逼近的

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。

We prove the fuzzy set-valued characteristicfunction of a compact Baire fuzzy set can be approached by fuzzy set-valuedcontinuous functions with fuzzy compact support sets,the integral of integrablesimple Baire fuzzy set-valued function can be approached not only by the integralsof integral simple fuzzy set-valued functions,but also by the integrals of fuzzy set-valued continuous function with fuzzy compact support sets.

定义了诱导空间上具有模糊紧支集的模糊集值连续函数，说明了它与分明的具有紧支集的连续函数的关系，证明了紧贝尔模糊集的模糊集值特征函数可以用具有模糊紧支集的连续函数列来逼近，可积简单贝尔模糊集值函数的积分可以用可积简单模糊集值函数的积分来逼近，还可以用具有模糊紧支集的模糊集值连续函数的积分来逼近。

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。

Firstly, we combine the theories of monotone operator and maximal monotone operator's Yosida approaching with domain method to prove the solution's existence of single input-output equation in R n in the similar economical backgrounds in present articles and then gain the solution's continuity by exterior approaching method,at last we give the responding economical meaning about the solution's existence and continuity.

就R n空间中消耗为单调单值型的投入产出方程，在现有文献类似的经济背景之下，利用单调算子的理论以及极大单调算子的Yosida逼近结合邻域逼近法给出了投入产出方程的解的存在性的证明，然后利用外部逼近法结合方程截断技巧证明了投入产出方程的解的连续性，最后给出了相对应于存在性和连续性的经济解释。

Night time Journey to the moon On the back Of a big firefly Take me up above the city Your hair Picks up all the light Tropical fish in sky Take a ride take a ride take a ride take a Come on Take me for a ride Open window's the sign Staining blue, soaked into my cotton skin See now tinkerbell's in bloom Leave your room for the sky Take a ride take a ride take a ride take a ride Nightline glowing from the wall Little god Scare away, keep at bay Elfish shadows want to fool me Dimly, dimly lt's the road Creatures move very slow Coming close coming close coming close coming close Join them underneath the fern Lit right through from the moon Looking down, I don't mind if she can see me

夜间 月球之旅背面一个大萤火虫请带我去了城市上空你的头发拿起所有的光线热带鱼的天空坐一坐坐一坐坐一坐采取来吧以我的车打开窗口的标志染色蓝，湿透了我的棉皮看到现在的Tinkerbell在盛开给您房间的天空坐一坐坐一坐坐一坐坐一坐夜线从墙上发光小神吓跑，保持海湾如小精灵的阴影要骗我昏暗，隐约失怙的道路生物移动速度很慢逼近逼近逼近即将结束加入他们的行列下方的蕨类通过点燃权从月球展望未来，我不介意，如果她能看到我

The thesis first recommends the famous fuzzy Gaussian approximation system which is based on the Gaussian membership function, the fuzzy logic of product reasoning and the fuzzy law of weight approach. This thesis is discusses the general fuzzy Gaussian membership function that can approximate the form of triangular, trapezoid and Gaussian function , and its basic form is .The general fuzzy Gaussian membership function is to be generally used in the field of approximation .

模糊逼近是近年来发展比较迅速的一个新兴方向，论文首先给出了模糊理论中著名的基于高斯隶属函数、乘积推理模糊逻辑和重心解模糊法的模糊高斯型万能逼近定理，在此基础上本文进一步给出了可以用来逼近三角形、梯形和高斯形的广义高斯隶属度函数形式，它的基本形式是。

In the following part,we define a couple of new approximate operators and a couple of corresponding new approximate measure operators,in this way,inner measure belief function and lower probability all can be considered as the particular cases of this lower approximate measure .

通过定义一对新的逼近算子以及相应的一对逼近测度，使内测度、信任函数、随机集上的下概率均可表示为此下逼近测度结构下的一种特例。

A neural network is then used to represent the estimation of potentials,both the parameterized TD(0) learning formulas and algorithm are also derived for approximating the policy evaluation.By the approximation values of potentials and approximation policy iteration,a unified neuro-dynamic programming optimization approach is consequently proposed for both two criteria.

根据定义式，建立性能势在平均和折扣性能准则下统一的即时差分公式，并利用一个神经元网络来表示性能势的估计值，导出参数TD(0)学习公式和算法，进行逼近策略评估；然后，根据性能势的逼近值，通过逼近策略迭代来实现两种准则下统一的神经元动态规划(neuro-dynamic programming，NDP)优化方法。

In the final chapter, we discuss interval polynomial approximation of rational surfaces. Firstly, we briefly state the interval-surface approximation based on the Taylor Expansion, and later, we give out a better interval-surface approximation based on the optimization method, which is also the main work of this paper.

第四章主要介绍了有理曲面的区间多项式的逼近，首先简单介绍了基于泰勒展开来做的区间曲面逼近，后面是本文的主要工作，我们基于优化方法得到了更好的区间曲面逼近，它也是本文的重要部分。

The adaptive compensation term of the optimal approximation error and a new robust term are adopted to minify the influence of modeling error and parameter estimation error.

该方案通过引入最优逼近误差的自适应补偿项和新的鲁棒项，削减建模误差和参数估计误差的影响，从而在稳定性分析中取消了要求逼近误差平方可积或逼近误差的上确界已知的条件。

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。