可逼近的

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。

One bases on function value and another bases on arithmetic average difference quotient. In this paper, the author mainly studies the approximation properties of both the function value and the derivative of two kinds of splines interpolation mentioned before, and the optimal error constants are obtained finally.

文中分别就这两类插值样条的函数值及一阶导数的逼近性质展开讨论，相应得出这两种插值函数在被插函数分别为一阶连续可导和二阶连续可导情况下的最佳误差常数。

Properties of measurable functions; approximation by simple functions and by continuous functions; convergence in measure; Egoroff's theorem; Lusin's theorem; Jensen's inequality.

可测函数。可测函数的性质；简单和连续函数逼近；测度收敛；叶果洛夫定理；鲁津定理；詹森不等式

We get to the conclusion that the function set of DCRBFN is dense in a varible-decomposable function set. The result shows that DCRBFN has excellent approximation ability.

DCRBFN系统的逼近能力分析，我们得到DCRBFN的函数集在变量可分离函数集中稠密的结果，因此DCRBFN具有良好的逼近能力。

Also the constructed curve is a shape-preserving curve for the original curve. We can also adjust the shape of curves by parameters of trigonometric uniform polynomial curve to approach the polygon closer. The general trigonometric polynomial curves with m degree and C(superscript 2m-1)(m=1, 2, 3) continuity are further presented.

除了通过切点参数，还可以通过三角均匀多项式曲线参数来调整曲线形状，使所得曲线更加逼近多边形，并可进一步、类似地可构造与给定多边形相切的C(上标 2m-1)(m=1， 2， 3)连续的m次三角多项式曲线。

The powerful function of a new computer language MATLAB, produced by the America Mathworks company, is the mathematical software system for the calculation in science engineering. It can efficiently solve problems in science and engineering such as numerical linear hypercomplex system, digital approximation, optimization, numerical quadrature etc. It also has characters of beautiful interface and convenience for users.

MATLAB是Mathworks公司推出的适用於科学和工程计算的数学软件系统，可高效地解决数值线性代数、微分方程数值解、数值逼近、最优化、数值积分等科学和工程问题，且具有可视化图形处理、使用方便、开放式多功能於一体的新一代计算机语言。

In this paper,we give the error expressions of piecewise linear Lagrange polynomial interpolation and piecewise cubic polynomial interpolation using the Taylor expansions.

中文摘要：本文利用Taylor展开得到三角形上线性Lagrange插值和三次Lagrange插值的导数余项公式，对这些余项公式进行分析，给出了两类能以四阶精度逼近被插函数在对称点的导数值的格式，一种是在均匀剖分时其分片线性插值的相邻单元的导数值的后处理格式，一种是在六片强正规剖分时的三次插值在对称点上的导数值的后处理格式，使得在已知原函数在各节点的值后，通过一个简单的线性计算就可得到原函数在对称点的导数的一个超逼近值，将以往提出的平均导数的二阶精度提高到四阶。

The main achievements of this dissertation are as follows: Let W be a nonsingular matrix. 1. Problem I and Problem II are considered under the matrix set S is as the following: 1 the set of real W-symmetrizable matrices; 2 the set of real W-symmetrizable nonnegative definite matrices; 3 the set of real W-symmetrizable matrices on the linear manifold.

对于问题I和问题II，本文就S是W可对称化矩阵集合、W可对称非负定化矩阵集合以及线性流形上W可对称化矩阵集合等三种情况进行了研究，分别给出了这三种情况下问题I的解存在的充分必要条件，以及解集合的通式表达式，给出了这三种情况下的最佳逼近解，并提供了相应的数值算法和数值实例。

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

The TST was applied to multi-scaling vector to increase it's approximation order, and with PR condition, the dual of transformed multi-scaling vector was obtained. Then the special TST was taken for this dual, the dual of original multi-scaling vector with higher approximation order obtained, finally the multi-wavelet function with higher vanishing moment maybe constructed.

我们先对已知的尺度向量进行双尺度相似变换，以提高其逼近阶，再求出变换后的尺度向量的对偶，对这个对偶再进行特定的双尺度相似变换，就可得到原尺度向量的有高逼近阶的对偶，从而可能得到具有高阶消失矩的多小波函数。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。