主法向量

Chapter 2 introduces some propaedeutics of classic differential geometry, which include the first basic form, the second basic form, normal curvature, main curvature, mean curvature, Gauss curvature, unit normal vector, main vector, etc.

第二章介绍一系列的预备知识，主要是关于古典微分几何中第一，第二基本形式的定义，法曲率，主曲率，平均曲率，Gauss曲率，单位法向量，主方向等的定义。

It is based on the discrete model of finite analysis to get curvature ,normal vector, direction and geodesic curve,then to analyze and design the structure.

基于有限元分析的离散模型，将离散微分几何领域的最新成果运用于膜结构设计，求解曲面曲率，法向量，主方向及测地线，进行结构分析设计。

Triangular mesh, normal vector, principal curvature, gaussian curvature, mean curvature

三角网格，法向量，主曲率，高斯曲率，平均曲率

The shape-form analysis and load analysis were done by nonlinear FEM. On the basis of surface FEM grid nodes, geometry property research of structure curved surface was progressed, including normal vector, GAUSS curvature, mean curvature and principal direction vector. In this process, the approximate expression of surface didn't need to he known.

采用非线性有限元法进行了膜结构的形态分析和荷载分析，得到了曲面有限元网格；通过离散微分几何方法，研究了薄膜结构曲面的几何性质，包括曲面的法线向量、高斯曲率、平均曲率和主方向矢量，避免了复杂的曲面拟合过程。

We propose a unified method to approximate important geometric attributes, including normal vector, gauss curvature, mean curvature, principal curvatures and principal directions on point sampled surface. Based on MLS projection our method is robust to noise and stable to the sampling density.

曲面的微分性质包括法向量和切平面、高斯曲率、平均曲率、主曲率和主方向，在计算机图形学、机器视觉和计算机辅助设计等领域发挥了重要的作用，比如曲面绘制、内外测试、曲面重建、曲面简化、去除曲面噪声和模型分割等。

Based on the research work of basic theories including phase space reconstruction,embedding theorem,correlation dimension,local dynamics,Lyapunov exponents,surrogate data etc,based on the research work of general methods such as principal component analysis,correlation dimension GP algorithm,false neighbors method,nonlinear time series prediction,local prediction, adaptive prediction,neural network model,support vector machines regression model, prediction power,nonlinear detection,coarse-graining methodology,conditional entropy and so on,the framework of nonlinear time series analysis are constructed.

在对包括相空间重构、嵌入定理、关联维数、局部动力学、Lyapunov指数、替代数据(来源：A97BC论文网www.abclunwen.com)、等基本理论与其物理意义的研究和讨论基础上；在对包括主分量分析、关联维数GP算法、伪邻近点法、非线性时间序列预测、局域预测、自适应预测、神经网络模型、支持向量回归模型、预测效果、非线性检测、粗粒化方法、条件熵等非线性时间序列一般分析方法的原理和算法研究基础上；构建了新的非线性时间序列分析的理论体系，归纳总结了非线性时间序列分析的基本问题和主要研究方面。2。

First, the reason behind the negative data is analyzed and a nonnegative constraint is imposed on the classic PCA. Then a set of nonnegative linear independence weight vectors of principal components is obtained, by which a low dimensional space is constructed. Finally, a nonlinear optimization technique is used to determine the projection vectors of the high-dimensional multi-spectral data in the constructed space.

首先分析主成分分析法产生非光谱数据的原因，据此对经典主成分分析模型增加非负约束；然后求出一组线性无关的非负主成分权向量，用该组向量构造低维空间；最后用非线性优化技术确定高维数据在该低维空间中的投影值，实现了高维空间与低维空间的相互转换。

The framework established was practical and universal, and could provide abase for specific area to select its assessment indicators. The operable indicatorsystem developed which synthetically reflected the sustainable development status ofliling could fill up the blank of regional sustainable development evaluation in liling,and this work was of practical and strategic significance to a certain extent. Inallusion to the flaw existed indimensionlessness of original data in grey system,mean value method was adopted instead of traditional standardized method, and theguidance for confirming the direction of eigenvector was first brought to grey systemin the application of sustainable development evaluation aimed to increase theobjectivity and accuracy of evaluation. The evaluation results on liling could supplybeneficial references for decision makers to make and adjust sustainabledevelopment strategic goal and counter measures.

本文所构建的区域可持续发展指标体系框架具有实用性和通用性，可作为特定区域在筛选具体评价指标时的参考依据；针对醴陵市建立的区域可持续发展指标体系易于操作，能够综合反映醴陵市可持续发展的各个方面，在很大程度上填补了区域可持续发展评价研究的空白，具有一定的实践意义和战略意义；应用主成分分析法评价各子系统的可持续发展水平时，针对原始数据处理存在的弊端，提出以均值法代替传统的标准法，并首次引入了特征向量确定的原则，从理论上可提高评价的客观性与准确性；对醴陵市区域可持续发展状况的评价结果，可以为醴陵市可持续发展总体战略目标及相关措施的制定与结构调整提供有益参考。

The WYD method is improved on the basis of analysis and research of free interface modal synthesis method that regards the Ritz vector formed by WYD method as reserved main modal set, and influence of modal truncation on synthesis precision is discussed.

在分析研究了以WYD法形成的Ritz向量作为保留主模态集的自由界面模态综合法基础上，改进了WYD方法，并讨论了模态截误差对综合精度的影响。

This paper expoles an algorithm about dearing surface defects detection by Support Vector Machines and principal component analysis that is the new branch of machine learning, in which the defective area and non-defective area are treated as two different textures and are sampled respectively to be learned, in order to reduce dimension, the image data can be processed by PCA.

提出了一种基于支持支持向量机和主成分分析的轴承表面缺陷检测算法，该算法把轴承中的非缺陷区域和缺陷区域分别看作两种不同的纹理模式，先利用主成分分析法对图像进行降维处理，然后用支持向量机方法对降维后的样本采样学习，然后进行分类判断。

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。