期刊：
Applied Mathematics and Computation,2011年218(7):3649-3653 ISSN：0096-3003
通讯作者：
Liu, Yiliang
作者机构：
[Xiao, Cuie] Hunan City Univ, Dept Math, Yiyang 413000, Hunan, Peoples R China.;[Liu, Yiliang] Guangxi Univ Nationalities, Sch Math & Comp Sci, Nanning 530006, Guangxi, Peoples R China.;[Liu, Jinbo] Changsha Univ Sci & Technol, Dept Math, Changsha 410114, Hunan, Peoples R China.
通讯机构：
[Liu, Yiliang] G;Guangxi Univ Nationalities, Sch Math & Comp Sci, Nanning 530006, Guangxi, Peoples R China.
关键词：
Existence of quasisolutions;Integro-differential parabolic equations;Inverse problems;Porous media
摘要：
In this paper, we deal with an inverse source problem of integro-differential parabolic equations, which comes from nonlinear pollution problems in porous media. We study the existence and uniqueness of solutions for the direct problem as well as the existence of quasisolutions of the inverse source problem in an appropriate class of admissible source functions.
摘要：
The Merrifield-Simmons index of a graph G, denoted by i(G), is defined to be the total number of its independent sets, including the empty set. Let theta(a(1), a(2), ..., a(k)) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a(1), a(2), ..., a(k) respectively, we named it as multi-bridge graphs for convenience. Tight upper and lower bounds for the Merrifield-Simmons index of theta(a(1), a(2), ..., a(k)) are established in this paper.
摘要：
In this paper, we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation. The model consists of a system of the hemivariational inequality of hyperbolic type for the displacement, the time dependent elliptic equation for the electric potential. The contact is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form. The existence of a weak solution to the model is proved by embedding the problem into a class of second-order evolution inclusions and by applying a surjectivity result for multivalued operators.
关键词：
Root-square mean;arithmetic mean;Seiffert mean
摘要：
In this paper, we establish two new inequalities between the root-square, arithmetic, and Seiffert means. The achieved results are inspired by the paper of Seiffert (Die Wurzel, 29, 221-222, 1995), and the methods from Chu et al. (J. Math. Inequal., 4, 581-586, 2010). The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal. Mathematics Subject Classification (2010): 26E60.
摘要：
Let G is a connected graph with vertex set V, then the eccentric connectivity index of G is defined as Σ v∈V(G) deg(v)ecc(v) where deg(v) is the degree of a vertex v and ecc(v) is its eccentricity. The nanostar dendrimer is part of a new group of macromolecules that appear to be photon funnels just like artificial antennas. We obtain exact formulas for calculating the eccentric connectivity index of dendrimer nanostars.
期刊：
Ars Combinatoria,2011年101:353-358 ISSN：0381-7032
通讯作者：
Chen, Shubo
作者机构：
[Chen, Shubo] Hunan City Univ, Dept Math, Yiyang 413000, Hunan, Peoples R China.;[Liu, Weijun; Chen, Shubo] Cent S Univ, Coll Math, Changsha 410075, Hunan, Peoples R China.;[Yan, Fengming] Hunan Inst Humanities Sci & Technol, Loudi 417000, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Dept Math, Yiyang 413000, Hunan, Peoples R China.
摘要：
Let G = (V, E) be a simple connected graph, d(v) is the degree of vertex v. The zeroth-order Randic index of G is defined as R-alpha(0) (G) = Sigma(v epsilon V) d(v)(alpha), where alpha is an arbitrary real number. Let G* be the thorn v graph of G by attaching d(G)(v(i)) new pendent edges to each vertex v(i)(1 <= i <= n) of G. In this paper, we investigate the zeroth-order general Randic index of a class thorn tree and determine the extremal zeroth-order general Randic index of the thorn graphs G* (n, m).
摘要：
Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.
期刊：
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY,2011年66(3):825-836 ISSN：0340-6253
通讯作者：
Huang, Ziwen
作者机构：
[Huang, Ziwen; Wan, Xuegang] JiangXi BlueSky Univ, Dept Common Math & Phys, Nanchang 330098, Jiangxi, Peoples R China.;[Chen, Shubo] Hunan City Univ, Dept Math, Yiyang 413000, Hunan, Peoples R China.;[Deng, Hanyuan] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China.
通讯机构：
[Huang, Ziwen] J;JiangXi BlueSky Univ, Dept Common Math & Phys, Nanchang 330098, Jiangxi, Peoples R China.
摘要：
The Merrifield-Simmons index i(G) of a (molecular) graph G is defined as the total number of the independent sets of the graph, i.e., i(G) = Sigma(n)(k=0) i(G, k). In this paper, we characterize acyclic molecular graphs with the largest and second largest Merrifield-Simmons indices among all n-vertex acyclic molecular graphs with a given size matching.
期刊：
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS,2011年(41):1-11 ISSN：1417-3875
通讯作者：
Yang, Mingquan
作者机构：
[Long, Fei] Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.;[Yang, Mingquan] Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314001, Peoples R China.
通讯机构：
[Yang, Mingquan] J;Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314001, Peoples R China.
关键词：
Nicholson's blowflies model;positive periodic solutions;coincidence degree;existence and uniqueness;harvesting term
摘要：
This paper is concerned with a class of Nicholson's blowflies model with a linear harvesting term. By applying the method of coincidence degree, some criteria are established for the existence and uniqueness of positive periodic solutions of the model. Moreover, an example is employed to illustrate the main results.
期刊：
Journal of Computational and Theoretical Nanoscience,2011年8(4):656-658 ISSN：1546-1955
通讯作者：
Chen, Shubo
作者机构：
[Chen, Shubo] Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
关键词：
DENDRIMER;HOSOYA INDEX;MATCHING;NANOSTARS
摘要：
A dendrimer nanostar is a tree-like highly branched polymer molecule. Dendrimer nanostars are synthesized from monomers with new branches added in discrete steps to form a tree-like architecture. They have some proven applications, and numerous potential applications. Let G is a connected graph with vertex set V and edge set E, the Hosoya index of a graph is defined as the total number of its matchings. We obtain exact formulas for calculating the Hosoya index of dendrimer nanostars.
期刊：
Optoelectronics and Advanced Materials-Rapid Communications,2011年5(1-2):160-163 ISSN：1842-6573
通讯作者：
Hua, Hongbo
作者机构：
[Yang, Lihui] Hunan City Univ, Dept Math, Yiyang City 413000, Hunan, Peoples R China.;[Hua, Hongbo] Huaiyin Inst Technol, Fac Math & Phys, Huaian City 223003, Jiangsu, Peoples R China.
通讯机构：
[Hua, Hongbo] H;Huaiyin Inst Technol, Fac Math & Phys, Huaian City 223003, Jiangsu, Peoples R China.
关键词：
Dendrimer nanostar;Modified terminal wiener index;Terminal wiener index
摘要：
The terminal wiener index (TIN) of a tree T was defined recently by Gutman et al [1] as TW(T)= Sigma(e=uv is an element of E(T)) n(e;u)n(e;v), where n(e;u) is the number of pendent vetices in T lying closer to u than to v. In this paper, we first introduce a new topological index, named modified terminal wiener index (MTW), by extending the definition of terminal wiener index to any connected graph. Then we investigate the mathematical property of MTW and compute the MTW for a type of dendrimer nanostars.
摘要：
For a graph G = (V, E), the modified Schultz index of G is defined as S*(G)= Sigma({u, v} subset of V(G)) (d(G)(u) . d(G)(v))d(G)(u, v) where d(G)(u) (or d(u)) is the degree of the vertex u of G, and d(G)(u, v) is the distance between u and v. Let U(n) be the set of unicyclic graph with n vertices. In this paper, we study the modified Schultz index of U(n) by introducing some transformations. Unicyclic graphs with the maximum and minimum modified Schultz index are determined.
期刊：
Digest Journal of Nanomaterials and Biostructures,2011年6(2):717-723 ISSN：1842-3582
通讯作者：
Hua, Hongbo
作者机构：
[Yang, Lihui] Hunan City Univ, Dept Math, Yiyang City 413000, Hunan, Peoples R China.;[Wang, Maolin; Hua, Hongbo] Huaiyin Inst Technol, Fac Math & Phys, Huaian City 223003, Jiangsu, Peoples R China.
通讯机构：
[Hua, Hongbo] H;Huaiyin Inst Technol, Fac Math & Phys, Huaian City 223003, Jiangsu, Peoples R China.
摘要：
The Omega polynomial of a connected graph G, denoted by Ω(G,x), is defined as, and the Sadhana polynomial of G is defined as, where m(G, c) is the number of strips of length c and |E(G)| is the number of edges in G. In this paper, the Omega and Sadhana polynomials are computed for the pericondensed benzenoid graphs.
期刊：
Journal of Computational Analysis and Applications,2011年13(3):514-531 ISSN：1521-1398
通讯作者：
Liu, Zhenhai
作者机构：
[Liu, Guifang] Hunan City Univ, Dept Math, Yiyang 413000, Hunan, Peoples R China.;[Liu, Zhenhai; Han, Jiangfeng] Guangxi Univ Nationalities, Sch Math & Comp Sci, Nanning 530006, Guangxi, Peoples R China.;[Chen, Shiping] Hunan Univ Technol, Hunan Inst Technol, Zhuzhou 412008, Hunan, Peoples R China.
通讯机构：
[Liu, Zhenhai] G;Guangxi Univ Nationalities, Sch Math & Comp Sci, Nanning 530006, Guangxi, Peoples R China.
关键词：
boundary value problems;monotone iterative technique;upper and lower solutions;maximal and minimal solutions
摘要：
This paper is concerned with the existence and approximation of solutions for second order impulsive functional differential equations with boundary value conditions by monotone iterative technique. Sufficient conditions are obtained for the existence of extremal solutions.
