分布矩

On the basis of that, in this paper, we deal with the distributions and moments of integral type functional for nonhomogeneous processes, and obtain computational formula of the distributations and moments.

在此基础上，对马氏骨架过程中非齐次过程积分型泛函作讨论，并且得到了它的分布与矩的具体计算公式。长沙铁道学院科研所！湖南长沙410075

The second moment of the beam distribution function is discussed in detail.

详细地讨论了束流分布函数的二次矩。

There are totally five chapters in the paper. Chapter 1 is the introduc-tion,and extreme value theory and methods and modelling for returns fat tails are introduced systematically in Chapter 2.This chapter also presents mean excess function and de Haan's moment estimate to decide on the reasonable exceedance threshold. Chapter 3 describes in detail non-linear time series mod-els such as GARCH models and the corresponding statistical inferences,and it also gives modelling and statistical analysis methods for returns series. Chap-ter 4 uses the models in Chapter 2 to analyzes the daily returns for Shanghai complex index and Shenzhen complex index in the Shanghai and Shenzhen stock markets. Chapter 5 applies the models in Chapter 3 to the volatility analysis of the two stock indices returns.

论文总共五章：第一章是引言部分；第二章系统介绍了极值理论方法和收益率厚尾的建模方法，给出了平均剩余函数法和de Haan矩估计相结合的方法确定合理的超越门限；第三章详细论述了非线性时间序列模型GARCH类模型及其统计推断，并且给出了收益率时间序列波动的建模和统计分析方法；第四章利用第二章的模型对国内沪深两市大盘指数上证综指和深证综指日收益率数据分布的厚尾进行了实证分析；第五章将第三章的模型应用到两个股指日收益率时间序列的波动分析。

In our recent work of simulating the chemical process of polymerization by matho-matical models,problems involving Flory distribution and its moments of different orders have been frequently encountered.

最近我们在成纤高聚物反应工程数学模拟研究过程中，多次碰到Flory分布高阶统计矩的问题——级数？

The diffraction distributions of Gaussian beam limited by the circular apertures with different sizes in scanning objectives focal plane were studied, and then the effective spot radius in focal plane was calculated using second moment and compared with the ideal one. The influence of apertures with different sizes on resolution was analyzed.

在不同孔径圆孔的限制下，对扫描物镜焦面上的衍射光场分布进行数值计算，并利用二阶矩统计的方法对焦面上的等效光斑半径进行数值计算，将其与不受限时的理想情况进行对比，分析孔径尺度对激光束扫描系统分辨率的影响。

At last the light intensity distribution of Fresnel diffraction at several rectangular apertures is calculated and analyzed.

最后计算分析了多矩孔菲涅尔衍射的光强分布。

In this paper,taking advantage of some properties of Gamma function,we get the explicit solution. Some simulation results are also given in this paper. In chapter three, we discuss the problem under censored data in three circumstances.

一直以来，对Weibull分布参数的矩估计都是采用数值方法求解，本文利用Gamma函数的一些性质，得到了估计的显式解，并从理论和数值模拟说明此种方法相比其它方法的优越性。

The sufficient and necessary conditions of complete moment convergence for sequence of identically distributedρ-mixing random variables are obtained, which extent and generalize the well-known results.

获得了同分布ρ混合序列的矩完全收敛性成立的充分必要性条件，推广和改进了已有的结果。

The discrete velocity ordinate method in the kinetic theory of gases is developed and applied to discretize the correspo

借助非定常时间分裂法和无波动无自由参数的NND耗散格式，建立直接求解微观分子速度分布函数的有限差分数值格式；研究并发展可用于离散速度坐标点选取和离散速度空间宏观取矩的高斯─埃尔米特无穷积分方法、等均间隔的牛顿─柯斯复合积分法、以勒让德多项式的根为积分结点的高斯─勒让德数值积分法，并应用于不同马赫数绕流模拟；通过对不同流域一维激波管问题、二维圆柱绕流问题和三维球体绕流的计算研究，并将计算结果与其他途径得到的研究结果诸如DSMC模拟值、N-S解及有关实验数据进行比较分析，创建了一套能有效模拟稀薄流到连续流不同流域气体流动问题简化的统一数值算法研究框架

The analysis indicates that the mean intensity distribution on the receiver plane is closely related to the ratio of the lateral correlation length to the surface root mean square height.

研究了粗糙目标对相干光场的散射，导出了在接收平面上光场的自相关函数、光强度的分布和光强度的二阶矩，在分析粗糙目标对激光脉冲后向散射的基础上，提出了后向散射光强度与目标均方根高度和相关长度的关系，阐明了粗糙目标的后向散射机理。

I use an example quoted by Hu Jiaqi:"It is reported that America separates the DNA of a kind of virus by making use of genetic technology and combines it with another kind of DNA. Finally, they get a kind of virulent biological agent called a "pyrotoxin". Someone discloses in private that 20 grams of such a kind of biological agent could result in the global death of 6 billion people due to infection."

我在这里例举胡家奇所引用过的例子："据报道，美国利用转基因技术，将一种病毒的DNA分离出来，与另外一种DNA进行结合，拼结成一种剧毒的"热毒素"生物战剂，且私下有人透露，这种生物战剂只需20克，就可以导致全球60亿人全部感染死亡。"

Waiting, for the queers and the coons and the Reds and the Jews.

等待着疯子和黑人还有红色共产主义者还有犹太人