期刊：
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY,2008年59(1):171-190 ISSN：0340-6253
通讯作者：
Deng, Hanyuan
作者机构：
[Deng, Hanyuan] Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China.;[Chen, Shubo] Hunan City Univ, Dept Math, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Deng, Hanyuan] H;Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China.
摘要：
The Hosoya index and the Merrifield-Simmons index of a graph are defined as the total numbers of its matchings and its independent sets, respectively. In this paper, we characterize the unicyclic graphs with extremal Hosoya indices and Merrifield-Simmons indices, respectively.
期刊：
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY,2007年58(3):663-673 ISSN：0340-6253
通讯作者：
Chen, Shubo
作者机构：
[Chen, Shubo; Xia, Fangli] Hunan City Univ, Dept Math, Hunan 413000, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Dept Math, Hunan 413000, Peoples R China.
摘要：
For a graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M 2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. This paper investigates the Zagreb indices of unicyclic graphs by introducing some transformations, and characterize the unicyclic graphs with the first five largest Zagreb indices and the unicyclic graphs with the first two smallest Zagreb indices, respectively.
摘要：
In this paper, the authors show a relation between the generalized convexity and super- (sub-)multiplicative property, and discuss some generalized convexity and inequalities involving the Gaussian hypergeornetric function, the generalized eta-distortion function eta(a)(K)(x) and the generalized Grotzsch function mu(a)(r). (c) 2007 Elsevier Inc. All rights reserved.
期刊：
Applied Mathematics and Computation,2006年177(1):105-110 ISSN：0096-3003
通讯作者：
Li, Fan-Liang
作者机构：
[Li, Fan-Liang] Hunan City Coll, Dept Math & Computat Sci, Yi Yang 413000, Peoples R China.;Hunan Univ, Coll Math & Econometr, Changsha 410082, Peoples R China.
通讯机构：
[Li, Fan-Liang] H;Hunan City Coll, Dept Math & Computat Sci, Yi Yang 413000, Peoples R China.
关键词：
skew-centrosymmetric matrix;left and right inverse eigenvalue;optimal approximation;EIGENVALUE PROBLEMS
摘要：
The left and right inverse eigenvalue problem of skew-centrosymmetric matrices and its optimal approximation are considered. New necessary and sufficient conditions for the solvability of the problem are derived, the general expression of the solution is given. The optimal approximate solution and some numerical experiments are also provided.
作者机构：
[Song, YQ] Hunan City Univ, Dept Math & Calculat, Yiyang 413000, Peoples R China.;Univ Sci & Technol, Sch Sci, Nanjing 210094, Peoples R China.
通讯机构：
[Song, YQ] H;Hunan City Univ, Dept Math & Calculat, Yiyang 413000, Peoples R China.
关键词：
SBV_H function;Heisenberg group;minimiser;energy;deviation;free discontinuity problem
摘要：
The purpose of this paper is to prove existence of minimisers of the functional J(K, u) := integral(Omega\K) f(L-u)dx + alpha integral(Omega\K) vertical bar u - g vertical bar(q) dx + beta S-d(Q-1) (K boolean AND Omega), where Omega is an open set of the Heisenberg group H-n , K runs over all closed sets of H-n, u varies in C-H(1) (Omega \ K), alpha, beta > 0, q >= 1, g is an element of L-q (Omega) boolean AND L-infinity (Omega) and f : R-2n -> R is a convex function satisfying some structure conditions (H-1)(H-2)(H-3) (see below).
作者机构：
[Zhang, ZZ] Hunan City Univ, Dept Math, Yiyang, Peoples R China.;Cent S Univ, Sch Math Sci, Changsha, Peoples R China.;Hunan Univ, Fac Math & Econometr, Changsha, Peoples R China.
通讯机构：
[Zhang, ZZ] H;Hunan City Univ, Dept Math, Yiyang, Peoples R China.
期刊：
Journal of Mathematical Analysis and Applications,2003年287(1):296-306 ISSN：0022-247X
通讯作者：
Song, YQ
作者机构：
Hunan City Univ, Dept Math & Calc, Yiyang 413000, Hunan, Peoples R China.;Nanjing Univ Sci & Tech, Sch Sci, Nanjing 210094, Peoples R China.;[Song, YQ] Hunan City Univ, Dept Math & Calc, Zhaoyang Rd 4, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Song, YQ] H;Hunan City Univ, Dept Math & Calc, Zhaoyang Rd 4, Yiyang 413000, Hunan, Peoples R China.
关键词：
Bvh function;Heisenberg group;Decomposition of a radon measure;Chain rule;Compactness theorem;Perimeter;Spaces
摘要：
At first in the setting of the Heisenberg group we show the chain rule for a function u is an element of BVH (Omega) when composed with a Lipschitz function f : R --> R and prove that nu = f o u belongs to BV (H) (Omega) and D(H)nu much less than D(H)u. More precisely the following result is shown: D(H)nu = f' ((u) over tilde)del(H)uL(2n+1) + 2omega(2n-1)/omega(2n+1) (f(u(+)) - f(u(-)))nu(u)S(d)(Q-1) [J(u) + f' ((u) over tilde) D(H)(c)u. Secondly using the chain rule above we prove a compactness theorem for SBVH functions. (C) 2003 Elsevier Inc. All rights reserved. [References: 16]
摘要：
In this Letter, we study BAM (bidirectional associative memory) networks with variable coefficients. By some spectral theorems and a continuation theorem based on coincidence degree, we not only obtain some new sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution but also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Moreover, these conclusions are presented in terms of system parameters and can be easily verified for the globally Lipschitz and the spectral radius being less than 1. Therefore, our results should be useful in the design and applications of periodic oscillatory neural circuits for neural networks with delays. (C) 2003 Elsevier B.V. All rights reserved.
摘要：
In this paper, we establish new criteria for the oscillation/nonoscillation of solutions of the nonlinear difference equation of the form del (r(n) Phi (Delta y(n))) + q(n) Phi(y(n)) = R-n, where Phi :--> R is defined by Phi(s) = \s\(p-1)s, p > 0 a fixed real number, and a Hille-Wintner type comparison theorem is established. (C) 2000 Elsevier Science Ltd. All rights reserved.
摘要：
We obtain sufficient conditions for the oscillation of the perturbed difference equation Delta(a(n-1)(Delta gamma(n-1))(sigma)) + F(n,gamma(n)) = G(n,gamma(n), Delta gamma(n)), n greater than or equal to 1 as well as for the existence of monotone solutions of the nonlinear difference equation Delta(a(n-1)(Delta gamma(n-1))(sigma))+k(n)f(gamma(p(n))) = 0, n greater than or equal to 1, where 0 < sigma = p/q with p even and q odd integers, and some incorrect results in a recent paper are pointed out. Examples which illustrate the importance of our results are also included. (C) 2000 Elsevier Science Inc. All rights reserved. [References: 18]
摘要：
In this paper, we correct a result stated in a recent paper related to the oscillatory behavior of solutions of certain second order nonlinear differential equations.
