向量和

It is the aim of this book to present various basic and important results of vector optimization in an abstract mathematical setting and to demonstrate its usefulness in vector approximation and cooperative differential game theory.

本书的目的是在抽象数学柜架下给出向量优化的各种基本和重要结果并阐述它们在向量逼近和合作微分对策理论中的应用。

Through the definition of symmetric circulant matrix, the nature of the study, we discuss a class of n-order symmetric circulant matrix of eigenvalues and eigenvectors, and parity check on n different values are given for the matrix eigenvalue and the characteristics of vector formula.

通过对称循环矩阵的定义、性质的学习，我们讨论了一类n阶对称循环矩阵的特征值和特征向量，并分别就n取奇偶等不同数值时，给出了求该矩阵的特征值和特征向量的公式。

A new concept on the continuously distributed directional image/field and the method to compute it in the fingerprint images are proposed,which exhibits not only good continuity,well gradualness,and excellent robustness to the noises,but very high precision,as well.

本文提出了指纹连续分布方向图的概念及其算法，连续分布方向图具有很好的连续性、渐变性、抗噪性和较高的精确度；对经典的PoincaréIndex计算公式和指纹奇异点检测算法进行了改进，改进后的PoincaréIndex不仅能精确表示向量场的旋转角度，而且还能精确表示向量场的旋转方向，能够在像素级水平精确定位指纹奇异点(core点和delta点)。

By combining the interval mathematics and the finite element analysis, the mass matrix, damping matrix, stiffness matrix and the external loads are represented as interval matrices and vector.

通过结合区间数学和有限元分析，结构质量矩阵、阻尼矩阵、刚度矩阵和外载荷列向量采用区间矩阵和区间向量来描述。

It is one of the important characters of the grey system theory to utilize grey generation modeling. The basis structures of generating space in AGO and in IAGO are respectively obtained by the mathematical research of r-AGO series and r-IAGO series. The results are the following: the coherent and direct expression of the generating basis vector in AGO and r-AGO, the relation expression between two r-AGO series and two r-IAGO series, the relation among generating basis vector, generating series and moving operator.

利用灰色生成建模是灰色系统理论的重要特点之一，通过对r次生成序列（包含r-AGO序列和r-IAGO序列）的数学研究，得到了AGO生成空间和IAGO生成空间的基本结构：AGO和r-AGO生成基向量的统一的直观表达式、任意两个r-AGO序列间与任意两个r-IAGO序列间的关系式、生成基向量生成序列与移动算子间的关系。

Moreover, their intrinsic connection, advantages and disadvantages were analyzed from the view of multilinear projections, essential differences and their own superiorities between tensor and vector patterns were clarified, and the problems to be solved and future research were discussed.

对现有张量型学习算法进行总结：针对向量模式表示存在的问题，讨论了设计张量型学习算法的必要性和重要意义；从特征提取和分类器设计2个层面，对现有张量型学习算法进行分类和汇总，并着重从多线性投影方式出发，讨论了其内在联系及优缺点；分析了张量模式与向量模式表示间的本质关系及各自优势；探讨了张量型学习算法有待解决的问题及可能的研究趋势。

The performance of the proposed method is compared with that of the well-known vector standard filters such as the VMF, progressive switch median filter, scalar median filter ,minimum distance between central sample and scalar median in its neighborhood vector median filter and the basic vector directional filter.

结果表明，DMNVM滤波性能明显优于现有的VMF、递进开关中值滤波、标量中值滤波、与标量中值距离最小向量滤波和方向矢量中值滤波；同近年提出的自适应向量滤波比较，AVMF客观指标平均绝对误差协MAE、均方误差和标准色差分别是DMNVM的1.81、2.59和2.17倍，这说明DMNVM的滤波性能有显著提高。

This chapter clarifies the nested relationship between the matrix family of unitary, orthogonal, Givens, Householder, permutation, and row or column symmetric matrices. A precise correspondence of the singular values and singular vectors between the unitary-symmetric matrix and its mother matrix is derived and proved (hence a fast algorithm of singular value decomposition for unitary-symmetric matrix is straightforwardly obtained), and the corresponding perturbation bound is provided.

该章揭示了酉对称矩阵、正交对称矩阵、 Givens 对称矩阵、 Householder 对称矩阵、置换对称矩阵和行对称矩阵之间的逐级包含关系；推导并证明了，酉对称矩阵的奇异值和奇异向量与母矩阵的奇异值和奇异向量之间的定量关系，据此可得酉对称矩阵奇异值分解的快速算法；给出并证明了摄动矩阵的摄动界。

In this paper, we first give an example that the bilateral weighted shift operator in c_0space is hypercyclic operator and first solve the existence problem of hypercyclic operator in c_0or c_0(Z space . And then we investigate the property of weighted shift operator in c_0 space and an important property of the hypercyclic vector of weighted shift operator in c_0 space and c_0 space. At last we give the concept of weak hypercyclic operator and weak hypercyclic vector , and give the equivalence between the weak hypercyclicity and the hypercyclicity in l~1 space.

本文首先给出了c_0空间上的一个双边左加权移位算子是超循环算子的一个例子，首次解决了c_0 或c_0(Z 空间中超循环算子的存在性问题；接下来分别研究了c_0和c_0空间上的加权移位算子的性质以及c_0和c_0空间上的加权移位算子的超循环向量的一个重要性质，最后提出了弱超循环算子和弱超循环向量的概念，并且给出了I~1空间中弱超循环性与超循环性的等价性。

The complexity of bodywork decides variety of it's error. The station and primary factor which cause error is inconstant change and using correlation analysis can find out the primary factor. With an project given, the theory of correlation analysis for dimension variation of bodywork is discussed through correlation analysis and the layer structure of the bodywork,the state in which the error happened can be found out. How to use eigenva...

车体装焊的复杂性决定了误差产生的多因素性，车体制造过程中产生误差的工位和主要因素是不断变化的，采用相关性分析方法从众多的误差根源中准确地发现最主要的误差源；结合工程实践，论述了车体尺寸波动的相关性分析方法的原理，根据测量点的相关性分析和车体焊接工艺的层次结构，可准确地找到产生车体尺寸误差的工位；讨论了如何利用相关系数矩阵的特征值和相应的特征向量判断尺寸波动的模式，指出测量数据的波动主要按最大特征值所对应的特征向量方式波动，引起这种波动的原因是车体误差产生的主要原因，应重点采取措施加以控制；提出了应用计算机进行相关性分析的解决方案。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。