On the Deleted Product Criterion For Embeddability in

For a space let . Let act on and on by exchanging factors and antipodes respectively. We present a new short proof of the following theorem by Weber: For an -polyhedron and , if there exists an equivariant map , then is embeddable in . We also prove this theorem for a peanian continuum and . We prove that the theorem is not true for the 3-adic solenoid and .

     

On induced and isometric embeddings of graphs into the strong product of paths

The strong isometric dimension and the adjacent isometric dimension of graphs are compared. The concepts are equivalent for graphs of diameter 2 in which case the problem of determining these dimensions can be reduced to a covering problem with complete bipartite graphs. Using this approach several exact strong and adjacent dimensions are computed (for instance of the Petersen graph) and a positive answer is given to the Problem 4.1 of Fitzpatrick and Nowakowski [The strong isometric dimension of finite reflexive graphs, Discuss. Math. Graph Theory 20 (2000) 23-38] whether there is a graph G with the strong isometric dimension bigger that ⌈|V(G)|/2⌉.     

On the geodetic number and related metric sets in Cartesian product graphs

A set S of vertices of a graph G is a geodetic set if every vertex of G lies in at least one interval between the vertices of S. The size of a minimum geodetic set in G is the geodetic number of G. Upper bounds for the geodetic number of Cartesian product graphs are proved and for several classes exact values are obtained. It is proved that many metrically defined sets in Cartesian products have product structure and that the contour set of a Cartesian product is geodetic if and only if their projections are geodetic sets in factors.     

On the order of the error in discretization methods for weakly singular second kind non-smooth solutions

In general, second kind Volterra integral equations with weakly singular kernels of the formk(t,s)(t –s)^– posses solutions which have discontinuous derivatives att=0. A discrete Gronwall inequality is employed to prove that, away from the origin, the error in product integration and collocation schemes for these equations is of order 2-.     

关于随机紧凸集的更新定理

该文在讨论了多维更新定理的基础上,重点研究了随机紧凸集的Minkowski和的更新定理,得到了一系列重要结论.     

On the Inequalities for Traces and Singular Values of the Quaternion Matrices

Ｔｏｏｕｒｋｎｏｗｌｅｄｇｅ,ｓｏｍｅｅｘｔｅｎｔｉｏｎ,ｉｍｐｒｏｖｅｍｅｎｔａｎｄｒｅｖｉｓｉｏｎｈａｖｅｂｅｅｎｄｏｎｅｔｏｍａｎｙｒｅｓｕｌｔｓｏｎｔｈｅｓｉｎｇｕｌａｒｖａｌｕｅｓａｎｄｔｈｅｔｒａｃｅｓｏｆｍａｔｒｉｃｅｓ［１－８］．Ｉｎｔｈｉｓｐａｐｅｒ,ｔａｋｉｎｇａｄｖａｎｔａｇｅｏｆｔｈｅｉｎｅｑｕａｌｉｔｉｅｓｏｂｔａｉｎｅｄｉｎｔｈｅｃｌａｓｓｉｃａｌｒｅａｌｆｉｅｌｄ,ｗｅｓｔｕｄｙｄｅｅｐｌｙｔｈｅｉｎｅｑｕａｌｉｔｙｐｒｏｂｌｅｍｓｒｅｌａｔｉｎｇｔｏｔｈｅｔｒａｃ…     

On Bayes linear unbiased estimation of estimable functions for the singular linear model

The unique Bayes linear unbiased estimator (Bayes LUE) of estimable functions is derived for the singular linear model. The superiority of Bayes LUE over ordinary best linear unbiased estimator is investigated under mean square error matrix (MSEM) criterion.     

Lower bounds for the domination number and the total domination number of direct product graphs

A sharp lower bound for the domination number and the total domination number of the direct product of finitely many complete graphs is given: . Sharpness is established in the case when the factors are large enough in comparison to the number of factors. The main result gives a lower bound for the domination (and the total domination) number of the direct product of two arbitrary graphs: γ(G×H)≥γ(G)+γ(H)−1. Infinite families of graphs that attain the bound are presented. For these graphs it also holds that γ_t(G×H)=γ(G)+γ(H)−1. Some additional parallels with the total domination number are made.     

关于一点的投影到一仿射集合的加权扰动分析

本文讨论了在C~n中一点的投影到一个仿射集合的加权扰动分析,我们假定长方矩阵A有任意秩,扰动是任意的这最一般性情形。分别研究了当A有扰动δA后为(?),当rabkA=rank(?)和rankA≠rank(?)两种情况下解x的相对误差界,推广了文献[3][4][11][12]的主要结果。     

A cancellation law for partially ordered sets and spaces

In this paper we prove a cancellation law in the category (1) of partially ordered sets and (2) of spaces, the respective conditions on the common factor being that it have (1) an irreducible bottom element and (2) an irreducible bottom element in its specialization order.

     

多维非退化扩散过程的象集与图集的一致Packing维数

设B(t)=(B(t))=(B1(t),B2(t),…,BN(t))为N维Brown运动,设α(x)=(αij(x),1(≤)I(≤)d,1(≤)j(≤)N),β(x)=(βi(x),1(≤)I(≤)d),x∈Rd,1(≤)d(≤)N,α(x)和β(x)有界连续和满足Lipchitz条件,且存在常数c0＞0,使得对每个x∈Rd,a(x)=α(x)α(x)*的每个特征根都不小于c0.设dX(t)=α(X(t))dB(t) β(X(t))dt,设d(≥)3.可以证明P(ωDimX(E,ω)=DimGRX(E,ω)=2DimE,(A)E∈B[0,∞))=1.这里X(E,ω)={X(t,ω)t∈E},GRX(E,ω)={(t,X(t,ω))t∈E},DimF表示F的Packing维数.     

On the topological centre problem for weighted convolution algebras and semigroup compactifications

Let be a locally compact, non-compact group (we make the non-compactness assumption, for the most part, simply to avoid trivialities). We show that under a very mild assumption on the weight function , the weighted group algebra is strongly Arens irregular in the sense of Dales and Lau; i.e., both topological centres of equal . Also, we show that the topological centre of the algebra equals the weighted measure algebra . Moreover, still in the same situation, we prove that every linear (left) -module map on is automatically bounded, and even --continuous, hence given by convolution with an element in . To this end, we derive a general factorization theorem for bounded families in the -module . Finally, using this result in the case where , we give a short proof of a theorem due to Protasov and Pym, stating that the topological centre of the semigroup is empty, where denotes the -compactification of . This sharpens an earlier result by Lau and Pym; moreover, our method of proof gives a partial answer to a problem raised by Lau and Pym in 1995.

     

关于向量组的秩与最大无关组的教学改革研究

对向量的秩与最大无关组的教学过程进行了分析研究，从教学内容组织与教学手段等方面提出了改革的方案．对有的教材的不足提出了改进办法.     

On the nonemptiness and compactness of the solution sets for vector variational inequalities

In this article, we investigate conditions for nonemptiness and compactness of the sets of solutions of pseudomonotone vector variational inequalities by using the concept of asymptotical cones. We show that a pseudomonotone vector variational inequality has a nonempty and compact solution set provided that it is strictly feasible. We also obtain some necessary conditions for the set of solutions of a pseudomonotone vector variational inequality to be nonempty and compact.     

On best possible order of convergence estimates in the collocation method and Galerkin's method for singularly perturbed boundary value problems for systems of first-order ordinary differential equations

The collocation method and Galerkin method using parabolic splines are considered. Special adaptive meshes whose number of knots is independent of the small parameter of the problem are used. Unimprovable estimates in the -norm are obtained. For the Galerkin method these estimates are quasioptimal, while for the collocation method they are suboptimal.

     

On the homotopy fixed point problem for free loop spaces and other function complexes

Let G be a finite group, let X and Y be finite G-complexes, and suppose that for each K G, Y ^K is dim(X ^K)-connected and simple. G acts on the function complex F(X, Y) by conjugation of maps. We give a complete analysis of the homotopy fixed point set of the space F(X, Y). As a corollary, we are able to analyze at a prime p, the homotopy fixed point set of the circle action on X, where X denotes the free loop space of X, and X is a simply connected finite complex.Supported in part by NSF DMS 86-02430.To A. Grothendieck on the occasion of his sixtieth birthday     

二元码的平均Hamming距离和方差

通过对二元ｎ长码Ｃ的对偶距离分布的研究,在码字数为奇数的情况下,改进了Ａｌ－ｔｈｏｆｅｒ－Ｓｉｌｌｋｅ［１］和［２］文关于Ｃ的码字间平均Ｈａｍｍｉｎｇ距离及其均方差的不等式,并在码字数为２ｎ－１或２ｎ－１－１时,确定了码Ｃ的最小平均距离及其均方差的精确值．     

L-统计量的Edgeworth展开和随机加权逼近

文［１］讨论了Ｌ－统计量的一种能达到Ｏ１√ｎ精确度的随机加权逼近,本文则给出了Ｌ－统计量的Ｅｄｇｅｗｏｒｔｈ展开和一种能达到ｏ１√ｎ精确性的新的随机加权逼近