随机

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。

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。

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。

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。

Trigonometric series is used to simulate stationary, non-stationary, Gaussian andnon-Gaussin stochastic processes by spectral representation in which the non-stationary stochastic processes are expressed as the product of determinate functionsand stationary stochastic processes.

结合随机变量的Monte Carlo模拟法，随机场的局部平均法与随机过程的三角级数模拟法，用均值、方差、相关长度及功率谱等，可有效地描述随机变量、随机场、随机过程，及同时具有场与过程随机的变量。

This paper is mainly the dynamic input-output model that the time lag is one, which is base on the above models. After studying, we consider stochastic factor step by step in it, namely when consumption coefficient matrix is stochastic (when investment matrix is stochastic, it is almost same. So we dont research it), and they are both stochastic, then we research the stable increase solution. We utilize the means of the modern stochastic analysis and Markov process, that the stochastic dynamic input-output model don not exist the stable solution is proved. Namely, economic system must is adjusted constantly. The probability that the collapse time of the economic system is o is one.

本文对在上述基础上构造的一类时滞为1的动态投入产出模型，进行了深入研究，将随机因素逐步考虑进去，即对投入产出消耗系数矩阵为随机的情况(投资系数矩阵为随机的情况与投入产出消耗系数矩阵为随机的情况大致相同，这里就不再证明)，以及二者同时为随机矩阵时所得到的动态投入产出模型的稳定增长解问题，利用现代概率分析及马氏过程的工具，证明了不存在随机动态投入产出模型的稳定增长解；即投入产出模型反映的经济系统必须经常进行调整，其崩溃时间为无穷大的概率为零。

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。

Then basic mathematical models of unrepairable systems with fuzzy random lifetimes are established.

此外，我们建立了模糊随机不可修系统的基本模型，包括模糊随机串联系统、模糊随机并联系统、模糊随机串—并联系统、模糊随机并—串联系统以及模糊随机冷贮备系统。

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。

Throughout comparing the above estimating methods, we have the following results: the estimators of the moments of the errors does not depend on the random effects, and that of the random effects does not depend on the errors, and then the corresponding asymptotic variances are very simple and optimal; when the random effects are multivariate, we can not construct different estimating equations for the random effects and errors respectively, which results that the asymptotic covariances of estimation are very complex and then the estimating efficiency is bad.

比较上述两种估计法，我们发现：当随机效应是一维的时侯，误差的各阶矩的估计不依赖不可观测的随机效应，随机效应的估计也不依赖误差，因此，估计的渐近方差结构特别简单也是最优的；而当随机效应是多维的，因为随机效应的协变量的影响，我们没有办法针对随机效应和误差的各阶矩分别建立估计方程，这导致所得的估计的渐近方差或者协方差矩阵特别复杂，从而估计的效果不是很好。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。