鳞状因子循环矩阵方程解的条件与求解的快速算法

利用多项式快速算法,给出了鳞状因子循环矩阵方程AX=b可解的条件与求解的快速算法.当鳞状因子循环矩阵非奇异时,该快速算法求出线性方程组的唯一解;当鳞状因子循环矩阵奇异时,该快速算法求出线性方程组的特解与通解.该快速算法仅用到鳞状因子循环矩阵的第一行元素及对角矩阵中的对角上的常数进行计算.在计算机上实现时只有舍入误差.特别地,在有理数域上用计算机求得的结果是精确的.     

高维非线性动力系统最简规范形的计算

运用可逆线性变换和近恒同变换,研究了不经计算传统规范形,直接计算高维非线性动力系统的最简规范形。引进可逆线性变换,将非线性动力系统的线性矩阵拓扑等价于符合实际研究需求的分块对角线矩阵：相伴矩阵分布在对角线上,其余元素均为0。利用低阶项来化简高阶项,得到了高维非线性动力系统的最简规范形。在该最简规范形中,对应于每一个相伴矩阵的非线性系数矩阵,只有最后一行含有非0元素,其余各行元素均为0。借助Mathematica语言,编制了计算任意高维非线性动力系统的最简规范形的通用程序。运行该程序,分别计算了4维、6维和7维非线性动力系统的直到4阶的最简规范形。     

一种基于多维矩阵的无线传感器网络密钥预分配算法研究

密钥分配是无线传感器网络通信安全的基础.在低成本、低功耗、资源受限的传感器节点上现在可行的密钥分配方案是基于对称密码体制的密钥预分配模型,随机预分配模型的优点是分配方法简便,缺点是节点问不能保证安全连通,连通概率与节点密钥存储量、抗俘获能力成反比,确定预分配模型的优点是任意节点间可建立直接安全通信,缺点是密钥协商的通信和计算开销较大.在多项式与LU矩阵分解的确定密钥预分配方案的基础上、挺出了一种基于多维矩阵的改进方案.分析研究表明对比传统方案,在保证安全连通的基础上,降低了存储量和通信计算的开销,提高了节点抗俘获能力与动态扩展能力.     

正可逆算子矩阵族

研究了Ｈｉｌｂｅｒｔ空间Ｈ＋Ｋ上缺项正算了矩阵族（Ａ（λ）？？Ｂ（λ）：λ∈∧其中∧为任意指标集）的一致补全问题，给出了存在非零算子把该族的每个缺项算子矩阵都补全为正可逆算子的充要条件。     

单元修改的特征结构分配方法

本文根据线性控制系统的输出反馈理论，利用特征结构分配修改技术，提出了有限元模型误差源于单元矩阵的假设，针对单元矩阵进行修改的思想，改进了特征结构分配方法，形成矩阵型法和元素型法相结合的修改方法．经该方法修改后的模型在形式上保持了原始模型的矩阵特点和物理意义，从而使之可以继续再修改，直到具有足够的模型精度。     

符号矩阵填充的修正增广拉格朗日乘子算法

矩阵填充问题是近年来的研究热点之一,特别地,符号矩阵填充问题在生物医学等领域有着很好的应用前景.本文以奇异值阈值方法为基础,针对符号矩阵填充提出了修正的增广Lagrange乘子法.修正算法对每步产生的阈值矩阵进行符号投影,形成新的符号矩阵,构成在符号矩阵离散集合上的迭代.同时证明了在合理条件下,当罚因子充分大时,修正算...     

最近点投影型反馈神经网络的临界分析

基于Lyapunov泛函方法和矩阵理论,本文研究一类被广泛应用的反馈神经网络-最近点投影型反馈神经网络的临界全局动力学性态,当网络具有非线性不扩张性质时,在临界条件下得到该类网络全局收敛性和渐近稳定性.所获结果改进了已知的有关该类网络临界分析的代表性结论(当连接矩阵拟对称时网络具有收敛性).数值试验表明结果的正确性和有效性.     

一种新颖的多用户OFDM资源分配算法

在多用户正交频分复用(OFDM)系统中设计一种新颖的子载波-功率分配方法来最大化用户数据传输速率.这个方案分成两部分,子载波分配和功率分配.其中,子载波分配方法是在信道容量矩阵中将信道容量最好的子载波首先进行分配,功率分配采用注水方法.研究和模拟结果表明,该算法在只改变各个子载波增益系数的基础上,基本保持了较低的复杂度,并且极大地提高了用户数据传输速率.     

公务员招聘方案的优化设计

本文建立了录用人员分配方案的数学优化模型.对应聘人员的特长、用人部门的要求、用人部门的情况和应聘人员的志愿分别赋值,构成相应的向量.利用欧氏距离计算应聘人员的特长与用人部门要求的贴近度,得贴近度矩阵,对该矩阵的元素进行模糊聚类,进而得出不考虑应聘人员意愿的择优按需分配方案.计算用人部门的情况与应聘人员意愿的贴近度,得贴近度矩阵,对两个矩阵分别赋权作线性组合,得综合贴近度矩阵,对该矩阵的元素进行模糊聚类,进而得出既考虑应聘人员意愿、又考虑用人部门要求的分配方案.并说明了上述方法也适用于N个应聘人员M个用人部门的情况.基于用人部门的要求和应聘人员意愿的优先权,对上述问题进行了深入讨论.最后,对上述方案进行了综合评价.     

YAMAHA DME24N／64N正式登陆中国市场

8月份,继DME32混音引擎后推出了新一代音频处理器。用过DME32的人对DME24N/64N有一种似曾相识的感觉,但是有些地方是不一样的。对于以前没有接触过DME32和不太了解矩阵以及最新的CobraNet技术的人来说,DME24N/64N无疑是一个新事物。 先从矩阵说起,现在的调音台上多有矩阵输出,一方面可以增加输出通路,另外一方面还可以对各母线的信号灵活分配。矩阵的输入可以分配到任意一个输出上,操作方便。2000年6月雅马哈推出了DME32,32路输入/输出,在矩阵的每通路上都可设置独立的动态,压限,扩展等效果模块,用户也可把不同的功能模块组合成一个新的模块。作为矩阵混音设备单独使用时,它的音频信号处理能力等于一     

Pseudo-Tournament Matrices and Their Eigenvalues

A tournament matrix and its corresponding directed graph both arise as a record of the outcomes of a round robin competition. An $n×n$ complex matrix $A$ is called $h$-pseudo-tournament if there exists a complex or real nonzero column vector $h$ such that $A+A^*=hh^*−I$. This class of matrices is a generalisation of well-studied tournament-like matrices such as $h$-hypertournament matrices, generalised tournament matrices, tournament matrices, and elliptic matrices. We discuss the eigen-properties of an $h$-pseudo-tournament matrix, and obtain new results when the matrix specialises to one of these tournament-like matrices. Further, several results derived in previous articles prove to be corollaries of those reached here.     

A matrix-based approach to properness and inversion problems for rational surfaces

We present a matrix-based approach for deciding if the parameterization of an algebraic space surface is invertible or not, and for computing the inverse of the parametrization if it exists.     

多变量矩阵方程异类约束解的修正共轭梯度法

基于求解线性代数方程组的共轭梯度法,通过对相关矩阵和系数的修改,建立了一种求多矩阵变量矩阵方程异类约束解的修正共轭梯度法.该算法不要求等价线性代数方程组的系数矩阵具备正定性、可逆性或者列满秩性,因此算法总是可行的.利用该算法不仅可以判断矩阵方程的异类约束解是否存在,而且在有异类约束解,不考虑舍入误差时,可在有限步计算后求得矩阵方程的一组异类约束解;选取特殊初始矩阵时,可求得矩阵方程的极小范数异类约束解.另外,还可求得指定矩阵在异类约束解集合中的最佳逼近.算例验证了该算法的有效性.     

On computational procedures for the force method

It is known that the matrix force method has certain advantages over the displacement method for a class of structural problems. It is also known that the force method, when carried out by the conventional Gauss-Jordan procedure, tends to fill in the problem data, making the method unattractive for large size, sparse problems. This poor fill-in property, however, is not necessarily inherent to the method, and the sparsity may be maintained if one uses what we call the Turn-Back LU Procedure. The purpose of this paper is two-fold. First, it is shown that there exist some close relationships between the force method and the least squares problem, and that many existing algebraic procedures to perform the force method can be regarded as applications/extensions of certain well-known matrix factorization schemes for the least squares problem. Secondly, it is demonstrated that these algebraic procedures for the force method can be unified form the matrix factorization viewpoint. Included in this unification is the Turn-Back LU Procedure, which was originally proposed by Topçu in his thesis.⁸ It is explained why this procedure tends to produce sparse and banded ‘self-stress’ and flexibility matrices with small band width. Some computational results are presented to demonstrate the superiority of the Turn-Back LU Procedure over the other schemes considered in this paper.     

基于四元数矩阵奇异值分解的彩色图像分解

讨论了四元数矩阵的奇异值分解（QSVD）,四元数矩阵的奇异值仍是正实数,但两个酉矩阵是含有四元数的四元数矩阵。给出通过四元数矩阵的等价实矩阵求解QSVD的有效算法。最后应用QSVD进行彩色图像分解,并给出了在Fruits、Baboon等图像上的实验结果。QSVD使许多基于SVD的图像处理方法可以推广到彩色图像处理上而不用再将彩色图像分解成三个通道图像进行处理。     

Iterative solution of large linear systems with non‐smooth submatrices using partial wavelet transforms and split‐matrix matrix–vector multiplication

The iterative solution of large linear systems with highly irregular matrices cannot be accelerated by wavelet transformation and subsequent sparsification if the transformed matrix is still highly irregular. In this paper we show that if the irregularity of the original matrix is limited to a relatively small known set of rows or columns (as is the case in significant applications), then acceleration can be achieved by a mixed approach in which only the ‘smooth’ submatrix is transformed and iterative solution is implemented using a novel ‘split‐matrix’ form of matrix–vector multiplication. Copyright © 2003 John Wiley & Sons, Ltd.     

A note on some properties of the Perron root of nonnegative irreducible matrices

This paper deals with the Perron root of nonnegative irreducible matrices, all of whose entries are continuous bijective functions of some parameter vector. It is known that if the functions are log-convex, then the Perron root is a convex function of the parameter vector. In this paper, we strengthen this result by showing that the log-convexity property is also necessary when the Perron root is required to be convex for any nonnegative irreducible matrix. Furthermore, we show that a less restrictive requirement is sufficient when the matrix is confined to belong to two subsets of irreducible matrices. In particular, in case of positive semidefinite matrices, convexity is sufficient for the Perron root to be convex. This work was supported by the German Ministry for Education and Research.     

MALDI matrices for biomolecular analysis based on functionalized carbon nanomaterials

When used in small molar ratios of matrix to analyte, derivatized fullerenes and single wall nanotubes are shown to be efficient matrices for matrix-assisted laser desorption/ionization (MALDI) mass spectrometry. The mixing of an acidic functionalized fullerene with a solution of bioanalyte, depositing a dried droplet, and irradiating with a pulsed nitrogen laser yields protonated or cationized molecular ions. Derivatized fullerenes could offer several advantages over conventional MALDI matrices: a high analyte ionization efficiency, a small molar ratios (less than 1) of matrix/analyte, and a broader optical absorption spectrum, which should obviate specific wavelength lasers for MALDI acquisitions. The major disadvantage to the use of fullerenes is the isobaric interference between matrix and analyte ions; however, it is overcome by using MALDI-ion mobility time-of-flight (IM-oTOF) mass spectrometry to preseparate carbon cluster ions from bioanalyte ions prior to TOF mass analysis. However, an alternative to the dried droplet preparation of fullerene MALDI samples is the aerosolization of matrix-analyte solutions (or slurries) followed by impacting the aerosol onto a stainless surface. We also demonstrate that the fullerene matrices can be used to acquire spectra from rat brain tissue.     

Improving the co-word analysis method based on semantic distance

We propose an improvement over the co-word analysis method based on semantic distance. This combines semantic distance measurements with concept matrices generated from ontologically based concept mapping. Our study suggests that the co-word analysis method based on semantic distance produces a preferable research situation in terms of matrix dimensions and clustering results. Despite this method’s displayed advantages, it has two limitations: first, it is highly dependent on domain ontology; second, its efficiency and accuracy during the concept mapping progress merit further study. Our method optimizes co-word matrix conditions in two aspects. First, by applying concept mapping within the labels of the co-word matrix, it combines words at the concept level to reduce matrix dimensions and create a concept matrix that contains more content. Second, it integrates the logical relationships and concept connotations among studied concepts into a co-word matrix and calculates the semantic distance between concepts based on domain ontology to create the semantic matrix.     

Normal form for Mueller Matrices in Polarization Optics

Abstract

The normal (canonical) form for Mueller matrices in polarization optics is derived: it is shown that a non-singular real 4 × 4 matrix M qualifies to be the bona fide Mueller matrix of some physical system if and only if it has the canonical form M = L′ ΛL, where L and L′ are elements of the proper orthochronous Lorentz group L ^↑ ₊, and where Λ = diag (λ₀, λ₁, λ₂, λ₃) with λ₀ ≥ ¦λ_j¦ > 0. It is further shown that λ₁ and λ₂ can be taken to be positive so that the signature of λ₃ is the same as that of det M. Several experimentally measured Mueller matrices are analysed in the light of the normal form. The case of singular Mueller matrices is briefly discussed as a limiting case.