期刊：
Algebra and Logic,2016年55(1):38-49 ISSN：0002-5232
通讯作者：
Muzychuk, M. E.
作者机构：
[Muzychuk, M. E.] Netanya Acad Coll, Netanya, Israel.;[Ponomarenko, I. N.] VA Steklov Math Inst, St Petersburg Branch, St Petersburg 191011, Russia.;[Chen, G.] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Muzychuk, M. E.] N;Netanya Acad Coll, Netanya, Israel.
期刊：
Archiv der Mathematik,2015年105(4):313-322 ISSN：0003-889X
通讯作者：
Blau, Harvey I.
作者机构：
[Blau, Harvey I.] No Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA.;[Chen, Gang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Blau, Harvey I.] N;No Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA.
摘要：
Table algebras all of whose nonidentity basis elements are involutions (in the sense of Zieschang), which serve as a counterpoint to the generic Hecke algebras parametrized by Coxeter groups, are classified. If two-generated, they are the family H (n) (for all n a parts per thousand yen 3), which for suitable n arise from schemes defined by affine planes of order n - 1. Otherwise, the basis involutions correspond to the points of a finite projective space whose incidence geometry determines the algebra multiplication. This generalizes to table algebras a previous result of van Dam for association schemes. An algebraic characterization is also given.
期刊：
Algebras and Representation Theory,2014年17(5):1527-1552 ISSN：1386-923X
通讯作者：
Blau, Harvey I.
作者机构：
[Blau, Harvey I.] No Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA.;[Chen, Gang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Blau, Harvey I.] N;No Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA.
关键词：
Table algebras;Union of closed subsets;Association schemes;Finite groups;Irreducible characters
期刊：
Journal of Graph Theory,2014年77(3):237-250 ISSN：0364-9024
通讯作者：
Chen, Guantao
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Ferrara, Michael; Jacobson, Michael] Univ Colorado Denver, Dept Math & Stat Sci, Denver, CO USA.;[Hu, Zhiquan] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;[Liu, Huiqing] Hubei Univ, Sch Math & Comp Sci, Wuhan, Peoples R China.
通讯机构：
[Chen, Guantao] G;Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.
关键词：
extremal spanning tree;broom
摘要：
A broom is a tree obtained by subdividing one edge of the star an arbitrary number of times. In (E. Flandrin, T. Kaiser, R. Kužel, H. Li and Z. Ryjáček, Neighborhood Unions and Extremal Spanning Trees, Discrete Math 308 (2008), 2343–2350) Flandrin et al. posed the problem of determining degree conditions that ensure a connected graph G contains a spanning tree that is a broom. In this article, we give one solution to this problem by demonstrating that if G is a connected graph of order with , then G contains a spanning broom. This result is best possible.
期刊：
Communications in Algebra,2013年41(6):2387-2404 ISSN：0092-7872
通讯作者：
Chen, Gang
作者机构：
[Blau, Harvey I.] No Illinois Univ, Dept Math Sci, De Kalb, IL USA.;[Chen, Gang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Chen, Gang] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
期刊：
Journal of Algebra,2013年373:340-355 ISSN：0021-8693
通讯作者：
Blau, Harvey I.
作者机构：
[Blau, Harvey I.] No Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA.;[Chen, Gang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Blau, Harvey I.] N;No Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA.
关键词：
C-algebras;Table algebras;Algebras with involution;Finite groups;Irreducible characters;Conjugacy classes;Matrices;Dual C-algebra;Association schemes
摘要：
A lower bound on the number of elements outside a closed subset of a C-basis of a commutative C-algebra with dual a table algebra is derived, as is an equivalent condition for when the lower bound is met. As corollaries, lower bounds are obtained on the number of primitive idempotent matrices of rank greater than 1 in the adjacency algebra of a commutative, imprimitive association scheme; and, for a given normal subgroup N of a finite group C. on the number of irreducible characters of G whose kernels do not contain N, and on the number of conjugacy classes of G not contained in N. Also found are equivalent conditions for when these lower bounds are met. (C) 2012 Elsevier Inc. All rights reserved.
作者机构：
[Chen, Gang; Chen, G] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Chen, Gang] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
character ring;induction theorem;p-elementary subgroups;characteristic class function
摘要：
Let G be a finite group, S a unitary subring of the complex number field ℂ and R(G) the character ring of G. Let π be the set of rational prime numbers whose inverses do not belong to S. Denote the family of all p-elementary subgroups of G by W(π), where p runs over π. It is proved that, in the sense of conjugation, W(π) is the least family of subgroups of G such that the S-linear map is surjective.
期刊：
Communications in Algebra,2012年40(4):1547-1562 ISSN：0092-7872
通讯作者：
Blau, Harvey I.
作者机构：
[Blau, Harvey I.] No Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA.;[Chen, Gang] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Blau, Harvey I.] No Illinois Univ, Dept Math Sci, 1425 W Lincoln Hwy, De Kalb, IL 60115 USA.
通讯机构：
[Blau, Harvey I.] N;No Illinois Univ, Dept Math Sci, 1425 W Lincoln Hwy, De Kalb, IL 60115 USA.
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Hu, Zhiquan] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Li, Hao] Univ Paris Sud, LRI, UMR CNRS UPS 8623, F-91405 Orsay, France.
通讯机构：
[Chen, Guantao] G;Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.
会议名称：
8th French Combinatorial Conference (FCC)
会议时间：
JUN 28-JUL 02, 2010
会议地点：
Orsay, FRANCE
会议主办单位：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.^[Hu, Zhiquan] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.^[Li, Hao] Univ Paris Sud, LRI, UMR CNRS UPS 8623, F-91405 Orsay, France.
关键词：
Cycle;Path;Degree;Toughness;Connectivity
摘要：
A path in a graph is called extendable if it is a proper subpath of another path. A graph is locally connected if every neighborhood induces a connected subgraph. We show that, for each graph G of order n, there exists a threshold number s such that every path of order smaller than s is extendable and there exists a non-extendable path of order t for each t is an element of {s, ... , n - 1} if G satisfies any one of the following three conditions: the degree sum d(u) + d(nu) >= n for any two nonadjacent vertices u and nu; P-4-free and omega(G - S) <= vertical bar S vertical bar for every cut set S of G: connected, locally connected, and K-1.3-free where P-4 and K-1,K-3 denote a path of order 4 and a complete bipartite graph with 1 and 3 vertices in each color class, respectively. (C) 2011 Elsevier B.V. All rights reserved.
期刊：
Journal of Graph Theory,2011年68(1):55-76 ISSN：0364-9024
通讯作者：
Wu, Yaping
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Hu, Zhiquan; Wu, Yaping] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Wu, Yaping] Jianghan Univ, Fac Math & Comp, Wuhan, Peoples R China.
通讯机构：
[Wu, Yaping] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
关键词：
circumference;connectivity;independence number
摘要：
By investigating the action of linear irreducible characters of a finite group on the product of all the irreducible characters and on a sum of certain irreducible characters, some results on vanishing elements of finite groups are obtained.
摘要：
In this paper, we study the following variable exponent system {−div(|∇u|p(x)−2∇u)+a(x)|u|p(x)−2u=f(x,u,v,λ)in Ω,−div(|∇v|q(x)−2∇v)+b(x)|v|q(x)−2v=g(x,u,v,λ)in Ω,B(u,v)=0, under some various conditions, we present several results for the existence of multiple nontrivial solutions.
摘要：
This paper investigates the existence of solutions and nonnegative solutions for prescribed variable exponent mean curvature impulsive system initialized boundary value problems. The proof of our main result is based upon Leray-Schauder's degree. The sufficient conditions for the existence of solutions and nonnegative solutions have been given.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2010年2010(1):1-24 ISSN：1029-242X
通讯作者：
Zhang, Qihu
作者机构：
[Wang, Shujuan; Zhi, Guizhen; Zhang, Qihu] Zhengzhou Univ Light Ind, Dept Math & Informat Sci, Zhengzhou 450002, Henan, Peoples R China.;[Zhao, Liang] Henan Inst Sci & Technol, Acad Adm, Xinxiang 453003, Henan, Peoples R China.;[Chen, Guangxia] Henan Polytech Univ, Sch Math & Informat, Jiaozuo 454003, Henan, Peoples R China.;[Zhang, Qihu] Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Zhang, Qihu] Z;Zhengzhou Univ Light Ind, Dept Math & Informat Sci, Zhengzhou 450002, Henan, Peoples R China.
关键词：
Full Article;Publisher Note
摘要：
This paper investigates the existence of solutions for weighted
-Laplacian impulsive integro-differential system periodic-like boundary value problems via Leray-Schauder's degree. The sufficient conditions for the existence of solutions are given.
作者机构：
[陈刚] School of Math.and Statistics,Central China Normal University;[王荣乾] Henan Polytechnic Institute;[孙大英] School of Information,Renmin University of China
期刊：
JOURNAL OF COMBINATORIAL THEORY SERIES B,2008年98(4):735-751 ISSN：0095-8956
通讯作者：
Chen, Guantao
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Chen, Guantao] Hubei Univ, Fac Math & Comp Sci, Wuhan 430062, Peoples R China.;[Chen, Yuan] Wuhan Univ Sci & Engn, Coll Sci, Wuhan 430073, Peoples R China.;[Gao, Shuhong] Clemson Univ, Dept Math Sci, Clemson, SC 29634 USA.;[Hu, Zhiquan] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Chen, Guantao] G;Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.
关键词：
Connectivity;Linkage;Bipartite index;Sumset
摘要：
A graph G is k-linked if G has at least 2k vertices, and for every sequence x (1), x(2),...,x(k), y(1), y(2),..., y(k) of distinct vertices, G contains k vertex-disjoint paths P-1, P-2,..., P-k such that P-i joins x(i) and y(i) for i = 1, 2,...,k. Moreover, the above defined k-linked graph G is modulo (m(1), m(2),..., m(k))-linked if, in addition, for any k-tuple (d(1), d(2),..., d(k)) of natural numbers, the paths P-1, P-2,..., P-k can be chosen such that P-i has length d(i) modulo m(i) for i = 1, 2,..., k. Thomassen showed that, for each k-tuple (m(1), m(2),....., m(k)) of odd positive integers, there exists a natural number f(m(1), m(2),..., m(k)) such that every f (m(1), m(2),..., m(k))-connected graph is modulo (m(1), m(2),.....,m(k))-linked. For m(1) = m(2) =...= m(k) = 2, he showed in another article that there exists a natural number g(2, k) such that every g(2, k)-connected graph G is modulo (2, 2,..., 2)-linked or there is X subset of V(G) such that vertical bar X vertical bar <= 4k - 3 and G - X is a bipartite graph, where (2, 2,..., 2) is a k-tuple. We showed that f (m(1), m(2),..., m(k)) <= max{14(m(1) + m(2) +...+ m(k)) - 4k, 6(m(1) + m(2) +...+ m(k)) 4k + 36) for every k-tuple of odd positive integers. We then extend the result to allow some m(i) be even integers. Let (m(1), m(2),..., m(k)) be a k-tuple of natural numbers and l <= k such that m(i) is odd for each i with l + 1 <= i <= k. If G is 45(m(1) + m(2) +...+ m(k))-connected, then either G has a vertex set X of order at most 2k + 2l - 3 + delta(m(1),..., m(l)) such that G - X is bipartite or G is modulo (2m(1),..., 2m(l), m(l+1),..., m(k))-linked, where [GRAPHICS] Our results generalize several known results on parity-linked graphs. (c) 2007 Elsevier Inc. All rights reserved.
