离散分布

Given a planar point set,the moving least squaremethod is adopted to denoise and resample it so that the resulting point set is with low noise and uniform sampling density.Then the reliable signed distance field of the preprocessed point set is constructed by using the Level Set method.Finally,an algebraic B-spline function is adopted to fit the signed distance field by solving a linear equation system.

首先给定一个表示封闭曲线、可能带有噪音且分布不均匀的平面点云，采用移动最小平方(moving least square，简称MLS)方法对点云去噪、重采样，得到一个低噪音、分布均匀的"线状"点云，再通过Level Set方法建立该"线状"点云的离散几何距离场，最后用一个代数B-样条函数光顺拟合该离散距离场，代数函数的零点集即为重建曲线。

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。

The application of the lattice Boltzmann method in unsteady open channel flows was studied in detail in the paper. An existing lattice BGK model was mended; For the problem of negative local equilibrium and evolutionary distribution, we proposed a lattice Boltzmann model based on cell-population equilibrium, which is a direct non-negative approximation to the continuous Maxwell distribution. The model reduces the transport and collision, two basic evolution steps in the LB model, to transport of the non-equilibrium distribution.

本文系统的研究了格子Boltzmann 方法在明渠非恒定流中的应用问题，改进了一个现有的LB 模型，数值实验表明此改进是有效的；在平衡态分布函数及分布函数的非负性问题上，作者提出了一个基于单元均衡的格子Boltzmann 模型，通过直接对Maxwell 分布函数的离散化实现对速度分布函数的非负离散，这种方法将传统模型演化过程中的碰撞和输运两个步骤直接表现为粒子的输运。

And we show that random walk model converges to the stable law of Lévy-Feller advection-dispersion equation by use of a properly scaled transition to vanish-ing space and time steps,We propose an explicit finite difference approximation for Lévy-Feller advection-dispersion equation.

第三章讨论描述服从某种稳定分布反常扩散的非对称空间分数阶对流-扩散方程——Lévy-Feller对流-扩散方程，首先利用Fourier变换和Laplace变换给出方程的基本解，然后利用Grünwald-Letnikov分数阶导数移位离散算子离散方程中的Riesz-Feller分数阶导数得到离散格式，证明此格式可以解释为离散随机游走模型，并且证明了当时间和空间步长以一定的比率同时趋于0时，所提出的离散随机游走模型收敛到Lévy-Feller对流-扩散过程的稳定分布。

For example, we use geometric distribution to describe the life distribution of runs of a species in transect surveys of plant populations and inventory demand distributions. In the theory of reliability, geometric distribution is one of the most important discrete probability distributions because of its loss of memory.

在可靠性理论中，由于几何分布的无记忆性，使得其是离散型寿命分布中最为重要的寿命分布之一，其相当于指数分布在连续型寿命分布中的地位，这正如程侃研究员在文献[5]中所指出的"在离散寿命的情形，几何分布起着连续情形下指数分布所起的作用"一样。

By analyzing the problem of hydrological 3D spatial dispersion in 3D finite differential numeric simulation of porous groundwater flow, as well as discontinuous spatial distribution and asymmetric thickness of porous aquiferous strata and partitive groundwater stratum, the paper presents the GIS-based technique of 3D spatial dispersion of porous aquiferous stratum system. Besides, the paper puts forward the 3D spatial dispersion method of irregular hexahedral unit based on GIS to guarantee to the greatest degree the uniqueness of the stratum types among the dispersed units and improve the precision of 3D spatial dispersion.

分析了目前孔隙地下水流三维有限差分数值模拟中对含水层系统三维空间离散存在的问题，针对自然界孔隙含水层与隔水层空间分布的不连续性与厚度的不均匀性，研究了基於GIS的孔隙含水层系统三维空间离散实现的技术路线，提出了基於GIS与不规则六面体元的孔隙含水层系统的三维空间离散方法，最大限度地保证了离散体元中含水层类型的单一性，提高了孔隙地下水流模拟模型三维空间离散的精度。

By analyzing the problem of hydrological 3D spatial dispersion in 3D finite differential numeric simulation of porous groundwater flow, as well as discontinuous spatial distribution and asymmetric thickness of porous aquiferous strata and partitive groundwater stratum, the paper presents the GIS-based technique of 3D spatial dispersion of porous aquiferous stratum system .

分析了目前孔隙地下水流三维有限差分数值模拟中对含水层系统三维空间离散存在的问题，针对自然界孔隙含水层与隔水层空间分布的不连续性与厚度的不均匀性，研究了基于GIS的孔隙含水层系统三维空间离散实现的技术路线，提出了基于GIS与不规则六面体元的孔隙含水层系统的三维空间离散方法，最大限度地保证了离散体元中含水层类型的单一性，提高了孔隙地下水流模拟模型三维空间离散的精度。

Many new detection techniques are proposed, that include: To overcome the faults of cross-terms and short unambiguity range for the common Wigner-Ville Distribution , short-time Fourier transform and Gabor transform are applied to SAR moving target detection. To improve the detection performance of WVD in noise environment, a new technique based on the Cross-WVD is proposed. The application of fractional Fourier transform to chirp signal detection is analyzed and extended to SAR moving target detection. To eliminate the restriction of chirp-Fourier transform, a new modified definition is proposed and applied to SAR moving target detection. To detect multiple moving targets whose scattering intensities are different heavily, the CLEAN technique is combined with the above techniques and the ideal detection performance is achieved. At last, the whole dissertation is concluded.

具体的研究成果如下：针对常用的Wigner-Ville分布在多目标情况下存在交叉项，并且多普勒不模糊范围小的缺点，提出将短时Fourier变换和Gabor变换应用于SAR运动目标检测，分析了其优势所在；为进一步提高Wigner-Ville分布低信噪比条件下的信号检测能力，提出基于互Wigner-Ville分布的运动目标检测方法；分析了分数阶Fourier变换在线性调频信号检测中的应用，提出基于分数阶Fourier变换的运动目标检测算法；对离散Chirp-Fourier变换的定义进行了修正，提出修正的离散Chirp-Fourier变换，克服了限制其应用的约束条件，并用于SAR运动目标检测当中；强度相差较大的多运动目标检测历来是机载SAR技术的一个重点和难点，我们将CLEAN思想融入上述多种算法当中，良好地解决了该问题。

Traditionally, a surface is usually scatted in an array of 3D data points which are topologically connected by rows and columns to form a rectangular mesh. This method can't meet the requirement of description and measurement for some complex surfaces. On the basis of tracing border points, a new method is proposed to deliver 3D data points of surfaces, which are topologically constructed with optimum rectangular and triangular mesh. In order to measure surface efficiently and safely with NC machine, an optimization of measurement paths is proposed to avoid interference between the measuring tool and the surface with holes. The curve design is the basis of surface modeling.

数控测量技术的发展为测量自动化、集成化、智能化提供了可能，而对于复杂曲面的自动测量规划则是测量技术中的难点问题，平行截面等数目测点分布和四边拓扑测点分布规划方法，不论在测点分布的合理性上还是在网格结构的优化方面，均难以满足形状或边界较复杂曲面的离散化描述和曲面造型的要求，为了实现任意拓扑曲面的自动测量，本文对复杂曲面的合理离散化描述和自动测量问题进行了研究，提出了基于边界跟踪、优化网格的测点自动分布规划和四边、三角混合网格的生成方法：同时对具有孔洞或测量干涉凸台等非完整曲面的测量路径优化问题进行了研究，提出了路径优化方法。

Within the active periods, recurrence interval distribution has relatively large discretion, and can be well-fitted by a Weibull distribution. While the duration's distribution of the quiet periods has relatively small discretion, and can be described approximately by some distributions as the normal and so on.

其中，活跃期内地震复发间隔分布的离散性较大，可用Weibull分布近似描述；而平静期的持续时间分布的离散性较小，可用正态等分布近似描述。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。