几何分布

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 paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component. For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper. For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space state informatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision. Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为（n-1）维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料（单质材料作为特殊的功能梯度材料看待）、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component.For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material .distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper.For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space stateinformatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision.Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为(n-1)维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料(单质材料作为特殊的功能梯度材料看待)、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

First of all, the paper gave a briefing on the development of white LED and the problems need to addressed of RGB LED mixed white lighting; Then established colors distributed computing model of the RGB LED white lighting module; Final designed a number of different geometric structure of the RGB LED light source module, by changing angles (interior angle or the angle Centre) of the geometry and the LED colors with different priorities, programmed by using of Matlab software, simulated the color distribution correspond to such light source models.

首先，本文简要介绍了白光LED的发展现状及RGB LED混合白光需要解决的问题；其次建立了RGB LED的颜色分布计算模型；最后设计了几种不同几何结构排列的RGB LED光源模块，通过改变几何结构中角度、不同颜色LED的排列次序，利用Matlab软件编程，模拟以及仿真得到这些光源模型相应的光源颜色分布，并评价其颜色均匀性，进而得到最佳几何排列结构的RGB LED光源模块。

To compare the performances of these algorithms, the Cramer-Rao lower bound of the location problem is given.

为比较算法性能，推导了该定位跟踪问题的克拉美罗下限，并利用计算机仿真给出了不同算法的跟踪误差几何分布。

At last, through the analysis of the T-stress, it is concluded that the T-stress plays an important role for the oriented microcrack cases. It is necessary to consider the effect of the T-stress in determining the shielding or amplification effect of the oriented microcracks.

最后，本文采用离散模型研究了各向异性材料主微裂纹干涉问题中T应力对主裂尖应力强度因子的影响：T应力对主裂尖应力强度因子的影响是不能被忽视的，这种影响不但与微裂纹的几何分布有关，而且还与T应力的大小和符号有关。

The problem of the determination of the final geometry of the single-layer reticulated shell with zero element internal force is also successfully solved by using this method. Based on the research on the shape determination theory a conclusion has been obtained: the distribution of the initial self-internal-force vector determines the initial shape of an assembly which has form finding problem.

通过对形状确定问题的研究，可得出如下的结论：体系自应力分布矢量的方向决定体系初始态几何；体系自应力分布矢量的大小只影响体系的零状态几何；体系各个单元的截面尺寸设计也将影响体系的零状态几何。

The scale-type geometric wear-resistant structure surface is characterized in being made up of a base and the bionic geometric units on the surface. The bionic geometric structure unit is a scale-type structure distributed regularly on the surface of the base, and the distribution density is that: the ratio between the geometric projection area of the scale-type structure on the base surface and the surface area of the base formed by all the edge ends is 50-100%; the scale-type geometric structure unit has a symmetric hexagon shape on the surface; the sides L2/L1=1.0-2.0, L1: 1mm-50mm, and the internal angle Alpha is 120 degree -130 degree, the internal angle Beta is 100 degree -110 degree; the A-A section is subtriangular, and the B-B section is a trapezoid, the height H of the scale-type is 1-5mm.

本发明由基体和其表面上的仿生几何结构单元组成，仿生几何结构单元为在基体表面规律分布的鳞片型结构，鳞片型的分布密度为：其在基体表面上的几何投影面积之和与所有棱端围成的基体表面积之比为50-100％，鳞片型几何结构单元的表面形状为对称六边形结构：边长L2/L1＝1.0-2.0，L1：1mm-50mm，内角α为120°-130°，内角β为100°-110°，鳞片型的A-A截面为近似三角形，B-B截面为梯形，鳞片型的高度H为1-5mm。

At the same time, different arrays of electrodes have been studied.

本文还研究了等离子体反应器电极的不同几何分布对流场的影响。

PVDF/PZT piezocomposite consisting of piezoelectric ceramic and polymer was made according the connection mode, volume fraction ratio or geometric distribution mode.

摘要压电复合材料一般是由压电陶瓷和聚合物基体按照一定的连接方式，一定比例和一定的空间几何分布复合而成。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。