逼近的

The new method is a combination of characteristic approximation to handle the convection part, to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion, a smaller time truncation is gained at the same time, and a mixed finite elementspatial approximation to deal with the diffusion part, the sealer unknown and the adjoint vector function are approximated optimally and simultaneously.

此方法即为对方程的对流项沿流体流动的方向即特征方向进行离散，从而保证格式在流动锋线前沿逼近的高稳定性，消除了数值弥散现象，并得到了较小的时间截断误差；另一方面，对方程的扩散项采用混合元离散，可同时高精度逼近未知函数及其伴随向量函数，理论分析表明，此方法是稳定的，具有最优的L~2逼近精度。

If we hope to use a sequence of finite objects to approximate infinite objects, then we should know what kinds of infinite objects are approximable and how to approximate them effectively.

无穷形式对象可逼近的充分条件为了研究哪一类无穷对象可以逼近以及如何有效地逼近它们，我们用过程模式作为无穷对象上的计算的模型，用以刻画接受无穷输入、生成无穷输出的无穷对象上的计算。

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

In the fourth chapter, firstly it introduces the Boolean functions algebraic expressions of the 2-value clock-controlled stop-and-go generator and Gunther generator. It reveals the balanced property of the two kinds of Boolean functions, and studies the Walsh cycle spectrum and the autocorrelation function. It also obtains the coincidence rate of their output sequences with affine sum of some bits of input sequences, and analyzes their ability of resisting the best affine approximation cryptanalysis and differential cryptanalysis. Secondly, we properly present a new definition of the Best Affine Approximation, namely BAA on the Boolean vector functions, followed by the spectral characteristic of such defined BAA attacks through using the decomposition formula of the union distribution for random variables. A lower bound of such BAA attacks is proposed. Finally, we also study the spectral characteristic of the second kind of nonlinearity of Boolean vector functions, followed by a higher bound of such nonlinearity. Furthermore, the limited relationship between the second kind of nonlinearity of Boolean vector functions and the linear structure of the linear combination of every component is analyzed.

在第四章中，首先给出了2值密钥流"停走生成器"和"衮特生成器"中实际存在的布尔函数的代数表示，揭示了这两类布尔函数的平衡性，随后研究了它们的Walsh循环谱和自相关函数等，得到了它们的输出序列与输入序列中的某些bit的仿射项的符合率，分析了它们抵抗最佳仿射逼近攻击和差分攻击的能力；其次，我们合理地给出了布尔向量函数最佳仿射逼近的新定义，利用布尔随机变量联合分布的分解式考察了相应的谱特征，并给出了布尔向量函数与其最佳仿射逼近的符合率的一个下界；最后，我们还考察了布尔向量函数第二类非线性度的谱特征，给出了布尔向量函数第二类非线性度的一个上界，并揭示了布尔向量函数第二类非线性度与其各个分量的线性和的线性结构之间存在的制约关系。

The number of the hidden neurons,the value of the weight and bias in RBF neural network are determined by the trained SVM.The approach is adopted in modeling and diagnosing the fault of gear case.

RBF网络由正则理论推导出来，具有最佳逼近的性质，与广义的样条函数相当，可以用局近的总和达到对全局的逼近，具有全局逼近的性质[3]。

A simple polynomial approach for A Class of nonlinear system modeling is presented. By this, the input-output data are firstly changed into [0, 1] by using topological homeomorphism conversion; then an initial polynomial model is selected. The parameters of polynomial model are estimated by using recursion least squares method. A final polynomial model is obtained by repeatedly estimating parameter and eliminating redundant terms.

给出一类非线性系统的实现简单的多项式逼近的建模方法，在此方法中，将输入输出数据通过拓扑同胚变换，变换到[0，1]区间内，用多项式逼近的方法进行建模，对初始给定的多项式模型，通过反复的参数辨识、去除模型中的冗余项，得到非线性系统的多项式逼近模型，再利用拓扑反变换，将数据还原回原始数据区间。

This project also obtained several limit theorems for some important dependent random variables and stochastic processes, such as the Strassen law of the iterated logarithm for negatively dependent random variables, strong limit theorems for mixing random vectors in Banach spaces, sample path properties for two-parameter fractional Wiener processes, and so on.

随机环境中的随机变量与随机过程的研究在国内外相当活跃，本项目主要研究它们的极限性质，着重研究了随机风景中随机变量与随机过程的极限性质，主要取得了以下几个结果：首先对简单对称的Kesten-Spitzer随机游动在低阶矩的条件下给出了强逼近，大大减弱了前人要求任意阶矩的条件，然后对独立风景中的一般随机变量给出了强逼近的一般性结果，由此导出在风景和随机变量都只具有低阶矩的条件下的独立但不同分布、混合相依变量的强逼近，在只有弱高于二阶矩的条件下得到了重相对数律和弱收敛；给出了连续时间参数的Brown风景中Brown运动和稳定风景中稳定过程的滞后增量和连续模等精确样本轨道性质；同时给出了一些重要的相依随机变量和过程的若干极限定理，如负相关随机变量的Strassen重对数律、抽象空间上混合相依变量的一些强极限定理成立的充分必要条件、两参数分数Wiener过程的样本轨道性质等。

This dissertation focuses on the spherical wavelet expansion of the earth gravity field and its application. Based on the concept of the integration approaches and radial basis functions the spherical wavelet is put forward, with that the earth gravity field is described in a new way, and some other researches are conducted, they are: spherical wavelet regularization, multiscale approximation of satellite gravity measurement, down continuation of airborne geavimetry data, the least squares properties of geopotential wavelet approximation, the spherical wavelet solution of two kinds of BVP and spherical selective multiscale reconstruction.

本文围绕地球重力场的球面小波展开及其应用进行研究，在积分逼近与径向基函数概念的基础上引入了球面小波，利用球面小波对重力场展开进行了重新表示，在此基础上进行了球面小波正则化、卫星重力多尺度逼近、航空重力数据向下延拓、重力场球面小波逼近的最小范数性质、两类边值问题的球面小波实用解、球面选择多尺度去噪方法等方面的研究。

After introducing the primary approximation approaches for curve and surface offset, we give an optimal approximation approach for offsetting curve based on shifting control points, which relies on approximating the normal by Legendre polynomial approximation.

在全面介绍了等距曲线曲面逼近的主要方法以后，作者首先利用Legendre多项式得到基曲线法矢曲线的最佳平方逼近，由此给出了基于控制顶点偏移的等距曲线最优逼近的算法，它在算法效果和效率上都远优于其他同类算法。

For problem II, many references have studied it and obtained its common solutions, symmetric solutions, skew-symmetric solutions and its optimal approximation constrained solution, but the representation of its solutions are complicated.

本文首次采用迭代法系统的研究了它求一般解、对称解、反求解约束矩阵方程及其最佳逼近的迭代法的研究对称解、中心对称解、中心反对称解、自反矩阵解、反自反矩阵解、双对称解、对称次反对称解及其最佳逼近问题，并首次成功地解决了它求中心对称解、中心反对称解、自反矩阵解、反自反矩阵解、双对称解与对称次反对称解及其最佳逼近的问题，拓广和改进了已有的研究成果。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。