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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。

Based on the fundamental principles of the improved method mentioned above, multi-functional computation software package, which can be used to analyze effectively the interference effects of random flaws in plane problem, boundary problem and space problem, is compiled and a number of problems involved in the interference effects of different kinds of flaws such as random equal length through-cracks, random branched throughcracks, random unequal length through-cracks, random holes to through-cracks, unequal length edge cracks, equal length and distance multiple edge cracks, random notches with different aspect ratio, random notch to edge crack, non-coplanar surface cracks with different aspect ratio, staggered surface cracks, surface crack to embedded crack and embedded cracks near free boundary are analyzed and computed by the package.

依据上述改进法的基本原理，本文编制了能有效地分析平面问题，边界问题及空间问题的任意缺陷群相互干涉效应的多功能计算软件包。据此，本文分析计算了各类缺陷群。诸如，任意等长裂纹群。任意折裂纹群；任意不等长裂纹群，任意孔与裂纹群，不等长边裂纹群。等长等间距多裂纹群，任意形状比缺口群，任意缺口与边裂纹，非共面不同形状比表面裂纹群，交错型表面裂纹群，表面裂纹与埋藏裂纹群及自由边界附近埋藏裂纹群等的相互干涉效应问题。

An equal cross-section blade was investigated and a finite element model was built parametrically. Geometrical parameters (such as length, width and thickness), material parameters (such as young's modulus and density) and speed of blade were considered as input random variables while the static frequencies and dynamic frequencies were output random variables. Combining the finite element method, response surface method and Monte Carlo method, the statistical properties and cumulative distribution functions of static frequencies and dynamic frequencies were obtained. Probability sensitivities analysis, which combined the slope of the gradient and the width of the scatter range of the random input variables, was applied to quantitatively evaluate the sensitivities of static frequencies and dynamic frequencies with respect to the random variables. The Scatter plots of structural responses with respect to the random input variables were illustrated how to adjust the values of the static frequencies and dynamic frequencies by changing input random variables.

文中以某试验台用汽轮机等直叶片为研究对象，考虑几何参数、材料参数和转速的随机性，通过有限元参数化建模，将确定性有限元方法、响应面方法和Monte-Carlo模拟法相结合，从而获得了叶片静频、动频的统计特性和累积分布函数；同时考虑随机变量的梯度和离散范围对静、动频的影响，通过概率敏感性分析，定量地判断出叶片静、动频对随机输入变量的敏感性；通过绘制叶片静、动频与输入变量的散点图，定量地分析了如何改变随机变量以调整静、动频率的方法。

In the second aspect, a systematic study is made on random ambiguous point、random asymptotic ambiguous point、random intrinsic value and random intrinsic element of random operator.

在随机非线性算子与随机算子方程方面，深入研究了随机不动点的存在性与随机算子方程的随机解。

Introduce the concept of random regular function and random potential function at first, a necessary and sufficient condition of random potential function for denumerable Markov chain in random environment is provided, and the unique decomposition property of nonnegative random super-regular function is discussed.

首先引入随机位势函数的概念，给出随机位势函数的一个首要条件，进而讨论非负随机上调和函数的唯一分解性。

The dynamic characteristics of stochastic truss structures and stochastic frame structures are analyzed by using Random Factor Method. Then, from the expressions of structural random response of the frequency domain, the computational expressions of the mean value, variance and variation coefficient of the mean square value of the structural displacement and stress response under the stationary random excitation or non-stationary random excitation are developed by means of the random variable's functional moment method and the algebra synthesis method.

考虑压电智能桁架结构物理参数、几何参数、结构阻尼和外荷载、闭环系统控制电压分别或同时为随机变量，构建了结构在随机力作用下的动力响应分析模型，提出了求解方法，推导出结构动力响应随机变量的数字特征计算表达式，通过算例验证了所建模型和所提求解方法的正确性和有效性。

Random recursive set; random self-similar set; random sub-self-similar set; random walk in random environment; skew product Markov chain; frac-tal set

随机递归集；随机自相似集；随机次自相似集；随机环境中随机游动；绕积马氏链；分形集

The holistic design of the system and resolved the designs of software and hardware based on VXI bus are put forward according to the demand of test system. The hardware and software is designed, including the formation and design of hardware system, visual instrument software architecture, program design for instrument driver, high speed real-time data collection. In the dynamic test program, the idea of"software is instrument"was applied to meet the diverse test demands. Last, it is proposed that the VXI test system be developed to more totalization and networked. The basic theory of system identification was introduced briefly at first. The principle of spectrum analysis system identification based on Wiener-Hopf equation was expatiated. and the questions in applying Peusdo Random signal as spectrum analysis methods stimulate signal was studied, The generation principle of the peusdo random signal is researched, the characteristic of peusdo random are analyzed from time domain and frequency domain, the inverse repeat peusdo random signal is brought forward to make up the shortage of ordinary peusdo random signal. And a new chaos genetic algorithmis presented to solve the unprecise problem of the traditional method. In the servo valve dynamic characteristic test system, the spectrum analysis methods was applied successfully, the servo valve dynamic characteristic could be acquired rapidly and exactly, the test results were analyzed and the ameliorate methods were brought forward at last.

结合航天某集团液压测试中心测试系统的需求，提出了基于VXI总线的液压测试系统的整体设计方案，完成了测试系统的硬件设计与软件设计，包括硬件系统构成与设计、虚拟仪器软件结构、仪器驱动程序设计、高速同步实时数据采集等内容；以伺服阀动态特性测试为例设计了测试模块，该模块体现了VXI总线仪器软件开发所倡导的"虚拟仪器"的思想，以软件的灵活应用满足了不同的测试需求；结合自动测试系统的发展，研究了VXI测试系统与网络技术结合，实现各种软硬件资源共享，进一步提高设备及数据的利用率和系统的扩展性，使自动测试向综合化、网络化方向发展；研究了伪随机信号作为谱分析法辨识的激励信号时存在的问题，讨论了伪随机信号的产生机理，从频域和时域分析了伪随机信号的性质及其应用，提出了用逆重复伪随机信号弥补了普通伪随机信号的不足，并以混沌遗传算法对逆重复伪随机信号产生过程中的参数进行优化，可以更合理而不是凭经验产生需要的逆重复伪随机信号。

The holistic design of the system and resolved the designs of software and hardware based on VXI bus are put forward according to the demand of test system. The hardware and software is designed, including the formation and design of hardware system, visual instrument software architecture, program design for instrument driver, high speed real-time data collection. In the dynamic test program, the idea of"software is instrument"was applied to meet the diverse test demands. Last, it is proposed that the VXI test system be developed to more totalization and networked. The basic theory of system identification was introduced briefly at first. The principle of spectrum analysis system identification based on Wiener-Hopf equation was expatiated. and the questions in applying Peusdo Random signal as spectrum analysis methods stimulate signal was studied, The generation principle of the peusdo random signal is researched, the characteristic of peusdo random are analyzed from time domain and frequency domain, the inverse repeat peusdo random signal is brought forward to make up the shortage of ordinary peusdo random signal. And a new chaos genetic algorithmis presented to solve the unprecise problem of the traditional method. In the servo valve dynamic characteristic test system, the spectrum analysis methods was applied successfully, the servo valve dynamic characteristic could be acquired rapidly and exactly, the test results were analyzed and the ameliorate methods were brought forward at last.

结合航天某集团液压测试中心测试系统的需求，提出了基于VXI总线的液压测试系统的整体设计方案，完成了测试系统的硬件设计与软件设计，包括硬件系统构成与设计、虚拟仪器软件结构、仪器驱动程序设计、高速同步实时数据采集等内容；以伺服阀动态特性测试为例设计了测试模块，该模块体现了VXI总线仪器软件开发所倡导的&虚拟仪器&的思想，以软件的灵活应用满足了不同的测试需求；结合自动测试系统的发展，研究了VXI测试系统与网络技术结合，实现各种软硬件资源共享，进一步提高设备及数据的利用率和系统的扩展性，使自动测试向综合化、网络化方向发展；研究了伪随机信号作为谱分析法辨识的激励信号时存在的问题，讨论了伪随机信号的产生机理，从频域和时域分析了伪随机信号的性质及其应用，提出了用逆重复伪随机信号弥补了普通伪随机信号的不足，并以混沌遗传算法对逆重复伪随机信号产生过程中的参数进行优化，可以更合理而不是凭经验产生需要的逆重复伪随机信号。

It also gives the definitions and stochastic properties of pure random process, random walk process and AR(1) autoregressive process, and analyses the simulative data of three typical random processes using wavelet analysis, frequency spectrum analysis and time-correlation analysis. The stochastic properties of time series and the trend component, the time length of time-correlation and the properties of main frequency of these three typical random processes are summarized as the templates for further research.

给出了包括纯随机过程、随机游走过程和 AR(1)自回归过程等在内的基本随机过程的定义和统计特征，并运用小波分析，时间相关和频谱分析对这三种基本随机过程的模拟数据进行分析，归纳出它们在时序上的随机特征、低频信号趋势项特征、时间相关的长短以及主频信号的位置等特点，作为研究 GPS 接收机误差和多路径效应的随机特征的模板。

Some questions asked by the adjudicators in one English Speaking Contest still run upon me very often.

我参加了一场以"我心中的奥运会"为主题的英语演讲竞赛，其间评判提的几个问题时时萦绕我的心头。

He called InTERActive our most profitable release of the year.

他呼吁互动的我们的最有利可图的释放一年。