函数的积分

It is pointed out at first time that two popular methods of investigating intermittency——-bin-wise integral and strip integral are inequivalent when the translational invariance of semi-inclusive density functions is destroyed, and the anomalous scaling of these two quantities may originate from different dynamics.

我们在研究中首次指出，研究间歇现象的实验中目前流行的两种统计阶乘矩方法：关联函数Bin-Wise和Strip积分方法并不等价，它们所得到的阶乘矩的不同标度行为可能反映了不同的物理起源。

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。

Limit theorems for the integration of function sequence with respect to weak convergence probability measure sequence are proved under the condition of the weak tight, which have been used to research the some convergence of expectant functional sequence,and a sufficient condition for the epi-convergence of expectant functional sequence is obtained.

提出了弱胎紧的概念，并在弱胎紧的条件下证明了函数序列关于弱收敛概率测度序列积分的极限定理，用其研究了期望泛函序列的若干收敛性，得到了期望泛函序列的、上图收敛的一个充分条件。

By transforming the interlace series type linear differential equation with coefficients containing negative second order power function and arrangement number into the linear differential equation of successive integral,the theory and method for the general solution of this kind of equation are determined.

通过把系数含有负二次幂函数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程，找出了求这类方程通解的方法与理论，所得定理给出了严格的证明，并通过实例介绍了它的应用

Pass the interlace series type linear differential equation that coefficient contains power function and arrangement number change into the linear differential equation of successive integral, have found out the theory and method that begs this kind of equation to know to untie.

通过把系数含有幂函数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程，找出了求这类方程通解的方法与理论，把所得定理给出了严格的证明，并通过实例介绍了它的应用。

Throush the interlace series type linear differential equation,coefficient containing three negative number of times,power function and arrangement number can be changed into the linear differential equation of successive integral.

通过把系数含有负三次幂函数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程，找出了求这类方程通解的方法与理论，把所得定理给出了严格的证明，并将其推广，同时通过实例介绍了它的应用。

In this method the transfer functions, which are the response of the temperature and thermal stress in the key parts of the special structures caused by the unit temperature load with the special loading model, are computed firstly using the detailed finite element analysis. Then both the thermal and stress responses and their sensitivities to any complex change of temperature can be obtained by the simple cirro-product integral.

该方法的基本思想是：基于一定的结构和热载荷模式，将事先通过详细有限元分析求出的单位突加热边界条件变化引起的结构控制区的温度和热应力响应作为传递函数，然后进行简单的卷积积分运算，就可以得到任意热载荷幅值变化历史所对应的温度和热应力，进而也可快速进行灵敏度分析。

The uniqueness of solution of field point, inside a convex region due to singular source with kernel function decreasing with distance increasing, outside-region-distribution such that the boundary condition expressed by the response of the source is satisfied, is proved by using the condition of kernel function decreasing with distance increasing and an integral inequality.

应用奇源解的核函数沿距离递减的条件和积分不等式，可证这类奇源在凸域外分布只要满足以它产生的响应来表达的边界条件时，所引起相应的域内场点解是唯一的。

To avoid the trouble to construct the basis functions, we introduce a Lagrange multiplier into the variational formulation to replace the constraint condition for the basis.

本文采用同样的思路用Galerkin 边界元方法求解带有约束条件的与第一类Fredholm 间接边界积分方程等价的变分方程，为避免构造基函数时约束条件的限制，我们采用Lagrange 乘子法，把约束条件放入变分方程中去，形成扩展的变分方程，用线形单元离散后求解。

Research results indicate that continuous Regional Identification Function is used in nodal virtual flux method, volumn integral and surface integral enhances the convergence and stabilization;using 'put a big number' to deal with the first boundary is faster than 'Remove row and column', the more the first boundary nodes are the more obvious advantage will display;PCG method is quite faster than Crout method to solve equations;it is reliable to use three-dimensional finite element simulation theories to simulate and predict deep foundation pit dewatering in such areas.

研究结果表明，在结点虚流量法及计算体积分和面积分时引入连续的区域识别函数增强了解的收敛性和稳定性；处理已知水头边界的&置大数&法在时间上要比&去行去列&法短一些，定水头边界节点越多，其优越性表现越明显；PCG法比直接解法快很多；三维有限元数值模拟理论用于模拟预测此类地区的深基坑降水具有较高的可信度。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。