色多项式的Akiyama—Harary问题

J.Akiyama和F.Harary提出:是否存在非自补图G,使得G与其补图有相同的色多项式,本文给出一个肯定的回答,并证明了:这样的平面图G仅存在有限多个。     

图的能量与哈密尔顿性

设G是一个无向简单图, A(G)为$G$的邻接矩阵. 用G的补图的特征值给出G包含哈密尔顿路、哈密尔顿圈以及哈密尔顿连通图的充分条件; 其次用二部图的拟补图的特征值给出二部图包含哈密尔顿圈的充分条件. 这些结果改进了一些已知的结果.     

几类图的匹配等价图类

两个图G和H的匹配多项式相等,则称它们匹配等价.用[G]表示图G的所有不同构的匹配等价图的集合.刻画了匹配次大根小于1的图及这些图的补图的匹配等价图类.     

图的能量与哈密尔顿性

设G是一个无向简单图,A（G）为G的邻接矩阵．用G的补图的特征值给出G包含哈密尔顿路、哈密尔顿圈以及哈密尔顿连通图的充分条件：其次用二部图的拟补图的特征值给出二部图包含哈密尔顿圈的充分条件．这些结果改进了一些已知的结果．     

一个伴随等价定理的推广及其简证

记 Gr为任意图 G的 r个拷贝中的对应点 ( r个 )分别与星图 Sr+ 1 的 r个 1度点粘接后得到的图 ,又记 H r为该图 G的相应点与星图 Sr+ 1 的 r度点粘接后得到的图 .如果 G不含三角形 ,则图 ( r- 1) K1 ∪ Gr和图 ( r- 1) G∪ H r伴随等价 ,进而它们的补图色等价     

一类完全三部图的色唯一性

用P(G,λ)表示简单图G的色多项式.设G是一个给定的简单图,若对任意简单图H,当P(H,λ)=P(G,λ)时都有H和G同构(记为H≌G),则称图G是色唯一的.本文证明了以下结果:设n,k,△都为非负整数,其中k≥0,△∈{4,5},若n≥1/3k~2+1/3△~2-1/3k△-1/3k-1/3△+4/3,则完全三部图K(n,n+△,n+k)是色唯一的.同时还给出了一个猜想.     

树的补图的区间图完全化问题

一个图G的区间图完全化问题包含两类子问题:侧廓问题和路宽问题,分别表示为P(G)和PW(G),其中侧廓问题是寻求G的一个边数最小的区间超图;路宽问题是寻求G的一个团数最小的区间超图.这两类子问题分别在数值代数、VLSI-设计和算法图论等学科领域中有重要的应用.对一般图来说,两类子问题都是NP-完全问题;但是对一些特殊图类来说,它们在多项式时间内可解.本文给出了树T的补图的具体侧廓和路宽值.     

有关完全图的图的紧性

双随机矩阵有许多重要的应用,紧图族可以看作是组合矩阵论中关于双随机矩阵的著名的Birkhoff定理的拓广,具有重要的研究价值.确定一个图是否紧图是个困难的问题,目前已知的紧图族尚且不多,给出了三个结果:任意多个完全图的不交并是紧图;圈C_3与圈C_n(n3)的不交并是非紧图;当n是大于等于3的奇数时,完全图K_n与图K_(n+1)的不交并是非紧图,其中图K_(n+1)是从完全图K_(n+1)删去一因子而得到的图.     

无爪图上团横贯数的界

设 G=(V,E) 为简单图,图 G 的每个至少有两个顶点的极大完全子图称为 G 的一个团. 一个顶点子集 S\subseteq V 称为图 G 的团横贯集, 如果 S 与 G 的所有团都相交,即对于 G 的任意的团 C 有 S\cap{V(C)}\neq\emptyset. 图 G 的团横贯数是图 G 的最小团横贯集所含顶点的数目,记为~${\large\tau}_{C}(G)$. 证明了棱柱图的补图(除5-圈外)、非奇圈的圆弧区间图和 Hex-连接图这三类无爪图的团横贯数不超过其阶数的一半.     

A.KOTZIG关于自补图的一个待解问题的反例

本文所用的概念与符号与文献[2]相同,不相同的定义如下。 设G是一个自补图(下称s.c.图),p是G到它的补图G的同构映射,则称p是G的一个自补置换(下简称为s.c.置换)。我们用符号P(G)表示s.c.图G的全体s.c.置换的集合。设p∈P(G),若p是m个轮换的乘积,则记p=p_1p_2…pm,并记pi的长为|pi|。     

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.     

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.     

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.     

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     

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     

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).     

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.     

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.