查询词典 generalized coordinates

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。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

By means of traditional criterions of generalized integral's convergence and divergence, this paper, from the analysis of integrated function's nature, discovers a series of new criterions, which are briefer and more suitable: on the aspect of generalized integral for functions of a single variable, through the investigation of integrated function, together with the inner relationship between positive series and generalized integral in infinite interval under the condition of positive function, it gives several criterions of generalized integral's convergence and divergence, which are similar to positive series' criterions of convergence and divergence.

本文从分析被积函数本身所具的性质出发，借助传统的广义积分敛散性判别方法，发现1系列更简捷适用的新判别方法：单变量函数广义积分方面，通过考察被积函数，结合正项级数与正函数情形下无穷区间上广义积分的内在联系，给出了几个与正项级数敛散性判别法相类似的广义积分敛散性判别方法；多变量函数广义积分方面，着重讨论了广义2重积分和广义3重积分，结合被积函数的特点，运用比较判别法和柯西判别法，本文给出了判别广义2重积分收敛的1种新方法。

In the mean time we also give out a reduction way for nonlinear generalized system F =0 by use of the special projection mappings Q . Based on these we prove that the qualitative structure near the isolated equilibrium point of regular nonlinear generalized system is qualitatively equivalent with the structure near the equilibriun point of the linearization system of nonlinear generalized system, so we give out a way for qualitative analysis near equilibrium point of nonlinear generalized system.

其次，对一般形式的非线性广义系统F=0，利用特殊选择的投影函数Q，给出了一种归约方法，在此基础上，并证明了正则非线性广义系统问题的孤立平衡点的小邻域的定性结构等价于其线性化后的线性广义系统平衡点的定性结构，从而为非线性广义系统的平衡点的定性分析提供了一条途径。

Moreover, we get the sufficient and necessary condition of in Orlicz spaces.Chapter 3 Extreme points and strongly extreme points in Orlicz spaces equipped with the generalized Orlicz norm: In this paper, the conceptions of the generalized Orlicz norm and the generalized Luxemburg norm are introduced, and the criteria of extreme points and strongly extreme points of Orlicz function spaces equipped with the generalized Orlicz norm are obtained. Moreover, criteria of space strictly convex and mid-point locally uniform convex are given.

第三章 赋广义Orlicz范数的Orlicz函数空间的端点和强端点：本章在Orlicz空间推广了Orlicz范数和Luxemburg范数，引入了广义Orlicz范数和广义Luxemburg范数的定义，并给出了赋广义Orlicz范数的Orlicz函数空间的端点和强端点的判据，进而得到了赋广义Orlicz范数的Orlicz函数空间严格凸和中点局部一致凸的充要条件。

This paper studies the invariant, which is the linear preserving problem based on generalized inverse of matrices. The generalized inverse of matrices and the research status of preserving problems of generalized inverse are outlined. In the basis of deeply understanding the basic knowledge of linear maps, the definition, characteristics of generalized inverse and decomposition of matrix, the author analyzes the decomposition form of preserving idempotence and preserving tripotence in the PID, then studies on the linear maps form of preserving group inverses of symmetric matrices.

本文研究的不变量是矩阵广义逆线性算子的保持问题，概述了广义逆矩阵，广义逆保持问题的研究现状，在对线性映射的基础知识，广义逆矩阵的定义、性质和矩阵的分解深入理解的基础上，深入分析了保幂等、保立方幂等矩阵在主理想整环上的分解形式，继而研究了保对称矩阵群逆的线性算子形式。

This paper generalizes the conclusion of Perfect nonlinear S-boxes by Nyberg(1991), and introduces the conception of inverse regular generalized vector Bent function. It shows that for inverse regular generalized vector Bent function f with even variables, m is no more than half of?. It also shows that when the input dimension n is odd, the regular generalized vector Bent function and the inverse regular generalized vector Bent function do not exist. This may prevent the cryptology designer from seeking the inexistent function.

摘要该文完善并拓展了Nyberg(1991)的关于广义向量Bent函数性质的结论，相应于Nyberg给出的正则广义向量Bent函数，提出了&负则的广义向量Bent函数&的概念：得到有偶数个输入的负则的广义向量Bent函数输出维数也不大于输入维数的一半；证明了奇数个输入的正则和负则的广义向量Bent函数都不存在，这些结果的给出，可使密码设计者避免一味去寻找某类不存在的函数。

The purpose of this paper is to extract the coupling matrix of generalized chebyshev filter, model the four-port rectangular junctions, multiple-stepped rectangular waveguide bend and T-septum rectangular waveguide junction by full-wave methods and design generalized chebyshev filters and diplexers. The main works are as follows: 1. Systematically research on the theory of generalized chebyshev filters The generalized chebyshev filters are based on the all-coupled model.

本文主要目的是研究广义切比雪夫滤波器拓扑结构、物理结构上可实现的耦合矩阵提取及其特性分析和基于模式匹配法全波建模四口矩形结、多阶梯矩形波导弯头、T—scptum矩形波导接头，最后，设计了一系列高性能的滤波器和双工器。

There are fourteen chapters, including introduction, plane stress and plane strain, two-dimensional problems in rectangular coordinates, two-dimensional problems in polar coordinates, photoelastic and moire experimental methods, two-dimensional problems in curvilinear coordinates, analysis of stress and strain in three dimensions, general theorems, torsion, bending of bars, axisymmetric stress and deformation in a solid of revolution, thermal stress, the propagation of waves in elastic solid media, at last there is an appendix on the application of finite-difference equations in elasticity.

全书共十四章，包括绪论、平面应力和平面应变、直角坐标中的二维问题、极坐标中的二维问题、光弹性与云纹实验方法、曲线坐标中的二维问题、三维应力和应变问题、一般定理、简单的三维弹性问题、扭转、杆的弯曲、回转体中的轴对称应力和变形、热应力、弹性固体介质中波的传播，最后有一附录，讲述差分方程在弹性理论中的应用。

By introducing the two dimensional homogeneous coordinates of an infinite point on Euclidian plane,the point coordinates and linear coordinates of an infinite point in straight lines,some theorems and conclusions referred to infinite points are applied in the classifications of structures in this paper.

引入了欧氏平面上无限远点的二维齐次坐标和直线上无限远点的点坐标及线坐标，引用了与无限远点有关的一些定理及结论于结构的分类中。从而给出了可变体系中的常变与瞬变在结构形式上的区别，完善了杆系平面结构几何组成规则的内容

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。