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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。

Numerical result describes flow characteristics of diffuser pipe and lockage gate etc. Model test shows that the method is reliable, and accuracy of the numerical model is approximate to 3-D numerical model, which is helpful for shape optimization.

数值计算结果的合理性得到了模型试验结果的验证，这表明轴对称模型接近三维模型的模拟精度，为竖井式进／出水口优化提供可靠、详细的依据，从而提高了模型试验的效率。

Support has been provided for that annulus fluid instances were numerical simulated with PHOENICS, PHOENICS is used to set up a numerical model of power-law fluid in a concentric annulus flow, by comparing the numerical simulation results for the axis velocity of the power-law fluid in a concentric annulus flow with two dimensional PIV experimental results.

为应用PHOENICS数值模拟环空管道内其它流体情况提供借鉴，利用PHOENICS建立幂律流体环空流动的数值模型，将同心环空幂律流体轴向速度数值模拟结果与二维PIV实验结果对比。

In the brain mechanism researches of Numerical Processing, Subitizing, Counting and SNARC Effect all presented that there is intense relationship between numerical processing and spatial coding, which strongly activates the IPS, considered as numerical processing main field.

在数量认知加工的脑机制研究中，顿识、数数、SNARC效应都表明了数字加工与空间编码有密切关系，在大脑的顶内沟附近皮层有较强的激活，有关研究表明这是数量化专门区。

In order to evaluate each performance index of a numerical control machine tool, the comprehensive performance evaluation index system of a numerical control machine tool was established, and the performance index weight coefficient of the numerical control machine tool was determined by using the 1-9 scale law in the analytic hierarchy process.

为了全面评价数控机床的各项性能指标，建立了研究数控机床综合性能的评价指标体系，采用层次分析法中的1～9标度法确定了数控机床各项性能指标的权重系数。

Without the need of traditional numerical optimization method, solution for particular numerical problem can be obtained by substituting numerical values of each coefficient into the symbolic solution.

有效子问题是指子问题的最优解中至少有一个是原问题的最优解，多余子问题是指子问题的最优解中没有一个解是原问题的最优解。 3）求解方面：在国内外首次提出了求解最优解的符号表达式的思想。

This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.

本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。

This course provides a basic introduction of topics such as: interpolation, solution of nonlinear equations, curve fitting to measured data, numerical linear algebra, numerical integration, numerical differentiation, etc..

本课程介绍内容包括：内插法，非线性方程式求解，曲线近似法，线性代数数值运算，数值积分，数值微分等课题。

The research on generalized numerical ranges of operator contains n-numerical ranges and numerical ranges of operator polynomial.

在广义数值域方面，深入研究了算子数值域的重要推广：算子n-次数值域、算子多项式数值域及其谱理论两大问题。

The numerical results indicate that the operator splitting method effectively suppresses numerical oscillations in the cases of high air bearing number. The numerical results show that both air lift force and pitch moment increase with the ratio of the slider's rail height to the air film characteristic height and the air bearing number, and finally reaches to stable value.

比较在不同轴承数下的气浮力和纵倾力矩发现：同一轴承数下，气浮力随气膜特征厚度减小而增加；当磁头槽台高度与气膜特征厚度的比值相同时，气浮力随轴承数增大而逐渐增加直到达到某一值后保持不变；纵倾力矩随轴承数增加而增大到某个最大值后减小。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。