Hamilton连通性和邻域并条件

设G＝（V，E）为简单图，δ为图G的最小度，1987年Faudree等人给出NC＝min{|N(x)∪N(y)‖x,y∈V(G),xy∈N(G)}，有关文献曾研究3连通的H连通图，本文进一步得到：若G是n阶2连通图，且NC≥n-δ，则G除几个图外均是H连通图，从而，完成了邻并条件的H连通图问题。     

图有[a,b]因子的邻域条件

不含有图K1，R的图称为K1,r-free图，设G是一个具有顶点集V（G）的图，设n(≥3),a和b是整数，使得b≥a≥1，若b是奇数，设b≥n-1。我们证明了每个连通的K1,r-free图G在b|V(G)|为偶数，它的最小度至少是a n-1,|V(G）≥ （2(a b)-1)(a b-1)/b，以及|NG(x）∪NG（y)|≥a|V(G)|a b对V的任意两个不邻接的点x和y都成立时，G有一个[a,b]因子。     

导出子图和周长的局部定理

设G是n阶2-连通图，3≤c≤n.本文绘出对于图G的每一个同构于K1.3或Z1的导出子图L，若d（u）且如果dL（u，v）=2有（v）=min{，|M3（u）|/2}这里M3（u）={v|dc（u,v）≤3}，则G包含长至少为c的圈．     

图的笛卡儿积的测地数

对于图G内的任意两点u和v，u-v测地线是指u和v之间的最短路．I（u，v）表示位于u-v测地线上所有点的集合，对于．S∈V（G），I（S）表示所有I（u，v）的并，这里“u,v∈．S．G的测地数g（G）是使I（S）=V（G）的点集．S的最小基数．在这篇文章，我们研究G×K3的测地数和g（G）与g（G×K3）相等的充分必要条件，还给出了T×Km和Cn×Km的测地数，这里T是树．     

完全二部图的Kp,p-分解大集的存在谱北大核心CSCD

令H,G是两个简单图,G是H的一个子图.H的G-分解,记为（λH,G）-GD,是指将图λH的所有边分拆为若干个与G同构的子图（称为G-区组）.H的G-分解的大集,记为（λH,G）-LGD,是指图H的所有与G同构的子图的一个分拆Β1,Β2,…,Βm,使得每个Bj（1≤j≤m）为一个（λH,G）-GD （称为小集）.本文中,我们对完全二部图的K（p,p）-分解的大集进行了研究,利用Kv的λ重Kκ-因子大集的存在性结果,采用直接构造的方法,得到了大集（λK（m,n）,K（p,p））-LGD的存在谱,其中p为任意素数.     

偶图的K3.3剖分

设G＝（X，Y；E）是一个偶图。如果|X|≥2|Y|-3且d(v)=3对任意v∈X,那么G含有K3.3的剖分。有例子表明|X|的下界在一定程度上是不可改进的。     

图和有向图的测地数

对于图G（或者有向图D）内的任意两点u和υ,u-υ测地线是指在u和υ之间的最短路（或者从u到υ）.I（u,υ）表示位于一条u-υ测地线上所有点的集合,对于S（U∣）V（G）,I（S）表示所有I（u,υ）的并,这里u,υ∈S.图G（或者有向图D）的测地数g（G）（g（D））是使J（S）=V（G）（J（S）=V（D））的最小点集S的基数.定义G的所有定向图中测地数的最小值为G的下测地数,即g-（G）=min{g（D）：D是G的定向图）;定义G的所有定向图中测地数的最大值为G的上测地数,即g＋（G）=max{g（D）：D是G的定向图）.本文的主要目的是研究G V H 的上、下测地数,此外,文章给出了g（G）=g（G×P3）的一个充分必要条件.     

关于代数连通度的一个注记

图G=(V,E)的次小的拉普拉斯特征值称为G的代数连通度,记为α(G).设δ(G)为G的最小度.Fiedler早在1973年便证明了α(G)≤δ(G),但他未能给出等号成立的极图刻划.后来,我们在[6]中确定了当δ(G)≤1/2|V(G)|时α(G)=δ(G)的充要条件.本文中,我们将确定任意情况下α(G)=δ(G)成立的所有极图.     

3-正则Halin-图全色数的注(英文)

本文讨论了△（G）＝3的Halin-图的金色数Xr（G）＝4的充分条件，并提出了3－正则Halin-图Xr（G）＝5的充分必要条件的猜想，其中△（G），Xr（G）分别表示G的最大度和全色数．     

极大非独立集可削去的因子临界图

如果对一个简单图G的每一个与G的顶点数同奇偶的独立集I，都有G-I有完美匹配，则称G是独立集可削去的因子临界图．如果图G不是独立集可削去的因子临界图，而对任意两个小相邻的顶点x与y，G xy足独立集可削去的因子临界图，则称G足极大非独立集可削去的因子临界图，本刻画了极大非独立集可削去的因子临界图。     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

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

正August 10-14,2015Beijin,China The 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     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.