距离函数

Real Number System, Euclidean Space and Metric Spaces, Sequences in R and R^n, Differentiability on R and Rn, Integration on R and Rn, Infinite Series of Functions, Fourier Series, Fundamental Theorems of Vector Calculus, Inverse Function Theorem, Implicit Function Theorem and its Applications.

课程内容：实数系，Euclidean空间与距离空间，函数数列，函数级数，连续函数，可微分函数，可积分函数，反函数，隐函数定理及其应用，向量微积分基本定理，富氏级数。

This paper provides the analytic method to calculate the value of Green s functions in space domain at the zero distance by the discrete complex image theory,that is ,to express the finite progressional sum of Green.

对此，本文在讨论采用离散复镜象理论计算空间域Green函数时，提出了采用该镜象理论计算空间域Green函数零距离处奇异值的解析方法，即，采用Taylor公式展开镜象理论得到的空间域Green函数的有限级数和形式，并结合特定的分域基函数来得到零距离处Green函数奇异值的解析计算式进行计算。

This paper provides the analytic method to calculate the value of Green"s functions in space domain at the zero distance by the discrete complex image theory,that is ,to express the finite progressional sum of Green"s functions detained with DCIT into Taylor expansion and deduce the analytic expression of the singularities at the zero distance with the help of the specific subdomain base functions.

对此，本文在讨论采用离散复镜象理论计算空间域Green函数时，提出了采用该镜象理论计算空间域Green函数零距离处奇异值的解析方法，即，采用Taylor公式展开镜象理论得到的空间域Green函数的有限级数和形式，并结合特定的分域基函数来得到零距离处Green函数奇异值的解析计算式进行计算。

Theoretical analysis proves that,when the pixel number,pixel size and reconstructed wavelength of the hologram are certain,computer simulated algorithms of Fresnel diffraction integral fall into convolution algorithm,angular spectrum algorithm and direct Fourier trans...

通过对相位函数局域空间频率的分析，给出了判定算法适用范围的特征再现距离，并分析得出，再现距离大于特征再现距离时，适合用卷积法；小于特征再现距离时，适合采用角谱法；等于特征再现距离时三种方法都适用。

Firstly, Geodesic distance is introduced to overcome the weakness of Euclidean distance. Then, neighborhood rough set model is introduced to make full use of neighborhood local information and also can avoid the discrete process of numerical attributes.

最后将一个二进制DE算法运用到特征选择，为了设计合理的适应度函数，本文首先针对基于欧氏距离类内类间评价函数的不足，引入流形中的测地线距离，力求保持数据集内在特性的基础上，提出了一个基于测地距离的适应度函数。

A generalized Gaussian Laplacian eigenmap algorithm based on geodesic distance is proposed,which incorporates geodesic distance and generalized Gaussian function into the original Laplacian eigenmap algorithm.GGLE algorithm can adjust the similarities between nodes of neighborhood graph,and can preserve the different degrees of local properties by using super-Gaussian function,Gaussian function or sub-Gaussian function.Moreover,GGLE can avoid the deficiency of Euclidean distance by using geodesic distance when neighborhoods of data points are enlarged for preserving more neighborhood relations.Experimental results show that the global low-dimensional coordinates obtained by GGLE have different clustering properties and different degrees of preserving local neighborhood structures when different generalized Gaussian functions are used to measuring the similarities between high-dimensional data points.(3) An ensemble-based discriminant algorithm based on GGLE is proposed.

该算法将测地线距离和广义高斯函数融合到传统的拉普拉斯特征映射算法中，可以调整近邻图结点间的相似度，通过选择超高斯、高斯或者次高斯函数来实现不同程度的近邻局部特性的保持；而且当需要保持更多的近邻关系使得数据点邻域增大时，采用测地线距离可以避免欧氏距离度量不合理的缺陷；实验结果表明在用不同的广义高斯函数度量高维数据点间的相似度时，局部近邻结构保持的程度是不同的，GGLE获得的全局低维坐标也呈现出不同的聚类特性。

According to the structured element representation theorem of fuzzy number and fuzzy-valued function, we obtained one-to-one isometric mapping from the family of standard bounded monotone function with same monotonic formal on [-1, 1] to the fuzzy number space, and proved they are homeomorphic.

在模糊值函数的模糊结构元表述理论的基础上，利用[-1，1]上同序标准单调函数类上的距离诱导出模糊值函数空间上的距离，证明了模糊实数空间与[-1，1]上同序单调函数类同胚。

Calculated value of radial dose function, g, is in the rang of 0.1-10.0 cm at transverse axis. Anisotropy function, F, is calculated in 0°-90° of θ with increment of 10° and 0.5-9.0 cm of r with increment of 1 cm. Empiric equations are acquired for radial dose function and anisotropy function by curve fitting.

在源中垂轴0.1~10.0cm距离范围内计算径向剂量函数的数值，在角度0°~90°（10°间隔）、距离0.5~9.0cm（1cm间隔）范围内计算各向异性函数的数值，最后对径向剂量函数和各向异性函数进行拟合，得到实用性较强的经验公式。

Using the theories of fuzzing mathematics and distance function,the model can evaluate the comprehensive development level ,degree of sustained development and degree of coordination of economy,environment and resources.

该模型利用模糊数学和距离函数的思想对经济、社会、环境、资源的综合发展水平、可持续发展度以及相互之间的状态协调度进行分析和评价。

The upper bound of error probability is used as the criteria of clustering and the evaluation of the clustering result. On the basis of initiatory clustering based on distance functions, the algorithms named"pick-over"and"fill-up"are proposed to minimize the upper bound of error probability.

我们将聚类准则即模式相似性测度问题和聚类结果的评价指标统一为总的最小错误概率上界，在算法实现上，首先先用基于距离函数的聚类方法得到初分类，然后采用基于最小错误概率的&抽取&和&回填&算法得到使总的错误概率上界最小的聚类结果的分析方法。

What are your goals and strategies for growth?

你的成长目标和策略是什么？

And unto the angel of the church in Sardis write; These things saith he that hath the seven irits of God, and the seven star I know thy works, that thou hast a name that thou livest, and art dead.

3：1 你要写信给撒狄教会的使者，说，那有神的七灵和七星的，说，我知道你的行为，按名你是活的，其实是死的。