相似函数

So this paper based on Fisher discriminant function estimating images similarity, and determine similarity queue of all images in database and query image.

因此本文依Fisher判别函数来判定图像相似度，决定数据库中所有图像与查询图像的相似队列。

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。

In this work, we have made an approximate to the one-electronics radial function, namely only the leading term of Slater-type orbital, which is the same as the modified hydrogen-like wave function, are taken into consideration.

在这一工作中，我们对单电子径向函数作了近似处理，即只取斯莱特型单电子径向波函数的领头项，其形式与类氢离子的径向函数相似。

Field data of pedestrian flow was collected in Chinese comprehensive passenger transport terminal—Xizhimen underground station using video recording, and then selected and analyzed by statistic analysis software SPSS. Parameters relation models for pedestrian flow on different terminal facilities were established based on data statistics. The results show that the pedestrian flow-density relation model is quadratic equation in corridor; the flow-space relation model is quadratic equation when space is below a certain value and is logarithmic equation when space is above the value; the speed-density relation model is linear equation. The models on stairs show the similar characteristics, but the eigenvalue is different.

对国内综合交通客运枢纽——北京西直门地铁站行人流数据进行视频采集，采用统计分析软件SPSS对行人流参数数据进行筛选及拟合分析，建立了不同设施的行人流参数关系曲线及函数模型，研究结果表明，水平通道处行人流量与密度呈二次函数关系、流量与空间在某一临界点两侧分别呈二次函数及对数函数关系、速度与密度呈线性关系，楼梯处与之相似但特征点数值存在差异。

This approach was based on the NonSubsampled Contourlet Transform. The means and variables of NSCT coefficients matrix in different subbands and various directions were extracted to form the feature vectors which were regarded as indexes of texture images in image database. Two similarity functions were used to compute the similarity between images. A texture retrieval system based on query image was developed.

该方法利用非下采样Contourlet变换对图像进行分解，提取不同子带和不同方向变换系数矩阵的均值和方差为特征向量，作为数据库中纹理图像的索引，并利用两种不同的相似度函数计算图像之间的相似度，建立了一套基于示例查询图像的纹理图像检索系统。

An approach to image interpolation based on local fractal similarity transformation suitablefor complex images in natural scenes is described. Similarity transformation of rectangular image blocks are added and the extremem method in the function with two variables is used to obtain the optical similarity transformation.

提出了适用于复杂自然景物图像的基于局部分形自相似变换的图像插值方法，在常用的局部分形自相似变换基础上增加了矩形图像块的自相似变换，并采用二元函数的极值方法求最佳相似变换。

The TST was applied to multi-scaling vector to increase it's approximation order, and with PR condition, the dual of transformed multi-scaling vector was obtained. Then the special TST was taken for this dual, the dual of original multi-scaling vector with higher approximation order obtained, finally the multi-wavelet function with higher vanishing moment maybe constructed.

我们先对已知的尺度向量进行双尺度相似变换，以提高其逼近阶，再求出变换后的尺度向量的对偶，对这个对偶再进行特定的双尺度相似变换，就可得到原尺度向量的有高逼近阶的对偶，从而可能得到具有高阶消失矩的多小波函数。

A numerical approach is proposed to quantity the dominance degree of all dimensionless parameters based on the analysis of the sensitivity factor defined as the variation ration of a target function with respect to the variation of dimensionless parameters.

系统介绍了相似参数敏感性分析方法，定义了表征目标函数对相似参数依赖程度的敏感因子，结合数值方法便可定量地确定复杂体系主要相似参数，并实际应用于工程问题。

And by using the initial conditions as well as the end conditions, the dynamic problem is then transferred to a second kind Volterra integral equation about the function of the axial strain with respect to time which can also be solved successfully by the interpolation method. For piezoelectric and pyroelectric hollow cylinders, by following the solving procedure for elastic hollow cylinder and by using the electric boundary conditions, the dynamic problems are transferred to two Volterra integral equations about two functions of time, one is axial strain and the other is related to electric displacement, which can also be solved efficiently and quickly by employing interpolation method. The elastodynamic solutions of hollow spheres, which are made of elastic, piezoelectric and pyroelectric materials, respectively, for spherically symmetric problems are also obtained.

对于弹性空心圆柱，通过引入一特定函数将非齐次边界条件化为齐次边界条件，然后利用正交展开技术，导出关于时间函数的方程，再结合初始条件和端部边界条件，将原问题转化为关于一个时间函数的第二类Volterra积分方程，运用插值法可给出此积分方程的解；对于压电和热释电空心圆柱，利用求解弹性空心圆柱相似的方法，再结合电学边界条件，原问题转化为关于两个时间函数（轴向应变和与电位移有关的函数）的第二类Volterra积分方程组，同样可用插值法来构造相应的递推公式高效地求解此积分方程组。

The notion of weak fuzzy similarity relations,a generalization of fuzzy similarity relations,is used to represent indiscernibility of elements.

为此提出用模糊相似关系和弱模糊相似关系的概念来代替等价关系，同时引入了弱模糊相似关系的相似度概念和相似类概念，定义了基于弱模糊相似关系的广义粗糙集及标准的广义粗糙集上下近似；研究了两对上下近似算子的性质，讨论了3种粗糙隶属函数的性质并验证了它们的性质。

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。