最小化

The research of both theories and practices of gridding in the dissertation shows that: Linear interpolation based on triangulation is simple computationally and fast, but its gridding results isn't smooth and its precision is low; Multiquardric method is also simple computationally with high precision and good effect, but its gridding is slow because it is based on global calculation; Minimum curvature method is fast with high precision and good effect, but its gridding quickly degrades over areas with sparse data control when grid spacing smaller than the actual grid spacing is used; Ordinary Kriging method is high-precision, but its gridding is slow because of large calculation; Inverse interpolation is a computationally fast, efficient and robust method with high accuracy and perfect effect, and its gridding results of different gridding orientations are basically identical. Inverse interpolation is suitable for thegridding of geophysical irregular data, especially for large-scale geophysical irregular data.

本文的方法研究和数据试验分析表明：基于三角网的线性插值法计算简单，速度快，但其网格化结果不光滑，精度不够；多元二次函数法计算简单，网格化精度高，效果良好，但它是基于全局计算的，计算速度较慢；最小曲率法计算速度快，网格化精度高，效果良好，但其在稀疏控制点的网格化容易出现振荡现象；普通克里格法网格化精度高，效果良好，但其计算量较大，一般计算速度慢；反插值法网格化计算稳定，速度快，精度高，效果好，而且在网格化方向不同的情况下其网格化精度效果都达到基本一致，适合于地球物理不规则分布数据的网格化，特别是大规模地球物理不规则分布数据的网格化。

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。

In addition, an experimental system using C language is established, including modules such as representation of waveform polynomial, decision of path senstization, delay computing, clocking based on single-period sensitization, clocking based on multi-period sensitization, test generation considering noise and transformation from bit-level waveform polynomial to word-level polynomial model. They respectively used to test models and techniques proposed in this paper.

另外，：基于C语言本人设计开发了一个实验软件系统，该系统包括波形多J一贞式表示模块、敏化通路判定模块、延时计算模块、单周期敏化的最小时钟周期精确确定模块、多周期敏化的最小时钟周期确定方法模块、考虑噪声的测试生成模块和位级波形多项式描述转化成字级多项式描述模块，分别用于对本文各章中提出的自动化设计的模型和方法进行实验验证。

A new method that transforms bitlevel waveform polynomial to word-level polynomial model is given, allowing for simple composition This method offers an efficient way to determine whether two descriptions from different design levels are equivalent, so component reuse, synthesis and verification across design levels can be realized. In addition, an experimental system using C language is established, including modules such as representation of waveform polynomial, decision of path senstization, delay computing, clocking based on single-period sensitization, clocking based on multi-period sensitization, test generation considering noise and transformation from bit-level waveform polynomial to word-level polynomial model. They respectively used to test models and techniques proposed in this paper.

另外，基于C语言本人设计开发了一个实验软件系统，该系统包括波形多项式表示模块、敏化通路判定模块、延时计算模块、单周期敏化的最小时钟周期精确确定模块、多周期敏化的最小时钟周期确定方法模块、考虑噪声的测试生成模块和位级波形多项式描述转化成字级多项式描述模块，分别用于对本文各章中提出的自动化设计的模型和方法进行实验验证。

This thesis introduces the basic principle of the least square data fitting.. According to the least square data fitting ,the paper studies and analyzes the linear least square fitting ,the quantic least square fitting and nonlinear least square fitting respectively . By using the mathimatic instrument Matlab , this paper shows a lot of examples of interrelated questions. Using Matlab makes the theory of data fitting easier to be understood.

本文介绍了最小二乘数据拟合法的基本原理，并根据最小二乘数据拟合方法，分别针对线性最小二乘拟合、多项式最小二乘拟合，非线性最小二乘拟合（lsqcurvefit、nlinfit、lsqnonlin、以及非线性的线性化）、多元最小二乘拟合进行了分析和研究，并通过数学工具Matlab实现了对相关问题的举例应用，使相关数据拟合理论更加生动易懂。

The agglomerations sizes of fine particles in the fluidized bed are smaller under higher SPL. The sound waves have little effect on the agglomerations when it is under 120dB. But the agglomerations sizes will be dramatically reduced to 180μm from 720μm when the SPL is above 130dB. The umf has a minimum value at an appropriate frequency of sound and a good quality of fluidization can exist in a greater ranges of frequency of sound when the SPL is higher.

当频率高于120Hz，流化床中形成聚团尺寸随着频率的增加而增大，最小流化速度也随着频率的增加而增大，当频率低于120Hz，流化床中形成聚团尺寸随着频率的减小而增大，最小流化速度也随着频率的减小而增大；料层越高，声波的衰减越大，超细颗粒的流化效果越差，最小流化速度越大。

The minimum fluidization velocity has a minimum value when the frequency of sound waves is 120Hz and it will decrease as the sound pressure level increases. The degree of sound attenuation will increase while bed material is higher and the fluidization quality of fine particles will become poor and the minimum fluidization velocity will increase. Compared with TiO2, the SiO2 fine particles have a better quality of fluidization at the same fluidized conditions.The cluster/subcluster model and oscillators model are used to describe the fluidization characteristics of fine particles in a sound-assisted fluidized bed. The theoretical calculations show that the minimum fluidization velocity umf is decreased with the SPL increased at the same frequency of sound and the quality of fluidization is better.

论文还系统的考察了声压和频率对纳米SiO2和TiO2颗粒流化特性的影响，结果表明：在频率一定的情况下，声压越高，流化床中形成的聚团尺寸越小，最小流化速度越低，流化质量越好；当声压低于120dB时，声场对超细颗粒流化特性的影响减小，当声压大于130dB时，则能显著改善流化效果，使流化床内的颗粒聚团明显减小，最小流化速度明显降低，粉体带出减小；声压一定，频率为120Hz左右时，最小流化速度最低，此时流化床中形成的聚团尺寸最小，流化效果最好；超细颗粒达到较好的流化状态存在一个最佳频率范围，随着声压增高，这个频率范围将增大。

Or 10.40％ of the variation was partitioned among voltinism populations. The Nm (4. 3065) showed that there was to some extent gene flow among three voltinism populations. The average Nei's genetic identity was 0.9637. The genetic distance between V1 population and cultivated V1 population was the biggest (0.0438) and the less was 0.0370 between V1 population and V2 population.

Nei基因多样性指数也是2化群体最大（0.2631），1化群体次之（0.2485），培育1化性群体最小（0.1709），3个群体之间的遗传分化系数为0.1040，即3个化性群体之间的遗传变异占到总遗传变异的10.40％。3个化性群体之间的基因流达到4.3065，表明化性群体间存在着一定程度的基因交流。3个群体之间的遗传一致度为0.9637，遗传距离以培育1化性群体与1化性群体最大（0.0438），以1化群体与2化群体最小（0.0370）。

Energy in , obtain the chemical potential of the superflow state.

通过最小化中的能量，获得超流态的化学势。

We apply the Lagrange theory to obtain this rule.

我们应用Lagrange理论证明了基于学习时间最小化的分解原则。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。