周期矩阵

Some useful notations and definitions are give in this chapter.In Chapter 2,a class of discrete-time model of two-cell cellular neural networks with symmetric temptate are investigated. We obtain some results about the stability,asymptotic stability,the existence and attractability of 2-periodic solutions.

第三章讨论了反馈矩阵为非对称矩阵的二元离散细胞神经网络模型的稳定性与渐近稳定性、周期解的存在吸引性，除了得到系统稳定和存在2-周期解的相关结果外，还得到了系统在原点出现类似于Hopf分支的局部分支以及多个吸引4k-周期解的共同存在性。

We construct a family of iterative mappings, which yield cyclic windows of variant size in the dynamical plane by incorporating cosine functions and non-linear angle variables with parameters. Chaotic attractors and filled-in Julia sets in the different cyclic windows are created by establishing the coordinates of any cyclic windows and the maximal window, then clarifying the relationship of corresponding points between these cyclic windows. The respective images in different windows are continuous but with individual structures.

该算法采用余弦函数及含参的非线性角度变量构造一族使动力平面上各周期窗口的尺度变化的迭代映射；通过计算任意周期窗口和最大周期窗口得出窗口间相应点之间的非线性对应关系，并构造出各周期窗口中的混沌吸引子和充满Julia集，其图案是连续的且结构不同的；选用不同的周期窗口作为基本计算区域，使之与正方形像素矩阵对应，并构造出基本图元，实现了用一个映射构造出多个平面排列图案的算法。

A class of inverse eigenvalue problem for sub-periodic Jacobi matrices, as well as its properties, were discussed.

讨论了一类由谱数据构造子周期Jacobi矩阵的特征值反问题，以及子周期Jacobi矩阵的相关性质。

N[1] and[2], the classification theory of indices set of irreducible nonnegative matrices isstudied,according to that theory . An algorithm for the period and the classification of indices setof irreducible nonnegative matrices are given. Using this algorithm.

文［1］和［2］讨论了不可约非负矩阵指标集的分类理论，在此基础上，本文给出了不可约非负矩阵的周期与指标集的分类算法，这一算法能同时求出周期与同余类，当矩阵的阶不大时，该算法容易在图上实现。

The equivalent definition of the minimal strong component is given, and it discusses the relation between the standard form and the minimal strong component in the paper. Consequently, the theory is proved that the periodicity of a fuzzy matrix is the least common multiple of periodicity of its minimal strong component.

给出了极小强支的等价定义，讨论了模糊矩阵的标准型与极小强支关系，从而得到了模糊矩阵周期是极小强支周期的最小公倍数的定理。

Firstly, the connection matrices are strongly connected Boolean matrix, it is shown that the maximum length of limit cycles for FBAM is the period index of the product of the connection matrices. Thus, the maximum limit cycle is reachable. Secondly, two strongly connected components are connected by walks, it is proved that the maximum length of limit cycles for FBAM is the max. of the period index of the two strongly connected components if they are prime, otherwise, it is the least common multiple of the two period index. Finally, n strongly connected component are connected in succession, the method for computing the maximum length is described. By different patterns are presented to the networks, diminishing the number of the strongly connected components until only two components.

第一，连接权矩阵为强连通布尔矩阵，此时模糊双向联想记忆网络的最大极限环长度为连接权矩阵乘积的周期指数，从而极限环具有可达性；第二，两个强连通分支有路径连接，此时如果两个强连通分支的周期指数互素，那么网络的最大极限环长度为其最大者，否则，网络的最大极限环长度就等于二者的最小公倍数；第三，n个相邻强连通分支有路径连接，给出了计算最大极限环长度的方法，通过激发模式的变化，逐渐减少强连通分支的个数，直到只有两个分支。

With the sub-pixel calculation,the fingerprint periodicity matrix and normal direction image can be gotten accurately and the sharp corner of fingerprint image center line in existing direction image method can be avoided,the AFIS performance also can be improved significantly.

通过亚像素的计算，可以精确地输出指纹的周期矩阵和法向图，避免了方向图算法中无法计算指纹中心线急转弯的问题，使整个AFIS的性能得到了很大的提高。

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

Firstly,based on the B.Bowermans result about the rate of convergence in Cesaro sense of certain nonhomogeneous Markov chains which the transition matrices converge,we are to study a certain nonhomogenous Markov chains which the transition matrices average converge to a period strongly ergodic stochastic matrice,and control the average convergenc rate of transition matrices,then we get the rate of convergence in Cesaro sense about the nonhomogeneous Markov chains by used the character of norm and the character of nonhomogeneous Markov chains.It is an extension of a B.

首先在B.Bowerman等人研究转移矩阵列收敛的一类非齐次马氏链，其Cesaro平均收敛的收敛速度基础上，研究转移矩阵列平均收敛到一周期强遍历随机矩阵的一类非齐次马氏链，通过控制转移矩阵列平均收敛的收敛速度，利用矩阵范数的性质、非齐次马氏链的相关性质等，得到该非齐次马氏链转移矩阵Cesaro平均收敛的收敛速度，是B。

But the result of life cycle assessment shows that paper has not the advantage of plastics in environmental protection.This paper analyses and assesses both Plastics and paper package materials using sumple life cycle matrix.

然而生命周期的评价结果表明，纸在环境保护方面并不具有优势，本文采用简式生命周期矩阵对这两种包装材料进行了分析和评价。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。