斜Pairing,余循环变形与双交叉积

本文讨论了双代数的余循环变形和双交叉积．当双交叉积ＸＡ是ＸＡ的２ 余循环变形时，给出了ＸＡ为ＸＡ的某个斜Ｐａｉｒｉｎｇ变形ＸτＡ的一个充分条件．然后，利用函子间的自然同构，给出双交叉积ＸＡ为斜Ｐａｉｒｉｎｇ变形的一个充要条件．     

一个三角形不等式的简单证明

一个三角形不等式的简单证明７１０２００陕西高陵一中高凯庆本刊１９９４年第３期，刘健在《一个有价值的三角形不等式》一文中提出了如下一个三角形不等式：设Ｐ为ＡＢＣ内部任一点，ＡＰ、ＢＰ、ＣＰ分别交ＢＣ、ＣＡ、ＡＢ于Ｌ、Ｍ、Ｎ，记ＡＢＣ的边ＢＣ、ＣＡ、ＡＢ...     

关于完全正矩阵的几点注记

本文给出了一个ｎ&;#215;ｎ非负、对称、弱对角占优矩阵Ａ为完全正的一个充分条件。我们还给出了较好的算法,用以获得关于矩阵Ａ（当Ａ为完全正时）的分解指数的一个上界。     

关于严实Hilbert环

在本文中，严实Ｈｉｌｂｅｒｔ环得到了更进一步的刻划．本文的主要结果是：一个环Ａ是严实Ｈｉｌｂｅｒｔ环，当且仅当多项式环Ａ［Ｘ］的每个实极大理想在Ａ上的局限是Ａ的一个极大理想，当且仅当Ａ是实Ｈｉｌｂｅｒｔ环，且Ａ［Ｘ］的每个实极大理想是极大的．     

谈一类极值问题的解法

本文将利用集合的子集类的思想去解决一类较为复杂的极值问题 .为此我们引入以下的概念和定理 .设Ａ是一个非空有限集 ,集合Ａ的元素个数称为集合Ａ的阶 ,记作｜Ａ｜ .当｜Ａ｜=ｎ ,称Ａ是一个ｎ阶集 .对于一个集合Ａ的一个子集类 {Ａ1,Ａ2 ,… ,Ａｋ},若对任何二个子集Ａｉ,Ａｊ(ｉ≠ｊ)都有Ａｉ Ａｊ,Ａｊ Ａｉ,则称这个类是互不包含的子集类 .对这种子集类我们有定理　有一个ｎ(ｎ≥ 1 )阶集合Ａ的一切互不包含的子集类中 ,子集个数最多的类含有Ｃｎ2ｎ个子集 ,其中 ｎ2 表示不超过 ｎ2 的最大整数 .证明　记 {Ａ1,Ａ2 ,… ,Ａｋ}为Ａ的…     

关于严实Hilbert环

在本文中，严实Ｈｉｌｂｅｒｔ环得到了更进一步的刻划．本文的主要结果是：一个环Ａ是严实Ｈｉｌｂｅｒｔ环，当且仅当多项式环Ａ［Ｘ］的每个实极大理想在Ａ上的局限是Ａ的一个极大理想，当且仅当Ａ是实Ｈｉｌｂｅｒｔ环，且Ａ［Ｘ］的每个实极大理想是极大的．     

正多边形的又一个充要条件

正多边形的又一个充要条件李宗奇（甘肃省徽县一中７４２３００）《数学通报》９４年第５期刊登的《正多边形的一个充要条件》一文中指出：如果凸ｎ边形Ａ１Ａ２…Ａｎ，满足：１°Ａ１Ａ２＝Ａ２Ａ３＝…＝ＡｎＡ１那么Ａ１Ａ２…Ａｎ是正ｎ边形．本文给出另一充要条件定...     

圆锥曲线焦点弦的一个有趣性质及其简证

文 [1 ]指出了圆锥曲线焦点弦的一个有趣性质 ,读了有所启发 ,李老师对圆锥曲线是椭圆、双曲线、抛物线的情况分别给出了证明 ,由于证明较繁 ,笔者经过探索发现点Ａ可以是圆锥曲线上任意点的情况 ,并给出它们的一个统一命题及其简证 .引理　设Ｆ为圆锥曲线焦点 ,其相应准线为Ｌ ,作一直线交圆锥曲线于Ａ ,Ｐ两点 ,交Ｌ于Ｍ点 ,则ＦＭ平分△ＡＦＰ的∠ＡＦＰ外角 .图 1证　如图 1 ,从Ａ ,Ｐ分别向Ｌ引垂线ＡＡ1 ,ＰＰ1 垂足为Ａ1 ,Ｐ1 ,由圆锥曲线定义得 :｜ＡＦ｜｜ＡＡ1 ｜ =ｅ ,｜ＰＦ｜｜ＰＰ1 ｜ =ｅ ,所以 ,｜ＡＦ｜｜ＡＡ1 ｜ =｜ＰＦ…     

车站选址与绝对值函数

有这样一个实际问题：下面是一个工厂厂区的地图（图１），一条公路（粗线）通过这个地区，七个工厂Ａ１，Ａ２，Ａ３，Ａ４，Ａ５，Ａ６，Ａ７分布在公路两侧，由一些小路（细线）与公路相连．现在要在公路上设一个长途汽车站．车站到图１各工厂（沿公路、小路走）的路程...     

关于一个单形不等式的简单证明

关于一个单形不等式的简单证明杨定华（重庆师范学院数学系，重庆４０００４７）苏化明先生在文［１］建立如下与ｎ维单形外接超球心有关的一个不等式：定理设Ａ＝Ａ１Ａ２…Ａｎ＋１为Ｅｎ中的ｎ维单形，Ａ的外接超球心Ｏ位于其内部．记Ａｉ＝Ａ１Ａ２…Ａｉ－１ＯＡｉ＋...     

A Dai-Liao conjugate gradient algorithm with clustering of eigenvalues

A new value for the parameter in Dai and Liao conjugate gradient algorithm is presented. This is based on the clustering of eigenvalues of the matrix which determine the search direction of this algorithm. This value of the parameter lead us to a variant of the Dai and Liao algorithm which is more efficient and more robust than the variants of the same algorithm based on minimizing the condition number of the matrix associated to the search direction. Global convergence of this variant of the algorithm is briefly discussed.     

A numerical technique for structural damage detection

A computationally attractive method is proposed in this study to provide an insight to the location and extent of structural damage. The proposed method makes use of the matrix disassembly technique and approaches the damage location and extent problem in a decoupled fashion. First, a scheme is developed to determine the damage location by calculating a damage localization vector, which is derived from the modal residual force criteria. With location determined, the corresponding damage extent can be easily obtained only by the processes of division. The algorithm is applied to a numerical example and its efficiency is demonstrated through damage simulations.     

A problem in rearrangements of (0,1) matrices

We determine the patterns of an n × n (0, 1) matrix A, which give a maximal sum of the elements of A², for a given number of units in A.     

A modified bisection algorithm for the determination of the eigenvalues of a symmetric tridiagonal matrix

Summary A modification to the well known bisection algorithm [1] when used to determine the eigenvalues of a real symmetric matrix is presented. In the new strategy the terms in the Sturm sequence are computed only as long as relevant information on the required eigenvalues is obtained. The resulting algorithm usingincomplete Sturm sequences can be shown to minimise the computational work required especially when only a few eigenvalues are required.The technique is also applicable to other computational methods which use the bisection process.     

A Matrix of a Growth Optimization Model for the Production Activity of Cooperating Enterprises

This paper deals with direct and indirect growth rates of co-operating enterprises and with the corresponding matrix of growth. Its purpose is to determine through indirect growth rates the growth structure of co-operating enterprises and to construct, on the basis of the matrix of growth, a model which enables us to follow and program them. In other words, by means of the matrix of growth or the model which is based on it we can estimate the future development of co-operating enterprises. The conditions of optimality have been determined through linear programming, whereby account has been taken of the upper and the lower limit of development of the enterprise, the available funds and the efficiency of investments.     

論矩陣的一種變換

<正> 在本文中,數域限定為複數域.我們要來研究如下的變換:(1)(它將方陣A變成方陣B),式中P表示任意正則陣,P表示P的元素的共軛救構成的陣.所有的變换(1)顯然成羣.這種變換現在姑稱之為種變換.如果二方陣A與B可由一個種變換變此成彼,我們就說,A與B是對相似的.     

A factorization method for products of holomorphic matrix functions

A class of matrix functions defined on a contour which bounds a finitely connected domain in the complex plane is considered. It is assumed that each matrix function in this class can be explicitly represented as a product of two matrix functions holomorphic in the outer and the inner part of the contour, respectively. The problem of factoring matrix functions in the class under consideration is studied. A constructive method reducing the factorization problem to finitely many explicitly written systems of linear algebraic equations is proposed. In particular, explicit formulas for partial indices are obtained.     

确定递阶层次结构的简便方法

运用层次分析法(AHP)解决决策问题时,第一步就是要确定问题的递阶层次结构.对此,现有文献中给出的数学方法都是基于可达矩阵的,它通常需要借助计算机来完成.在文中充分考虑到AHP递阶层次结构的特点严格的逐层相关性及元素间无互相关性,给出一种非常简单的方法—划列法(DRM),并严格证明了其正确性,然后通过举例给予说明.该方法使递阶层次结构的确定不必再进行可达矩阵等计算,只依靠手工即可完成.     

A distance-metric methodology for the derivation of weights from a pairwise comparison matrix

A variety of approaches exist for the determination of a weighting scheme from a pairwise comparison matrix describing a scale-relation between objectives or alternatives. The most common context for such an algorithm is that of the analytic hierarchy process (AHP), although uses in other areas of the field of multicriteria decision making (MCDM) can also be found. Typically, the eigenvalue method is the standard method employed in the AHP to determine weights, as in the ExpertChoice software. However, another class of techniques are the distance-metric-based approaches, which are frequently proposed as alternatives to the eigenvalue method. This paper evaluates such distance-metric-based approaches comparing their effectiveness, using the eigenvalue method as a benchmark. A common framework is introduced to establish an efficient frontier for method comparison.     

A probing method for computing the diagonal of a matrix inverse

The computation of some entries of a matrix inverse arises in several important applications in practice. This paper presents a probing method for determining the diagonal of the inverse of a sparse matrix in the common situation when its inverse exhibits a decay property, i.e. when many of the entries of the inverse are small. A few simple properties of the inverse suggest a way to determine effective probing vectors based on standard graph theory results. An iterative method is then applied to solve the resulting sequence of linear systems, from which the diagonal of the matrix inverse is extracted. The results of numerical experiments are provided to demonstrate the effectiveness of the probing method. Copyright © 2011 John Wiley & Sons, Ltd.