关于π—矩阵

引进了π－矩阵的概念。π－矩阵是循环矩阵的一种推广,还包括了ｒ－循环矩阵。文中给出了π－矩阵的结构定理;讨论了π－矩阵的基本特征,如行列式、特征多项式、特征值和对角化问题等。     

广义等对角优势及其应用

提出了广义等对角优势矩阵的概念,得到了非奇H-矩阵的一个充分必要条件,并在此基础上对三角形矩阵‖A-1‖∞的上界进行了估计。最后基于迭代法的思想,我们给出了一种估计非奇M-矩阵的‖A-1‖∞上界和下界的方法。     

广义等对角优势及其应用

提出了广义等对角优势矩阵的概念,得到了非奇H-矩阵的一个充分必要条件,并在此基础上对三角形矩阵‖A-1‖∞的上界进行了估计.最后基于迭代法的思想,我们给出了一种估计非奇M-矩阵的‖A-1‖∞上界和下界的方法.     

双正交小波矩阵

本文引进了双正交（半正交）小波矩阵及对偶的概念。讨论了这些矩阵的一些性质，尤其是给出了利用小波矩阵的元素将离散函数展开为级数形式的结果，进而建立了半正交小波矩阵与［８］中正交小波矩阵，双正交小波矩阵与对偶双正交小波矩阵的关系。最后举例说明了本文引进双正交（半正交）小波矩阵及对偶概念和方法的合理性。     

非奇异H-矩阵的新判据

非奇异H-矩阵在矩阵分析和数值代数的研究中具有重要作用.本文利用广义α-对角占优矩阵、不可约α-对角占优矩阵和具非零元素链α-对角占优矩阵的概念和性质,通过对矩阵行标作划分的方法,首先给出了非奇异H-矩阵的两个新的判定条件.然后进一步将所得结果应用于比较矩阵和转置比较矩阵的和,得到了另一个更为实用的判据.最后,用数值例...     

广义严格对角占优矩阵的新判据

广义严格对角占优矩阵在数值分析和矩阵理论的研究中非常重要。本文利用广义Nekrasov矩阵的概念,给出了广义严格对角占优矩阵的两个充要判定条件,得到了广义严格对角占优矩阵的几个新的实用判据,包含和推广了文献中的相关结果。最后用数值例子说明了结论的有效性。     

关于区间H-矩阵的条件

在引入区间α-二重几何平均对角占优矩阵概念的基础上，讨论了区间H-矩阵的判别条件．把黄廷祝(1994)的结果推广到区间矩阵的情形，得到了区H-矩阵的几个充要条件和充分条件，从而推广和改进了黄廷祝，李有明等人相应的结果。     

多商品市场供需均衡的稳定性分析

应用需求弹性矩阵与供应弹性矩阵的概念,将单商品市场供需均衡的稳定性分析推广到了多商品市场的情形。     

块H-矩阵的简捷判据

Feingold与Varga引入了块对角占优的概念,基于它的优美性质,引起了许多学者的浓厚兴趣本文研究块H-矩阵(广义块对角占优矩阵)的实用判定,给出了块H-矩阵的两个新的简捷判据,并应用十矩阵正稳定性和亚正定性的判定。     

浅议双线性函数在不同基下的矩阵间的关系

在双线性函数的概念之下将矩阵合同与相似的关系统一起来,并将二次型与内积也统一到双线性函数之下。     

A fitness differential adaptive parameter controlled evolutionary algorithm with application to the design structure matrix

This paper investigates a methodology for adaptation of the mutation factor within an evolutionary algorithm by means of measuring the improvement differential between successive generations. When no improvement is obtained in an evolutionary algorithm and it has not located the global optimum, it is an indication that the algorithm may have become trapped within a local minimum or maximum. Mutation is a tool within the algorithm that is designed to assist in escaping from these local extremes. It is therefore the premise of this paper that if the preset value for mutation probability is proving insufficient to release the algorithm from entrapment in a local minima or maxima, then a temporary increase in this mutation probability may assist in freeing the algorithm and therefore increasing its chances of ultimately converging on a global optimum. In order to determine when to implement the increase in mutation probability our algorithm measures the fitness improvement between successive generations in the algorithm. When no improvement is detected for a number of successive generations the probability is increased. The design structure matrix (DSM), a scheduling tool that has previously been optimized via the application of evolutionary algorithms, has been used as a practical implementation of differential adaptation to investigate its effectiveness in solving real world problems. Solutions provided by Todd, D. (Multiple criteria genetic algorithms in engineering design and operation, PhD thesis, Department of Marine Technology, University of Newcastle, 1997), are used to benchmark the algorithm's effectiveness.     

准正交矩阵与准对称矩阵

利用次转置阵给出了准正交阵与(反)准对称阵的概念;研究了它们的基本性质及其之间的联系;取得了许多新的结果,推广丫正交阵、对称阵与反对称阵间的相应结果,特别将正交阵的广义Cayley分解推广到了准正交阵上;将各类正交阵、对称阵及广义逆矩阵统一了起来。     

Differentially Private Real-Time Streaming Data Publication Based on Sliding Window Under Exponential Decay

Continuous response of range query on steaming data provides useful information for many practical applications as well as the risk of privacy disclosure. The existing research on differential privacy streaming data publication mostly pay close attention to boosting query accuracy, but pay less attention to query efficiency, and ignore the effect of timeliness on data weight. In this paper, we propose an effective algorithm of differential privacy streaming data publication under exponential decay mode. Firstly, by introducing the Fenwick tree to divide and reorganize data items in the stream, we achieve a constant time complexity for inserting a new item and getting the prefix sum. Meanwhile, we achieve time complicity linear to the number of data item for building a tree. After that, we use the advantage of matrix mechanism to deal with relevant queries and reduce the global sensitivity. In addition, we choose proper diagonal matrix further improve the range query accuracy. Finally, considering about exponential decay, every data item is weighted by the decay factor. By putting the Fenwick tree and matrix optimization together, we present complete algorithm for differentiate private real-time streaming data publication. The experiment is designed to compare the algorithm in this paper with similar algorithms for streaming data release in exponential decay. Experimental results show that the algorithm in this paper effectively improve the query efficiency while ensuring the quality of the query.     

Noise reduction with perforated three-duct muffler components

This paper describes the authors’ distributed parameter approach for derivation of closed-form expressions for the four-pole parameters of the perforated three-duct muffler components. In this method, three simultaneous second-order partial differential equations are first reduced to a set of six first-order ordinary differential equations. These equations are then uncoupled by means of a modal matrix. The resulting 6 × 6 matrix is reduced to the 2 × 2 transfer matrix using the relevant boundary conditions. This is combined with transfer matrices of other elements (upstream and downstream of this perforated element) to predict muffler performance like noise reduction, which is also measured. The correlation between experimental and theoretical values of noise reduction is shown to be satisfactory.     

CONCOR聚类不动点研究

CONCOR聚类有着广泛的应用,其结果取决于CONCOR变换的不动点,然而CONCOR变换都有哪些不动点的研究至本文以前还是一个国际关注的开放问题.本文创新地提出了完美矩阵,朴素矩阵,0均值不动点等全新概念.证明了完美矩阵,朴素矩阵都是CONCOR变换的本原不动点,并给出了从本原不动点构造组合不动点的方法,从而解决了C...     

Note on algebraic solutions of differential equations with known finite Galois group

Given a linear differential equation with known finite differential Galois group, we discuss methods to construct the minimal polynomial of a solution. We first outline a well known general method involving a basis transformation of the basis of formal solutions at a singular point. In the second part we construct directly the minimal polynomial of an eigenvector of the monodromy matrix at a singular point. The method is very efficient for irreducible second and third order linear differential equations where a one dimensional eigenspace of some monodromy matrix always exists.     

余弦变换矩阵及其应用

本文介绍笛卡尔坐标与正交曲线坐标的＂余弦变换矩阵＂，证明这个变换矩阵是正交矩阵。利用这个变换矩阵可以方便地将笛卡尔坐标的张量表达式、微分算子及有关公式变换成正交曲线坐标的相应公式。     

变截面连续箱梁桥剪力滞及剪切变形双重效应分析的传递矩阵法

基于能量原理,考虑箱梁截面底板、顶板、悬臂板剪滞翘曲幅度一般各不相同的影响和轴力自平衡条件,计入腹板剪切变形,导出了箱梁的平衡控制微分方程组、边界条件;给出了该方程组在均布荷载作用下的初参数解,提出一种研究变截面连续箱梁桥剪力滞后效应的传递矩阵法。建立了相应的场矩阵和点矩阵,从而实现了变截面连续箱梁桥内力、应力及位移的一维递推求解。数值算例与模型试验及已有文献结果对比表明:该文方法计算精度好、效率高,为求解连续箱梁、变截面箱梁的剪力滞问题提供了强有力的计算手段。     

广义多体系统动力学的速度变换矩阵综合法

文中提出了广义多体系统和速度变换矩阵的概念,提出了一种新的加速度变换关系,以带不定乘子的拉格朗日方程为基础推导得到了求解复杂系统动力学问题的一种新方法,即广义多体系统的速度变换矩阵综合法。利用该方法,可根据无耦合广义体的动力学参数和系统的速度变换矩阵直接获得广义多体系统的动力学方程,其中不含拉格朗日不定乘子和约束反力,且方程中逆矩阵求解的维数等于系统的自由度数,因而有利于提高计算效率。该方法主要面向计算机实现程式化的算法,系统的动力方程可以由计算机自动完成运算,从而避免了繁琐的解析推导工作。