期刊：
Ars Combinatoria,2015年121:19-32 ISSN：0381-7032
通讯作者：
Chen, Shubo
作者机构：
[Chen, Shubo] Hunan City Univ, Coll Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.;Hunan First Normal Univ, Coll Math, Changsha 410205, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Coll Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
摘要：
Let G be a connected graph, the degree resistance distance of G is defined as Dr(G) = d{u) + d(v)]r(u,v), where d(u) (and (<,<}CV(G) d(v)) is the degree of the vertex u (and v), r(u,v) is the resistance distance between vertices u and v. A fully loaded unicyclic graph is a unicyclic graph with the property that there is no vertex with degree less than 3 in its unique cycle. In this paper, we determine the minimum and maximum degree resistance distance among all fully loaded unicyclic graphs with n vertices, and characterize the extremal graphs.
期刊：
JOURNAL OF MATHEMATICAL INEQUALITIES,2015年9(2):531-540 ISSN：1846-579X
通讯作者：
Qian, Wei-Mao
作者机构：
[Qian, Wei-Mao] Huzhou Broadcast & TV Univ, Sch Distance Educ, Huzhou 313000, Peoples R China.;[Shao, Zhi-Hua] Zhejiang Broadcast & TV Univ, Pinghu Coll, Pinghu 314200, Peoples R China.;[Chu, Yu-Ming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Qian, Wei-Mao] H;Huzhou Broadcast & TV Univ, Sch Distance Educ, Huzhou 313000, Peoples R China.
关键词：
Neuman means of the second kind;logarithmic mean;Seiffert mean;quadratic mean;Neuman-Sandor mean;contraharmonic mean
摘要：
In the article, we present several sharp inequalities involving the Neuman means of the second kind, and the logarithmic, Seiffert, arithmetic, Neuman-Sándor, quadratic and contraharmonic means.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2014年2014(1):1-6 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Qiu, Song-Liang; Zhang, Yan] Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, 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：
elliptic Neuman mean;Schur quadratically concave;quadratic mean
摘要：
For
and
, we prove that the elliptic Neuman mean
is strictly Schur quadratically concave on
if and only if
. As an application, the bounds for elliptic Neuman mean
in terms of the quadratic mean
are presented. MSC:26B25, 26E60.
期刊：
Abstract and Applied Analysis,2014年2014(2):1-5 ISSN：1085-3375
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Chu, YM] 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：
We prove that a homeomorphism f:R2→R2 is a quasiconformal mapping if and only if f(D) is an arcwise connected domain for any arcwise connected domain D⊆R2;and D is a quasidisk if and only if both D and its exterior D*=R2∖D¯ are arcwise connected domains. Published: 2014 First available in Project Euclid: 2 October 2014 zbMATH: 07022359 MathSciNet: MR3256246 Digital Object Identifier: 10.1155/2014/419850
摘要：
For x, y > 0, a, b is an element of R with a+ b not equal 0, the generalized Muirhead mean is defined by M( a, b; x, y) = (x(a)y(b) + x(b)y(a)/2) . In this paper, we prove that M( a, b; x, y) is Schur convex with respect to ( x, y) is an element of ( 0,infinity) x( 0,infinity) if and only if ( a, b) is an element of{( a, b)is an element of R-2 : ( a- b) (2) >= a+ b > 0& ab <= 0} and Schur concave with respect to ( x, y). ( 0,infinity) x( 0,infinity) if and only if ( a, b)is an element of{( a, b)is an element of R-2 + : ( a- b)(2) not equal a+ b & ( a, b) = ( 0,0)}.{( a, b). R2 : a+ b < 0}, where R+ : = [ 0,8)
摘要：
In this paper, we present a geometric interpretation of Blundon’s inequality and Ciamberlini’s inequality. Our results provide a useful method for proving the inequalities concerning sides, circumradius, and inradius of a triangle. As applications, some improved inequalities are established to illustrate the effectiveness of the proposed method. MSC: 26D15, 26D05.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2014年2014(1):1-13 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Qian, Wei-Mao] Huzhou Broadcast & TV Univ, Sch Distance Educ, Huzhou 313000, 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：
Schwab-Borchardt mean;Neuman mean;geometric mean;arithmetic mean;quadratic mean
摘要：
In this paper, we present sharp bounds for the two Neuman means
and
derived from the Schwab-Borchardt mean in terms of convex combinations of either the weighted arithmetic and geometric means or the weighted arithmetic and quadratic means, and the mean generated either by the geometric or by the quadratic mean. MSC:26E60.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2014年2014(1):1-14 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Wang, Hua] Changsha Univ Sci & Technol, Dept Math, Changsha 410077, Hunan, Peoples R China.;[Zhao, Tie-Hong] Hangzhou Normal Univ, Dept Math, Huangzhou 311121, 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：
Neuman mean;quadratic mean;second Seiffert mean
摘要：
In this paper, we prove that
and
are the best possible constants such that the double inequality
holds for all
with
, where
,
and
are the quadratic, Neuman and second Seiffert means of a and b, respectively. MSC:26E60.
摘要：
This paper is concerned with mean square exponential synchronization for a class of Markovian switching complex networks (MSCNs) with time-varying delay and stochastic noise under feedback control and M-matrix approach. Firstly, a class of MSCNs with time-varying delay and stochastic noise is considered. Secondly, by using M-matrix method and feedback control scheme, several sufficient conditions of mean square exponential synchronization are derived. At last, two numerical examples and simulations are given to illustrate the effectiveness of the theoretical results.
关键词：
Nonlocal source;The second critical exponent;Blow-up;Global
摘要：
This article considers the Cauchy problem for a semilinear nonlocal parabolic equation ut = Delta u + (f(R)n, K(y)u(q)(y,t)dy)p-(1/q) u(r+1) in Er x (0,T), where p, q >= 1, gamma >= 0 and p + gamma > 1. We study the second critical exponent, i.e. describing the critical smallness of initial data required by global solutions (non-global solutions) via the decay rates of the initial data at spatial infinity. Differently from other parabolic equations, the second critical exponent is related to n in this problem when K is not an element of L-1 (R-n). (C) 2014 Elsevier Inc. All rights reserved.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2014年2014(1):1-17 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Yang, Zhen-Hang] 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：
Wilker inequality;trigonometric function;hyperbolic function
摘要：
In this paper, we prove that the Wilker-type inequality
holds for any fixed
and all
if and only if
or
(
), and the hyperbolic version of Wilker-type inequality
holds for any fixed
(
) and all
if and only if
or
(
or
). As applications, several new analytic inequalities are presented. MSC:26D05, 33B10.
