期刊：
Discrete Mathematics, Algorithms and Applications,2010年2(2):143-150 ISSN：1793-8309
通讯作者：
Wang, CX
作者机构：
[Chunxiang Wang] School of Mathematics and Statistics, Huazhong Normal University, Wuhan, 430079, P. R. China
通讯机构：
[Wang, CX ] ;Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
关键词：
Super edge-connectivity;super-lambda;lambda'-graph;product graph G(m);* G(p)
摘要：
The super edge-connectivity λ′ of a connected graph G is the minimum cardinality of an edge-cut F in G such that every component of G–F contains at least two vertices. Let two connected graphs Gm and Gp have m and p vertices, minimum degree δ(Gm) and δ(Gp), edge-connectivity λ(Gm) and λ(Gp), respectively. This paper shows that min{pλ(Gm), λ(Gp) + δ(Gm), δ(Gm)(λ(Gp) + 1), (δ(Gm) + 1)λ(Gp)} ≤ λ(Gm * Gp) ≤ δ(Gm) + δ(Gp), where the product graph Gm * Gp of two given graphs Gm and Gp, defined by J. C. Bermond et al. [J. Combin. Theory B36 (1984) 32–48] in the context of the so-called (△, D)-problem, is one interesting model in the design of large reliable networks. Moreover, this paper determines λ′(Gm * Gp) ≤ min{pδ(Gm), ξ(Gp) + 2δ(Gm)} and λ′(G1 ⊕ G2) ≥ min{n, λ1 + λ2} if δ1 = δ2.
期刊：
Linear Algebra and its Applications,2010年433(8-10):1561-1572 ISSN：0024-3795
通讯作者：
Li, Shuchao
作者机构：
[Geng, Xianya; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Simic, Slobodan K.] SANU, Math Inst, Belgrade 11000, Serbia.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
期刊：
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS,2010年12(6):1069-1092 ISSN：0219-1997
通讯作者：
Li, Gongbao
作者机构：
[SHUANGJIE PENG; GONGBAO LI] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[SHUSEN YAN] Univ New England, Dept Math, Armidale, NSW 2351, Australia.
通讯机构：
[Li, Gongbao] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Infinitely many solutions;non-radial solutions;reduction argument;Schrödinger–Poisson system
摘要：
We consider the following nonlinear Schrodinger-Poisson system in R-3 {-Delta u + u + K(vertical bar y vertical bar)Phi(y)u = Q(vertical bar y vertical bar)vertical bar u vertical bar(p-1)u, y is an element of R-3, -Delta Phi= K(vertical bar y vertical bar)u(2), y is an element of R-3, (0.1) where K(r) and Q(r) are bounded and positive functions, 1 < p < 5. Assume that K(r) and Q(r) have the following expansions (as r -> +infinity): K(r) = a/r(m) + O (1/r(m+theta)), Q(r) = Q(0) + b/r(n) + O(1/r(n+kappa)), where a > 0, b is an element of R, m > 1/2, n > 1, theta > 0, kappa > 0, and Q(0) > 0 are some constants. We prove that (0.1) has infinitely many non-radial positive solutions if b < 0, or if b >= 0 and 2m < n.
作者机构：
[Feng, Yanqin; Hu, Xia] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.;[Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Clique;Cut edge;Randic connectivity index;Zagreb index
期刊：
LINEAR & MULTILINEAR ALGEBRA,2010年58(5):571-587 ISSN：0308-1087
通讯作者：
Li, Shuchao
作者机构：
[Geng, Xianya; Li, Shuchao] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Hu, Xia] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Laplacian matrix;Permanent;Tree
摘要：
Let G be a graph and L(G) be the Laplacian matrix of G. When G is a tree or a bipartite graph, Brualdi and Goldwasser [Permanent of the Laplacian matrix of trees and bipartite graphs, Discrete Math., 48 (1984), pp. 1-21] characterized the bounds for the permanent of L(G). In this article, as the continuance of it, we study the lower bounds for the permanent of L(G) when G is a tree. Here are some of our results: (1) Let J(n,k) be the collection of trees on n vertices with at most k pendent vertices and let J'(n,k) := {G is an element of J(n,k): there is a pendent vertex, say nu, in G such that G - nu is an element of J(n-1),(k-1)}. We determine the minimum permanent of L(G) for G in J'(n,k) and characterize the extremal graph. (2) Let F-n,F-Delta be the set of trees on n vertices with maximum degree Delta. We determine the first- and the second- minimal permanents of L(G) for G in F-n,F-Delta and characterize the extremal graphs. (3) Let G(n,m) be the collection of n-vertex trees each of which has an m-matching, where m >= 3. We determine the second- and the third-minimal permanents of L(G) for G in G(n,m) and characterize the extremal graphs.
作者机构：
[Tan, Liansheng; Zhu, Zhongxun] Cent China Normal Univ, Dept Comp Sci, Wuhan 430079, Peoples R China.;[Li, Shuchao] Cent China Normal Univ, Hubei Key Lab Math Sci, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Zhu, Zhongxun] S Central Univ Nationalities, Dept Comp Sci, Wuhan 430074, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Hubei Key Lab Math Sci, Fac Math & Stat, Wuhan 430079, Peoples R China.
作者：
Zhang, Xinan*;Zhao, Yingdong;Neumann, Avidan U.
期刊：
JOURNAL OF COMPUTATIONAL BIOLOGY,2010年17(12):1689-1696 ISSN：1066-5277
通讯作者：
Zhang, Xinan
作者机构：
[Zhang, Xinan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhao, Yingdong] NCI, Biometr Res Branch, Bethesda, MD 20892 USA.;[Neumann, Avidan U.] Bar Ilan Univ, Fac Life Sci, Ramat Gan, Israel.
通讯机构：
[Zhang, Xinan] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
chi-square test of goodness of fit;influenza type A;mathematical modeling
期刊：
Statistics & Probability Letters,2010年80(1):19-25 ISSN：0167-7152
通讯作者：
Qin, Hong
作者机构：
[Qin, Hong; Ou, Zujun] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Ou, Zujun] Jishou Univ, Coll Math & Comp Sci, Jishou 416000, Peoples R China.
通讯机构：
[Qin, Hong] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.
摘要：
The indicator function has been used to study the properties of factorial designs. This paper shows some applications of indicator functions in doubling design and uniformity pattern. Our results further provide that the indicator function is an effective tool in studying two-level factorial designs.
摘要：
We obtain an explicit description of the Wells map for the automorphism group of a group extension in the full generality and investigate the dependency of this map on group extensions. Some applications are given. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.
关键词：
Density-dependent;Vacuum;Existence of weak solutions;Asymptotic behavior of solutions
摘要：
This paper is concerned with existence of global weak solutions to a class of compressible Navier-Stokes equations with density-dependent viscosity and vacuum. When the viscosity coefficient mu is proportional to rho(0) with 1/2 < theta < max{3 - gamma, 3/2), a global existence result is obtained which improves the previous results in Fang and Zhang (2004) [4], Vong et al. (2003) [27], Yang and Zhu (2002) [30]. Here rho is the density. Moreover, we prove that the domain, where fluid is located on, expands outwards into vacuum at an algebraic rate as the time grows up due to the dispersion effect of total pressure. It is worth pointing out that our result covers the interesting case of the Saint-Venant model for shallow water (i.e., theta = 1, gamma = 2). (c) 2010 Elsevier Inc. All rights reserved.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2010年26(3):1055-1072 ISSN：1078-0947
通讯作者：
Peng, Shuangjie
作者机构：
[Peng, Shuangjie] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Zhou, Jing] S Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.
通讯机构：
[Peng, Shuangjie] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
关键词：
critical point;concentrating solutions.;variational method;Paneitz type problem
摘要：
By variational methods, we construct infinitely many concentration solutions for a type of Paneitz problem under the condition that the Paneitz curvature has a sequence of strictly local maximum points moving to infinity.
期刊：
Advances in Mathematics,2010年225(5):2741-2785 ISSN：0001-8708
通讯作者：
Cao, Daomin
作者机构：
[Daomin Cao] Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China.;[Shuangjie Peng] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Shusen Yan] Univ New England, Sch Math Stat & Comp Sci, Armidale, NSW 2351, Australia.
摘要：
Let Omega be a bounded domain in R(2), u(+) = u if u >= 0, u(+) = 0 if u < 0, u(-) = u(+) - u. In this paper we study the existence of solutions to the following problem arising in the study of a simple model of a confined plasma (P(lambda)) {Delta u - lambda u(-) = o, in Omega, u = c, on partial derivative Omega, integral partial derivative u/partial derivative nu ds = I, partial derivative Omega where nu is the outward unit normal of partial derivative Omega at x, c is a constant which is unprescribed, and I is a given positive constant. The set Omega(p) = {x is an element of Omega, u(x) < 0} is called plasma set. Existence of solutions whose plasma set consisting of one component and asymptotic behavior of plasma set were studied by Caffarelli and Friedman (1980) [3] for large lambda. Under the condition that the homology of Omega is nontrivial we obtain in this paper by a constructive way that for any given integer k >= 1, there is lambda(k) > 0 such that for lambda > lambda(k), (P(lambda)) has a solution with plasma set consisting of k components. (C) 2010 Elsevier Inc. All rights reserved.
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.
