ON A QUADRATURE FORMULA WITH FIRST DERIVATIVE AND ITS DEGREE OF ACCURACY

This paper develops a clase of quadrature formula with first derivativesIt is demonstrated that its degree of accuracy is not less than 2k+1 for a set of distinct nodes {x0,x1,...,xn} over interval [a,b],and just only 2k+1 for equally spaced nodes.Far overcoming the shortcoming of involving a great number of manual computations for the integration rules of the Hermitian interpolation formula,some simple formulas for computing automatically βi,γi and E [f] by computer are given,especially for equally spaced nodes.     

UNIFORM SUPERAPPROXIMATION OF THE DERIVATIVE OF TETRAHEDRAL QUADRATIC FINITE ELEMENT APPROXIMATION

In this paper,we will prove the derivative of tetrahedral quadratic finite element ap-proximation is superapproximate to the derivative of the quadratic Lagrange interpolant of the exact solution in the L^∞-norm, which can be used to enhance the accuracy of the derivative of tetrahedral quadratic finite element approximation to the derivative of the exact solution。     

On the relative merits of three-point integration rules for six-node triangles

There exist two three-point integration rules for triangular elements. Both rules are precise up to the second order and used for evaluating the six-node triangles. While one of rules has its sampling stations inside the triangle, that of the other coincide with the edge nodes. Though the former is commonly employed, it will be seen in this short paper that latter is indeed more favourable in view of element accuracy.     

对称群上的一类Cayley图的边传递性和Hamilton性

Let Sn be the symmetric group,g+I=(123i),g-I=(1i32) and M+n={g+I:4≤I≤n},then M+n is a minimal generating set of Sn,where n≥5.It is proved that Cayley graph Cay(Sn,M+n∪M-n) is Hamiltonian and edge symmetric.     

解第一类边界积分方程的高精度机械求积法与外推

０．引言使用单层位势理论把Ｄｉｒｉｃｈｌｅｔ问题：转化为具有对数核的边界积分方程：这里Г假设为简单光滑闭曲线．熟知,若Г的容度Ｃｒ≠１,（０．２）有唯一解存在［１］．借助参数变换这里的数值解法有Ｇａｌｅｒｋｉｎ法［２］,配置法［３］,和谱方法~［４］,这些方法有一个共同缺点就是矩阵元素的生成要计算反常积分,由于离散方程的系数矩阵是满阵,使矩阵生成的工作量很庞大,甚至超过了解方程组的工作量．显然,如能找到适当求积公式离散（０．２）,则可节省大量计算．使用求积公式法解（０．２）的文献不多,［５］中提…     

THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS

1. Notations and Basic ResultsLet G be a finite nonabelian group. Then frs(G/G') is an abelian group under themultiplication of characters and acts on the set of non-linear irreducible characters of G viathe multiplication of characters. The purpose of this paper is to investigate this action. Asan application of our theoryl in the end of Section 3 we give the classification of groupshaving exactly three non-linear irreducible caracters.All groups in the paper are finite. For a factor grou…     

一类对称多项式在微分几何中的应用

本文研究了卵形面特征刻画.利用麦克劳林不等式及对称多项式的性质,获得了一个An+1中的卵形面,若其任意三个连续高阶仿射平均曲率乘积为常熟,且Ln=0,则该卵形面为椭圆的结果.推广了现有文献关于卵形面的刻画结果.     

特征不为 2 的有限域上酉群的极小生成元集

设K=Fq2为含有q2个元素的有限域,q为奇素数的幂,*：a→a*=aq是Fq2的一个二阶自同构．本文用几何方法证明了除K为F32而n=4的情形外,Fq2上的酉群Un（V）可由2个元素生成．     

THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS

Let G be a nonabelian finite group. Then Irr(G/G′) is an abelian group under the multiplication of characters and acts on the set of non-linear irreducible characters of G via the multiplication of characters. The purpose of this paper is to establish some facts about the action of linear character group on non-linear irreducible characters and determine the structures of groups G for which either all the orbit kernels are trivial or the number of orbits is at most two. Using the established results on this action, it is very easy to classify groups G having at most three nomlinear irreducible characters.     

聚类分析中的对称原则

通过在集合上赋予对称关系 ,作者分析了对称结构与拓扑结构及等价划分的关系 ,指出 :一个对称关系可以唯一决定一种拓扑 ,也可以唯一决定一种等价划分 ;反之 ,赋予一种拓扑结构或等价划分 ,可以定出一种对称关系 .在此基础上 ,作者提供了由拓扑结构进行聚类的方案 ,并设计了聚类划分的数理统计方法     

ON THE ESTIMATION OF GENERALIZED LEBESGUE CONSTANT AND MODULUS OF GENERALIZED SINGULAR QUADRATURE FORMULAS AND ITS APPLICATION

This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the operator BLmp to the operator B.     

对称Z-矩阵的惯量以及其Schur补的若干交错性质

In this Paper,the inertia of a symmetric Z-matrix is studied,and bounds of the number of its positive eigenvalues are obtained.Also the interlacing theorem for Schur complement of a symmetric Z-matrix is established,which can be considered as a generalization Cauchy interlacing theorem in some extent.     

基于插值方法构造对称的矩形板单元

1　引　　言在有限元方法中,构造多项式类有限元的问题可以归结为多元多项式插值问题.在多元多项式插值的情形中,插值条件与插值多项式空间之间存在所谓的“匹配”(correct)问题,参见deBoor的论文[9].在构造非协调有限元时,关键的是设计适当的有限元形参数和适当的有限元形函数空间,再设计与之匹配的形参数.在经典的有限元构造方法中,例如,基于位移假设的板元的构造,就是首先定义好形函数空间.在这种情况下,所设计形参数必须满足两个条件:(1)形参数作为插值条件,必须与事先给定的形函数空间是插值匹配的,也即,由形参数定义的插值条件在形函…     

ON A SET OF h-HARMONIC HOMOGENEOUS POLYNOMIALS

1　IntroductionLet Sd- 1 bethe unitsphere of Rd,Πdthe space of allpolynomialsofd variables,and x(i)= (x1 ,… ,xi) (i=1 ,… ,d) .In this paper,we are concerned with the homogeneous polyno-mials orthogonal with the weightfunction h(x(d) ) =x2 k11 …x2 kdd on Sd- 1 ,where ki≥ 0 (i=1 ,… ,d) .Connected with the weightfunction h(x(d) ) are the following differential-differenceoperators introduced by Charles F. Dunkl in [3 ] ,Dip(x(d) ) = p(x(d) ) xi+ di=1kip(x(d) ) -p(x1 ,… ,-xi,… ,xd)xi,Δ…     

ON THE OPTIMAL CONVERGENCE RATE OF A ROBIN-ROBIN DOMAIN DECOMPOSITION METHOD

In this work, we solve a long-standing open problem： Is it true that the convergence rate of the Lions＇ Robin-Robin nonoverlapping domain decomposition （DD） method can be constant, independent of the mesh size h？ We closed this old problem with a positive answer. Our theory is also verified by numerical tests.     

THE SYMMETRIC AND SYMMETRIC POSITIVE SEMIDEFINITE SOLUTIONS OF LINEAR MATRIX EQUATION——B~TXB = D ON LINEAR MANIFOLDS

This paper discusses the solutions of the linear matrix equation B~T XB=D on some linear manifolds. Some necessary and sufficient conditions for the existence of the solution and the expression of the general solution are given. And also some optimal approximation solutions are discussed.     

ON THE PROJECTION OF THE EFFICIENT SET AND POTENTIAL APPLICATIONS

Abstract

We study the efficient set X _E for a multiple objective linear program by using its projection into the linear space L spanned by the independent criteria. We show that in the orthogonally complementary space of L, the efficient points form a polyhedron, while in L an efficiency-equivalent polyhedron for the projection P(X _E ) of X _E can be constructed by algorithms of outer and inner approximation types. These algorithms can be also used for generating all extreme points of P(X _E ). Application to optimization over the efficient set for a multiple objective linear program is considered.     

一类具指数系数的对称微分算子的谱及亏指数

就一类具指数函数系数的高阶对称微分算子得到了谱是离散的一些充分条件,并给出了完全可达的亏指数域.     

ON THE TITCHMARSH-WEYL THEORY OF ORDINARY SYMMETRIC ODD-ORDER DIFFERENTIAL EXPRESSIONS AND A DIRECT CONVERGENCE THEOREM

Abstract

In this paper the odd-order differential equation M[y] λ wy on the interval (O,∞), associated with the symmetric differential expression M of (2k-1)st order (k ≥ 2) with w a positive weight function and λ a complex number, is shown to possess k-Titchmarsh-Weyl solutions for every non-real λ in the underlying Hilbert space L² _w(O, ∞) having identical representation for every non-real λ. In terms of these solutions the Green's function associated with the singular boundary value problem is shown to possess identical representation for all non-real λ which has been further made use of in the third-order case to establish a direct convergence eigenfunction expansion theorem. The symmetric spectral matrix appearing in the expansion theorem has been characterized in terms of the Titchmarsh-Weyl m-coefficients.