该模型不需要对象的阶次和时延等结构知识，通过在线辨识对象的 Laguerre系数矩阵，能较好地逼近结构未知系统。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

At first, an approximated mathematical model is presented. Then, the system manager can compute the optimal control policy via the method of successive approximation. Based on the above-mentioned algorithm, we design an intelligent system with feedback control to regulate the allocation of limited channels of trunk circuit. This system will continuously detect the status of whole cellular network. Once the system parameters cross the predefined threshold, the recomputing mechanism will be activated.

首先针对系统的近似数学模型先將其定义出来，然后就可以用连续逼近法將最佳控管决策计算出来，这样的最佳决策演算法我们把它设计在一个有迴授机制的智慧型决策系统裹，此决策系统將不断地侦测行动通讯网路运作的情形，一旦网路参数变化超过某个预定的临界值时，整个最佳决策演算法將被启动，系统的近似数学模型將依新的参数重新定义，接下来同样地写出最佳方程式並用连续逼近法计算出新的最佳控管决策。

Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in differential mid-value are summarized.

对函数逼近论中等距节点和差分理论进行了研究，揭示了差分、差商与导数之间的联系；将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中，简明地推导出Lagrange差分中值定理等4个定理，并在此基础上对&中间点&的渐近性进行了研究，得出了一系列&中间点&的渐近性的结果，概括了有关文献对微分中值公式的&中间点&的渐近性的讨论；给出的引理改进了函数逼近论的证明方法，精简了函数逼近论中的一些内容。

For problem II, many references have studied it and obtained its common solutions, symmetric solutions, skew-symmetric solutions and its optimal approximation constrained solution, but the representation of its solutions are complicated.

本文首次采用迭代法系统的研究了它求一般解、对称解、反求解约束矩阵方程及其最佳逼近的迭代法的研究对称解、中心对称解、中心反对称解、自反矩阵解、反自反矩阵解、双对称解、对称次反对称解及其最佳逼近问题，并首次成功地解决了它求中心对称解、中心反对称解、自反矩阵解、反自反矩阵解、双对称解与对称次反对称解及其最佳逼近的问题，拓广和改进了已有的研究成果。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。