系数矩阵

To extract shaft orbit\'s features invariant to rotation, scaling and translation, the unique strengths of Haar orthogonal matrix type are found, the horizontal and vertical coordinates of shaft orbit are fast proceeded by Haar transform, respectively, and the slopes with different resolutions are obtained at different positions by using the corresponding transform coefficients, and then the multi-resolution angles between the adjacent slope straight line are extracted skillfully and used for the hierarchical recognition, the recognition process accords with the principle of human\'s recognizing things by using hierarchy analysis approach.

为提取轴心轨迹平移、旋转、尺度不变性特征，本文挖掘出Haar正交矩阵在图形识别中的独特优点，引入Haar正交矩阵分别对轴心轨迹的横、纵坐标进行快速变换，并利用变换后的对应系数得到轴心轨迹不同位置不同分辨率下的斜率，继而推求出相邻斜率直线之间的多分辨率夹角，所获夹角用于轴心轨迹的分层识别，其识别过程符合人类识别事物层次分析的规律。

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

Some basic properties of σ- LFSR over F4 are studied, such as nonlinearity, cycle structure distribution of state graph, the largest period and counting problem related. The conclusions are as follows:The coefficient ring of σ-LFSR is isomorphic to the matrix ring over F,. The cycle structure of σ- LFSR is consistent with that of the determinant of the corresponding polynomial matrix if and only if the feedback polynomial of - LFSR does not contain nontrivial factor over F2,. The counting formula of the number of σ- LFSR with inconsistent cycle structure is also showed in that part. The period of σ-LFSR with degree n is maximum if and only if the determinant of the corresponding polynomial matrix is the primitive polynomial with order 2n over F2,.

本文研究了有限域F_4上的σ-LFSR的一些基本性质，如非奇异性、状态图的圈结构的分布、最大圈的充要条件及相关的计数问题等，得到以下结论：σ-LFSR的系数环同构于F_2上的矩阵环；σ-LFSR的状态图的圈结构与对应的多项式矩阵的行列式的圈结构一致的充要条件为σ-LFSR的反馈多项式不含有非平凡的F_2上的因式，给出了圈结构不一致的σ-LFSR的计数公式； n次σ-LFSR周期达到最大，当且仅当对应多项式矩阵的行列式为F_2上的2n次本原多项式。

Then,a new fast algorithm of the minimal norm least squares solution for linear system whose coefficients is an m×n symmetric Loewner matrix with full column rank is given by forming a special block matrix and researching the triangular factorization of its inverse.

对于工程计算中常常遇到的一类线性方程组的求解，通过构造特殊分块矩阵并研究其逆矩阵的三角分解，给出了求秩为n的m×n阶对称Loewner矩阵为系数阵的线性方程组，及极小范数最小二乘解的快速算法，该算法的计算复杂度为O+O(n2)，而一般方法的计算复杂度为O(mn2)+O(n3)。

In this thesis, a semi-classical model of the force on an atom is used to describe the motion of a two-level atom interacting with a standing wave laser field. The velocity dependent force and momentum diffusion are derived through optical Bloch equations by using the matrix form of the continued fraction technique. By investigating the dynamic properties of atoms in laser field, we can control and manipulate the mechanical motion of an atom.

本文利用半经典理论，从二能级原子在激光驻波场中所满足的运动方程出发，推导出密度矩阵元所满足的递推关系，利用矩阵连分数方法求解出密度矩阵元，从而求出依赖于原子运动速度的光压力与动量扩散系数，通过讨论原子在激光场中的动力学行为，为原子在激光场中被囚禁、形成原子列阵以及可控制的量子态，从而为量子信息处理提供理论基础。

During the T-matrix method of calculating light scattering by particle, incident and scattered fields are expand into spherical vector wave functions: which, via their relationship derived from the Maxwell equations, leads to the T-matrix, a transferring matrix between expansion coefficients of fields.

在粒子光散射计算的T矩阵方法中，将入射场和散射场用球矢量波函数展开，通过Maxwell方程推出二者之间的关系-零场方程，可获得散射场和入射场展开式系数之间的传输矩阵-T矩阵。

The characteristic vector of the real symmetric matrix should be found out, which is orthogonalized and normalized to a standard orthogonal base and is used as row vector to construct the transformation matrix P, so the P~(-1)AP can be made into diagonal matrix.

实对称矩阵A经相似变换P-1AP可化为对角矩阵，在x =Py 下，不一定能化A的二次型为标准型；应寻求对称矩阵A的特征向量，将其正交化并单位化作为标准正交基，作为列向量构造变换矩阵P，可使P-1AP=Λ为对角阵，在x =Py 下，要将二次型化为标准型，且二次项系数即为对角阵Λ主对角线上元素。

This dissertation proposes group reasoning and group AHP-based GDSS structure and its decision steps to solve the problems existing in research of theory and application of GDSS. Besides, the dissertation also studies the method of group reasoning on rough-set and qualitative reasoning method basis in GDSS. It also studies on constructing method of hierarchy structure of group AHP in GDSS and combinative method of judgment matrixes. Moreover, it studies on method regarding construction of judgment matrixes on rough set based and optimization theory of convex combination parameters of judgment matrixes as well. Finally, it develops an AHP based GDSS to demonstrate the efficiency of these methods.(1) This dissertation also summarizes the developing trend of GDSS and analyses problems as regards the research of GDSS.

本论文针对GDSS理论研究及应用中存在的若干问题，提出了基于群体推理及群体层次分析法的GDSS结构，并给出了基于该结构的GDSS的决策程序；研究了GDSS环境下的基于粗糙集理论及定性推理技术的群体推理方法，并举例说明了方法的有效性；研究了GDSS环境下群体AHP层次结构的建立、判断矩阵集结的理论与方法；研究了判断矩阵凸组合系数的优化原理；探讨了基于Rough Set的判断矩阵构造方法；开发了一个基于AHP的GDSS原型系统，旨在验证本文关于GDSS环境下群体AHP有关方法的有效性。

This paper shows that the coupling coefficients for ideal modes, for local modes and for superlocal modes are all related by similar matrices in the sense of Lowey, and as far as discrete modes are concerned, the "equivalence"expressions derived by Marcuse are special cases of our general results.

本文将阐明：理想模式的耦合系数、本地模式的耦合系数以及超本地模式的耦合系数，三者之间通过在Lowey意义下的相似矩阵而发生联系；就离散模式而言，Marcuse导出的&等效&关系式，可以作为特例从我们得到过的结果直接推导出来。

By the use of the concept of "pseudo convected velocity" proposed by theauthor, mechanical influence coefficient is obtained with the physical meaning ofdepending only on configuration of mechanism explicitly revealed and therelationship between influence coefficient and Jacobian matrix of robots is analyzed.

采用作者提出的&拟牵连速度&的概念，推导出了机构的影响系数，明确地给出了影响系数只依赖于机构位形这一结论的运动学含义，分析了机构影响系数与机器人雅克比矩阵的关系。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新