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Events,Operation and Relation of Sets, Classical Probability, Geometrical Probability , Statistical Stability of a Frequency, Axioms of Probability, Conditional Probability, Total Probability Theorem, Bayes' Rule,Independent Events,Independent Repeated Trials, One Dimensional Random Variables, Discrete Random Variables, Distribution Function of a Random Variables , Continuous Random Variables, Normal Distribution, Distribution of a Function of a Random Variable, Multidimensional Random Variables, Joint Distribution Function, Marginal Distribution Function,Discrete Two—Dimensional Random Variables,Continuous Two—Dimensional Random Variables, Independent Random Variables, Distribution of Functions of Random Variables,Expectation,Variance, Covariance, Coefficient of Correlation, Bivariate Normal Distribution, Law of Large Numbers, The Central Limit Theorems, Sample and Population ,Chi—Squared, T and F Distributions , Sampling Distributions , Point Estimation , Interval Estimation , Testing Hypotheses , A Test of Significance for Parameters in a Single Sample From a Normally Distributed Population , A Test of Significance for Parameters in Two Sample From Normally Distributed Populations .

本课程的主要内容：概率的概念与运算、随机变量及其分布、随机变量的数字特征与极限定理、数理统计的基本概念、估计和检验的基本方法，随机事件与概率随机事件、事件的关系与运算、几何概率、统计概率等，条件概率、全概率公式、贝叶斯公式、事件的独立性、二项概率公式，随机变量的概念、离散型随机变量、随机变量的分布函数、连续型随机变量、随机变量函数的分布，多维随机变量及其分布函数、边缘分布函数、随机变量的独立性、二维随机变量函数的分布，数学期望、方差、协方差和相关系数、大数定律、中心极限定理，总体与样本， X 2-分布、 t-分布和 F-分布，统计量及抽样分布，假设检验的基本概念、单个正态总体参数的显著性检验、两个正态总体参数的显著性检验。

Central Limit Theorem -- States that distribution of sample means tends towards an approximate normal distribution.

中心极限定理--样本的均值近似服从正态分布。如果样本容量较大，那么其均值的分布越近似于正态分布。

Known by the central limit theorem, the distribution of the absurd will eventually converged on the Gaussian distribution, while the speed chosen by the decision of the tail function.

由中心极限定理所知，这个荒谬的分布将最终汇聚于高斯分布，而其速度由所选择的尾部功能决定。

The primary work of this paper includes: 1 The general process and the fundamental theory of genetic algorithm is introduced systematically, which is also be applied to an example; 2 The penalty function method and the constraint tournament method are introduced in the paper, which are used to process the constraint limit. Via analyzing the basic principle of NSGA-II ,which is elaborated in the paper, the fast non- dominated sorting method, congestion distance and its comparison operator, the elite strategy and the main process of NSGA-II is researched particularly. 3 Via modeling the fire distribution problem, the model is computed by the algorithm of NSGA-II, which is combined with both the penalty function method and the restraint league tournament method The optimization of two goals are also realized in the paper. The results derived from the VC++6.0 indicate that, two algorithms both have the high convergence, simultaneously the Pareto optimal solution also maintain the variety of distribution.

本文所作的主要工作如下：系统地介绍了遗传算法的一般流程和基本理论，并应用于一个函数优化的实例；研究了用于处理约束限制的罚函数法和约束联赛法，论述了NSGA-II的基本原理，并对其提出的快速非支配排序法、拥挤度及其比较算子、精英策略及NSGA-II的主要流程作了详细的研究；建立了火力分配问题的模型，并将NSGA-II算法分别与罚函数法和约束联赛法相结合对该模型进行了计算，实现了对两个目标的最优化；用VC++6.0编程计算后所得的结果表明，两种算法均具有很好的收敛性，同时Pareto最优解也保持了好的多样性分布。

Weibull distribution is widely used as a life distribution, and estimating lower confidence limit of reliability is important. But so far this problem has not been well solved if when the sample size is small.

威布尔分布是使用非常广泛的寿命分布，关于威布尔分布的可靠度的下限估计是一个有重要意义的问题，文献中有很多讨论，但当样本量较小时，关于二参数威布尔分布的可靠度的下限估计至今没有非常有效的方法。

By using the generalized central limit theorem, the heavy-tailed distributions (heavy-tailed Rayleigh distribution for amplitude image and heavy-tailed exponential distribution for intensity image) are obtained from the symmetric stable distributions of real and imaginary parts of echoes. Taking the heavy-tailed Rayleigh distribution as an example, the algebraic tails of heavy-tailed distributions are explained as well as the statistics of sharp peak and heavy tail.

本文使用广义中心极限定理，由雷达回波的实部和虚部的对称稳定分布，得到SAR图像的拖尾分布（幅值图像的拖尾Rayleigh分布以及强度图像的拖尾指数分布），并以拖尾Rayleigh分布为例，讨论了拖尾分布的代数拖尾特征以及尖峰厚尾的统计特性。

In the elastic limit state as defined in this paper, the stress distribution and the limit temperature of the plate are obtained.

对陶瓷 /金属功能梯度多层组合板进行了稳态热传导分析及热弹性极限分析，导出了稳态温度分布场，极限状态热弹性应力分布的计算式，并在弹性极限状态下，得到了弹性极限温度。

Based on the old algorithm, introduce new Linear Feedback Shift Register, new Central Limit Theorem, Maclaurin Equation to generate uniform distribution, gaussian distribution, exponential distribution's random number respectively and analyze them, compares the difference between new algorithm and old algorithm.

在原有算法的基础上，提出了改进型线性反馈移位寄存法、改进型中心极限定理法和麦克劳林展开法，并对其作测试仿真，比较传统算法与改进型算法之间的优缺点。

Dynamic reliability under Littlewood-Paley wavelet is the biggest, dynamic reliability under modified meyerwavelet and harmonic wavelet are close. Analyzing the dynamic reliability of structure under odd exponent wavelet is very simple, it doesn't calculate Power Spectral Density function integral, it is only to calculate the square of displacement standard deviation and the square of velocity, then the dynamic reliability of structure can be concluded by max distribution. In addition the effects of upper limit is considered, when upper limit is smaller, the dynamic reliability of structure is less, that is, the damage possibility is bigger.

通过结构地震反应在小波基下的动力可靠性分析说明：无论是单自由度还是多自由度从理论上推导在这四种小波下的结构动力可靠性是可行的，而且考虑的结构地震反应都是非平稳的高斯过程，方法实现也比较容易；在Littlewood—Paley小波基下求得的结构的动力可靠度比较大，由改造的meyer小波和谐波小波求得的动力可靠度略有差异；单边指数小波下的结构动力可靠性分析非常简单，不用求功率谱函数来积分，只需求得结构地震反应的位移方差，速度方差，利用最大值分布公式就可得到结构的动力可靠时程；另外也考虑了超越界限对结构动力可靠度的影响，超越界限越小，结构的动力可靠度越小，即破坏概率越大。

Dynamic reliability under Littlewood-Paley wavelet is the biggest, dynamic reliability under modified meyerwavelet and harmonic wavelet are close. Analyzing the dynamic reliability of structure under odd exponent wavelet is very simple, it doesnt calculate Power Spectral Density function integral, it is only to calculate the square of displacement standard deviation and the square of velocity, then the dynamic reliability of structure can be concluded by max distribution. In addition the effects of upper limit is considered, when upper limit is smaller, the dynamic reliability of structure is less, that is, the damage possibility is bigger.

通过结构地震反应在小波基下的动力可靠性分析说明：无论是单自由度还是多自由度从理论上推导在这四种小波下的结构动力可靠性是可行的，而且考虑的结构地震反应都是非平稳的高斯过程，方法实现也比较容易；在Littlewood—Paley小波基下求得的结构的动力可靠度比较大，由改造的meyer小波和谐波小波求得的动力可靠度略有差异；单边指数小波下的结构动力可靠性分析非常简单，不用求功率谱函数来积分，只需求得结构地震反应的位移方差，速度方差，利用最大值分布公式就可得到结构的动力可靠时程；另外也考虑了超越界限对结构动力可靠度的影响，超越界限越小，结构的动力可靠度越小，即破坏概率越大。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。