两维的

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。

Based on the CFD software FLUENT as well as experiments, the aerator internal fluidic field was computed and aspirating was analyzed. Conditions and status on inner aspirating were investigated in terms of pressure distribution, flowing velocity and volume fraction of air and water.

利用流体分析软件，结合试验现象，对内吸气部位的流场进行了CFD三维仿真及分析，从压力分布、流体流速与流动方向两方面，计算分析喷嘴及内吸气管内部的液、气两相流体运动规律，以判断喷嘴内能够形成吸气的条件及吸气状况。

Experiment Study on the Long-Term Stability of Bearing Load Cell in large turbine-generator sets;2. Study on the Assembly Shearing Bridge Load Cell for Two Pad Tilting Pad Bearing;3. D FEM analysis of a load cell with on 2 pad tilting pad bridge bearing in large turbine generator sets has been made.

本文对大型汽轮发电机组剪切桥式两可倾瓦轴承负荷传感器结构进行了二维有限元分析，研究了不同边界条件对传感器结构应力场的影响，计算与试验结果对比表明：所建立的有限元模型基本是正确的，可将其用于两可心倾瓦轴承负荷传感器结构设计。

In order to draw a photorealistic surface, Bidirectional Texture Functions, a 6D texture function which extends Bidirectional Reflectance Distribution Function to include the self-shadowing, self-occlusion and inter-reflection effects, has been mentioned frequently in recent years. Its main drawback is its massive data size. To solve this, Spatial Bidirectional Reflectance Function techniques compress BTFs into reflectance model parameters. However, SBRDF cannot producethe self-shadowing and self-occlusion effects in real-world surface geometry. This work is aimed to this drawback. I find how self-shadowing and self-occlusion affect the surface by additional physical-based analysis. And I rely on two physical phenomena to divide self-shadowing and self-occlusion into two independent effects. First, self-shadowing is view independent. Second, self-occlusion is independent of lighting direction changes. After these analyses, I use SBRDF and additional self-shadowing and self-occlusion I found to render a photorealistic surface as non-compressed BTFs doing.

为了把物体表面呈现的更真实，六维函数BTFs ( Bidirectional Texture Functions)目前已经被使用的相当频繁，但BTFs的资料量实在太大而没办法直接使用，为了解决资料庞大的问题，传统的SBRDF以逼近光反射模型参数，来达到资料压缩的效果，但是SBRDF对於表面的凹凸所产生的阴影及遮蔽，不能达到逼真的呈现，为了改善这个问题，我们选择从物理方面，找出资料中阴影和遮蔽等属於表面几何的资料并去除，使参数更正确，同时利用两个物理现象去区分阴影及遮蔽为两个互不干涉资料，第一是阴影不会因视角不同而改变，第二是遮蔽不因光线方向不同而改变，经过这些分析，我可以利用SBRDF加上附加的阴影及遮蔽两种独立的效应，来达到彷佛跟未压缩过的BTFs一样的真实绘图。

The business cost me three hundred roubles, but in a couple of days it had been arranged that I should stand in an adjoining room, behind closed doors, and listen to the first rendezvous between my wife and Efimovitch, tete-a-tete.

为这事我总共花费了将近三百卢布，在两天两夜中我作好了这样的安排：我将站在隔壁房里，站在虚掩的房门后面，倾听我妻子和叶菲莫维奇第一次rendes—vous①的情况。

Transmissions at 0.75 and 1.65 μm can also be used to retrieve τ and re. 2. Study the impact of cloud inhomogeneity on the satellite retrieval simultaneously. Two 3D cloud fields, cumulus and stratocumulus fields are used in our study. The two cloud fields are generated with LES model and are adopted by the I3RC phase II. The BRDF at the wavelengths of 0.65 and 2.13 μm are calculated with SHDOM, and then the cloud optical thickness and effective particle radius are simultaneously retrieved using the MODIS algorithm. We studied the impact of cloud inhomogeneity on the satellite retrieval at high and medium resolutions. Some conclusions have been made, such as the BRDF abnormal phenomenon, the reverse relationship between τ and re, the clustering effect of over and under estimation in the retrieval of τ and re .

我们选用为I3RC所采用的由LES模式给出的具有明确物理属性的两个高分辨率三维云场－积云场与层积云场，利用SHDOM三维辐射传输模式来模拟卫星观测的辐射值，并采用MODIS算法进行反演，同时研究了在高分辨云场及中低分辨率云场下，云的非均匀性对反演云光学厚度及有效粒子半径的影响，并得到了云的非均匀性会造成的双向反射率异常，反演结果中光学厚度与有效粒子半径的负相关关系，高估或低估现象是成&簇&出现的等结论。

The method is realized via the following steps: first to apply Isomap or LLE to get the embeddings of the original data set in the low dimensional space; then to obtain support vectors, which are the most significant and intrinsic data for the final classification result, by using support vector machine on these low dimensional embedding data; subsequently to get support vectors in the original high dimensional space based on the corresponding labels of the obtained low dimensional support vectors; finally to apply support vector machine again on these high dimensional support vectors to gain the final classification discriminant function.

数据挖掘是数据库知识发现中最重要的步骤之一，其目标是从获取的数据中高效准确地挖掘出我们所需要的信息。在实际应用中，数据往往呈现海量、高维、非线性等特性，这些特性给数据挖掘带来了很多问题，例如海量特性导致的计算效率低下问题、高维特性带来的维数灾难问题和非线性特性引起的线性模型失效问题等。幸运的是，实际中高维数据的属性之间往往存在一定的规律性和相关性，即实际数据经常存在着外在与内在两个维数。

We generally divide abstraction into two categories, namely, cold abstraction represented by Malevich and Mondrian and hot abstraction represented by Pollock and De Kooning. Both of them adopt a positive expression_r_r.

我们一般将抽象分为两类，即以马列维奇和蒙德里安为代表的冷抽象，以波洛克和德库宁为代表的热抽象，这两种抽象都采取了肯定的表现方式。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！