期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2012年2012(1):1-6 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Shi, Hong-Xing] Chuxiong Normal Univ, Sch Primary Educ, Chuxiong 675000, Peoples R China.;[Long, Bo-Yong] Anhui Univ, Sch Math Sci, Hefei 230039, Peoples R China.;[Chu, Yu-Ming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Chu, Yu-Ming] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
generalized Heronian mean;logarithmic mean;power mean
摘要：
In this article, we establish a double inequality between the generalized Heronian and logarithmic means. The achieved result is inspired by the articles of Lin and Shi et al., and the methods from Janous. The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal. 2010 Mathematics Subject Classification: 26E60.
期刊：
Optoelectronics and Advanced Materials-Rapid Communications,2012年6(5-6):660-663 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.
摘要：
The Harmonic index of a graph G is defined as H(G) = Sigma(uv is an element of E(G)) 2/d(G)(u)+d(G)(v), where d(G)(v) is the degree of vertex v in G. In this paper, we first report some further mathematical properties of Harmonic index for general connected graphs. Then we give explicit computing formulae for Harmonic index of nanocones and triangular benzenoid graphs, respectively.
关键词：
Fully loaded unicyclic graph;Independent set;Merrifield-Simmons index
摘要：
It is well known that the graph invariant, the Merrifield-Simmons index is important in structural chemistry. 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. We characterize the n-vertex unicyclic graphs whose vertices on its unique cycle all have degree at least three with the first, the second and the third largest Merrifield-Simmons indices, respectively.
关键词：
Constructing a new Lyapunov functional and employing inequality technique;the existence;uniqueness;and global exponential stability of the periodic oscillatory solution are investigated for a class of fuzzy bidirectional associative memory (BAM) neural networks with distributed delays and diffusion. We obtained some sufficient conditions ensuring the existence;uniqueness;and global exponential stability of the periodic solution. The results remove the usual assumption that the activation functions are differentiable. An example is provided to show the effectiveness of our results. Published: 2012 First available in Project Euclid: 14 December 2012 zbMATH: 1235.93150 Digital Object Identifier: 10.1155/2012/136048
摘要：
Constructing a new Lyapunov functional and employing inequality technique, the existence, uniqueness, and global exponential stability of the periodic oscillatory solution are investigated for a class of fuzzy bidirectional associative memory (BAM) neural networks with distributed delays and diffusion. We obtained some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution. The results remove the usual assumption that the activation functions are differentiable. An example is provided to show the effectiveness of our results.
期刊：
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY,2012年38(3):597-606 ISSN：1017-060X
通讯作者：
Chu, Y. M.
作者机构：
[Chu, Y. M.] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Hunan, Peoples R China.;[Shi, M. Y.] Heibei Univ, Coll Math & Comp Sci, Baoding 071002, Hebei, Peoples R China.;[Jiang, Y. P.] Hunan Univ, Sch Math & Econometr, Changsha 410082, Hunan, Peoples R China.
通讯机构：
[Chu, Y. M.] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Hunan, Peoples R China.
关键词：
Harmonic mean;Logarithmic mean;Power mean
摘要：
For all a, b > 0, the following two optimal inequalities are presented: H-alpha(a, b)L1-alpha (a, b) >= M1-4 alpha/3 (a, b) for alpha is an element of [1/4, 1), and H-alpha (a, b)L1-alpha (a, b) <= M1-4 alpha/3 (a, b) for alpha is an element of (0, 3 root 5-5/40]. Here, H(a, b), L(a, b), and M-p(a, b) denote the harmonic, logarithmic, and power means of order p of two positive numbers a and b, respectively.
关键词：
We present the best possible power mean bounds for the product M p α ( a;b ) M - p 1 - α ( a;b ) for any p > 0;and all a;b > 0 with a ≠ b . Here;M p ( a;b ) is the p th power mean of two positive numbers a and b . Published: 2012 First available in Project Euclid: 14 December 2012 zbMATH: 1244.26044 MathSciNet: MR2910901 Digital Object Identifier: 10.1155/2012/182905
摘要：
We present the best possible power mean bounds for the product M-p(alpha)(a, b)M--p(1-alpha) (a, b) for any p > 0, alpha is an element of (0, 1), and all a, b > 0 with a not equal b. Here, M-p (a, b) is the pth power mean of two positive numbers a and b.
期刊：
Abstract and Applied Analysis,2012年2012(SI01):1-24 ISSN：1085-3375
通讯作者：
Chu, Yu-Ming
作者机构：
[Cheng, Jin-Fa] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China.;[Chu, Yu-Ming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Chu, Yu-Ming] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Hunan, Peoples R China.
关键词：
We independently propose a new kind of the definition of fractional difference;fractional sum;and fractional difference equation;give some basic properties of fractional difference and fractional sum;and give some examples to demonstrate several methods of how to solve certain fractional difference equations. Published: 2012 First available in Project Euclid: 7 May 2014 zbMATH: 1259.39010 MathSciNet: MR3004928 Digital Object Identifier: 10.1155/2012/918529
作者机构：
[Chu Yuming] Hunan City Univ, Dept Math, Yiyang 413000, Peoples R China.;[Wang Miaokun] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.;[Wang Gendi] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China.
通讯机构：
[Chu Yuming] H;Hunan City Univ, Dept Math, Yiyang 413000, Peoples R China.
关键词：
generalized logarithmic mean;Seiffert’s mean;power mean
摘要：
For p ∈ R, the generalized logarithmic mean L p (a, b) and Seiffert’s mean T (a, b) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p and least q such that the double-inequality L p (a, b) < T (a, b) < L q (a, b) holds for all a, b > 0 and a ≠b.
关键词：
Neuman-Sandor mean;generalized logarithmic mean;power mean;Seiffert mean
摘要：
In this paper, we find the largest value alpha and least value beta such that the double inequality L-alpha(a,b) < M(a,b) < L-beta(a,b) holds for all a,b > 0 with a not equal b. Here, M(a,b) and L-p(a,b) are the Neuman-Sandor and p-th generalized logarithmic means of a and b, respectively.
摘要：
In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation x(n+1) = Ax(n) + x(n-1)/B + x(n-1), n = 0, 0, ..., where (x(n)) is a sequence of positive fuzzy number, A, B are positive fuzzy numbers and the initial conditions x(-1), x(0) are positive fuzzy numbers.
期刊：
Ars Combinatoria,2012年107:17-32 ISSN：0381-7032
通讯作者：
Deng, Hanyuan
作者机构：
[Huang, Ziwen] JiangXi BlueSky Univ, Dept Math & Phys, Nanchang 330098, Jiangxi, Peoples R China.;[Deng, Hanyuan] Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China.;[Chen, Shubo] Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Deng, Hanyuan] H;Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China.
关键词：
Cactus;Perfect matching;Randić index
摘要：
The Randic index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))-1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. In this paper, we give a sharp lower bound on the Randie index of cacti with perfect matchings.
摘要：
We find the greatest value α
1 and α
2, and the least values β
1 and β
2, such that the double inequalities α
1
S(a,b) + (1 − α
1) A(a,b) < T(a,b) < β
1
S(a,b) + (1 − β
1) A(a,b) and
$S^{\alpha_{2}}(a,b)A^{1-\alpha_{2}}(a,b)< T(a,b)< S^{\beta_{2}}(a,b)A^{1-\beta_{2}}(a,b)$
hold for all a,b > 0 with a ≠ b. As applications, we get two new bounds for the complete elliptic integral of the second kind in terms of elementary functions. Here, S(a,b) = [(a
2 + b
2)/2]1/2, A(a,b) = (a + b)/2, and
$T(a,b)=\frac{2}{\pi}\int\limits_{0}^{{\pi}/{2}}\sqrt{a^2{\cos^2{\theta}}+b^2{\sin^2{\theta}}}{\rm d}\theta$
denote the root-square, arithmetic, and Toader means of two positive numbers a and b, respectively.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2012年2012(1):1-6 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming] Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Peoples R China.;[Hou, Shou-Wei; Shen, Zhong-Hua] Hangzhou Normal Univ, Dept Math, Hangzhou 310012, Zhejiang, Peoples R China.
通讯机构：
[Chu, Yu-Ming] H;Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Peoples R China.
关键词：
Seiffert mean;root mean square;power mean;inequality
摘要：
We find the greatest value α and least value β in (1/ 2,1) such that the double inequality
holds for all a,b > 0 with a ≠ b. Here, T(a, b) = (a-b)/[2 arctan((a-b)/(a + b))] and S(a, b) = [(a2 + b2)/2]1/ 2are the Seiffert mean and root mean square of a and b, respectively. 2010 Mathematics Subject Classification: 26E60.
