逼近的

Based on wave propagation feature, this paper analyses 3D seismic migration algorithms such as alternating direction implicit method, LU decomposition method, and inverse operator approach method. The result shows that the alternating direction implicit method is fast but causes distortion in wave field extrapolation and affects image accuracy; however LU decomposition and inverse operator approach methods are fast while holding circular symmetry of wave field, and are promising in oilfield exploration and development.

在波的传播特征分析基础上，对交替方向隐式法、LU分解法、逆算子逼近法等三维地震偏移算法进行了分析研究，结果表明，交替方向隐式法虽然快捷但是在波场外推中明显产生畸变并影响成像的准确性，而LU分解和逆算子逼近法是保持波场圆对称特征前提下的快速算法，在油田勘探开发中具有较好的应用前景。

We investigate mainly solving the hyperbolic and parabolic equations by using the MQ quasi-interpolation. The underlying idea of our means is that: employing the derivative of the MQ quasi-interpolation to approximate the spatial derivative of the PDE, while the approach of the temporal derivative of the PDE is used a finite difference.

我们主要就MQ拟插值在双曲型方程和抛物型方程中的应用进行了研究，其基本思路是：利用MQ拟插值的导数逼近微分方程的空间导数，而微分方程的时间导数则采用有限差分逼近。

Since the structure self-organization and self-learning abilities of GFNN, it is different from the universal approximation theorem of FLS and BP theorem of NN.

由于GFNN的结构自组织和参数自学习能力，使得它与模糊逻辑系统中的万能逼近定理以及人工神经网络的BP逼近定理不同，GFNN不再只是一个存在性定理，它给出了GFNN的实现过程。

To cousider the least,we have to establish these facts under some comparablystrong but not the most proper conditions.From [12] and [13],if we suppose thatfis Lipschitz continuous in t,then all the above conditions(H1)-(H3) canbe established to a class of approximating problems of (1)(2).So the followingtheorem can be proved by theorem 5 through approximation process.

这时，我们只好"退而求其次"，在较强的"看来不是最适当的条件"下，来建立这些事实，从[12]和[13]中我们看到，只要加上"〓对t为Lipschitz连续"，则对（1）（2）的逼近问题族，上述条件（H1）-（H3）都可建立起来，从而，通过逼近过程，用定理5就可得到如下的定理。

In this paper we use pointwise modulus of smoothness to study approximation direct theorem and equivalent theorem for some linear operators and quasi-interpolant operators; Using pointwise modulus we discuss the strong converse inequality on K-functional; and using a modified weighted K-functional and weighted modulus of smoothness we study approximation with Jacobi weight on operator with non-zero first order moments.

本文利用点态光滑模ω_~(2r)来研究某些线性算子及逆中插式逼近正定理和等价定理；利用点态光滑模讨论其关于K-泛函的强逆不等式；同时利用一种改变的带权K-泛函和带权光滑模研究一阶矩不为零的算子的点态带Jacobi权逼近。

The paper is organized as follows:In chapter 1 we give a brief review of approximation theory of operators,and present the corresponding research background.

本文由四章组成，其内容如下：第一章首先回顾了算子逼近论的发展及本文所做研究课题的进展情况，并简要介绍了本文的主要内容。第二章主要讨论了q-Bernstein算子对各种函数的逼近性质。

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。

As a result, we have demonstrated that the best approximating operator and the best approximating of bounded linear operator in H10 and H1a,+∞ are consistent and, at the same time, we have generalized the theorem of the best approximating of bounded linear operator to the more universal H1

然后，我们说明了在这样的索伯列夫空间上定义的样条插值算子和最佳逼近算子是一致的，同时把有界线性算子的最佳逼近定理也推广到了一般的索伯列夫空间H~1a，+∞上去。

The solutions of ProblemⅠ,ⅡandⅢare discussed by using the generalized conjugate gradient method. When the equation is consistent, the solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are successfully found; When the equation is inconsistent, the least-squares solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are also found successfully. The generalized conjugate gradient method has the following traits:(1) It can judge automatically the information of solutions.

利用广义共轭梯度法，讨论了问题Ⅰ、Ⅱ和Ⅲ解的情况：当方程相容时，研究了方程的一般解、对称解、中心对称解、自反矩阵解、双对称解、对称次反对称解及其最佳逼近等问题；当方程不相容时，研究了方程的最小二乘一般解、最小二乘对称解、最小二乘中心对称解、最小二乘自反矩阵解、最小二乘双对称解、最小二乘对称次反对称解及其最佳逼近等问题。

The study of direct and inverse theorems on the approximation of linear operators to functions in normed linear spaces is an important subject in the approximation theory.

线性算子对赋范线性空间中函数逼近正逆定理的研究是逼近论中重要的研究课题之一，在理论和实际应用上都具有重要的意义。

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。