折叠立方体网络的最小反馈点集

对简单图G=(V,E),顶点子集F V,如果由V\F导出的子图不含圈,则称F是G的反馈点集。点数最小的反馈点集称图的最小反馈点集,最小的点数称为反馈数。一个k维折叠立方体是由一个k维超立方体加上所有的互补边构成的图。本文证明了k维折叠立方体网络的反馈数f(k)=c.2k-1(k 2),其中c∈k-1     

交叉立方体网络的反馈数

对于简单图G=(V,E),顶点子集F■V,如果由V\F导出的子图G′= (V\F,E′)是不含圈的,则称F是图G的一个反馈点集.点数最少的反馈点集称图的最小反馈点集,最小的点数称为反馈数.文章给出了交叉立方体网络的一个等价定义,用递归的方法构造出交叉立方体网络的诱导树,证明了诱导树的阶数Fibonacci数,进而得到叉立方体网络反馈数的上下界.     

广义de Bruijn和Kautz有向图的距离控制数

对于任意的正整数(?),强连通图G的顶点子集D被称为距离(?)-控制集,是指对于任意顶点v(?)D,D中至少含有一个顶点u,使得距离dG(u,v)≤(?)．图G距离(?)- 控制数γe(G)是指G中所有距离(?)-控制集的基数的最小者．本文给出了广义de Bruijn 和广义Kautz有向图的距离(?)-控制数的上界和下界,并且给出当它们的距离2-控制数达到下界时的一个充分条件．从而得到对于de Bruijn有向图B(d,k)的距离2-控制数γ2(B(d,k))= ．在该文结尾,我们猜想Kautz有向图K(d,k)的距离2-控制数γ2(K(d,k))= .     

本原对称有向图上广义指数的极图

设D是n阶有向图(允许有环但不允许有重复弧),X C V(D),集指数expD(X)是这样的最小正整数P,使得对D中每个点v,存在从X的至少一个点到V的长为P的途径.若这样的正整数P不存在,则定义expD(X)=∞.D的第k重上广义指数F(D,k):=max{expD(X)| X C V(D),|X|=k},1≤k≤n.如果F(D,k)<∞,则称D是k-上本原的.本文完全刻划了k-上本原对称有向图的第k重上广义指数的极图.     

有向循环图强连通度的下界

为简便计,本文采用文[1]中的定义和符号,而未说明的概念或符号引自[3].本文仅讨论有限、简单有向图. 有向图D=(V,A)称为强连通的,如果对D的任两顶点u与v,在D中同时存在(u,v)—有向路和(v,u)—有向路,C(?)V称为D的点割集,如果D—C非强连通或是单点.D的所含点数最少的点割集称为最小点割集,其阶数定义为D的强连通度,记为k(D)或k. 循环有向图D(n,S)定义如下:     

强定向图的k-强距离

对强连通有向图D的一个非空顶点子集S,D中包含S的具有最少弧数的强连通有向子图称为S的Steiner子图,S的强Steiner距离d(S)等于S的Steiner子图的弧数. 如果|S|=k, 那么d(S)称为S的k-强距离. 对整数k≥2和强有向图D的顶点v,v的k-强离心率sek(v)为D中所有包含v的k个顶点的子集的k-强距离的最大值. D中顶点的最小k-强离心率称为D的k-强半径,记为sradk(D),最大k-强离心率称为D的k-强直径,记为sdiamk(D). 本文证明了,对于满足k+1≤r,d≤n的任意整数r,d,存在顶点数为n的强竞赛图T′和T″,使得sradk(T′)=r和sdiamk(T″)=d;进而给出了强定向图的k-强直径的一个上界.     

广义de Bruijn和Kautz有向图的双向控制集

设G=(V,A)是一个有向图,其中V和A分别表示有向图G的点集和弧集.对集合TV(G),如果对于任意点v∈V(G)\T,都存在点u,w∈T(u,w可能是同一点)使得(u,v),(v,w)∈A(G),则称T是G的一个双向控制集.有向图G的双向控制数γ~*(G)是G的最小双向控制集所含点的数目.提出了广义de Bruijn和Kautz有向图的双向控制数的新上界,改进了以前文献中提出的相关结论.此外,对某些特殊的广义de Bruijn和Kautz有向图,通过构造其双向控制集,进一步改进了它们双向控制数的上、下界.     

有向笛卡尔积图的有向度量维数(英文)

设D是一个有向图,w={w_1,w_2,…,w_k}是D的一个有序点子集,v是D中任意一点。我们把有序k元素组r(v|w)=(d(v,w_1),d(v,w_2),…,d(v,w_k))称为点v对于W的(有向距离)表示。如果在D中,任意两个不同的点u和v对W的(有向距离)表示都不相同,则称W是有向图D的一个分解集。我们把D的最小分解集的基数称为有向图D的有向度量维数,并用dim(D)来表示。本文研究了有向笛卡尔积图D_1×D_2的有向度量维数。设P_m和C_m分别是长为m的有向路和有向圈。在文中我们分别给出了dim(D_1×D_2)的一个下界与dim(D×P_m)和dim(D×C_m)的上界,并通过确定dim(P_m×P_n),dim(C_m×P_n)和dim(C_m×C_n)的精确值说明了我们给出的上界是紧的。     

有向图的L(j,k)数的上界

给定正整数j≥k,有向图D的一个L(j,k)-标号是指从V(D)到非负整数集的一个函数f,使得当x在D中邻接到y时|f(x)-f(y)|≥j,当x在D中到y距离为二时|f(x)-f(y)|≥k.f的像元素称为标号.L(j,k)一标号问题就是确定(?)j,k-数(?)j,k(D),这个参数等于(?) max{f(x)|x∈V(D)},这里f取遍D的所有L(j,k)-标号.本文根据有向图的有向着色数及最长有向路的长度来研究(?)j,k-数,证明了:(1)对任何有向着色数为(?)(D)的有向图D,(?)j,k(D)≤((?)(D)-1)j;(2)对任何最长有向路的长度为l的有向图D,如果不含有向圈或者D中最长有向圈长度为l 1,则(?)j,k(D)≤lj.并且这两个界都是可达的.最后我们对l=3的有向图给出了3j-L(j,k)-labelling的一个有效算法.     

有向路和有向圈的控制集数

1引言设G=(V,E)为无向图．子集D (?)V(G)是无向图G的控制集,如果对于任意的y,∈V(G)-D,都存在x∈D,使xy∈E(G)．G的控制集D是G的分裂控制集,如果G中由V(G)-D导出的子图G〈V(G)-D〉是不连通的．G的一个控制集D是G的一个强(弱)控制集,若dG(x)≥d_G(y)(d_G(x)≤d_G(y)),其中d_G(x)表示G中与点x关联的边数．对于有向图H=(V,A),子集D(?)V(H)称为H的控制集,如果对于任意的y∈     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.