摘要：
For a nontrivial graph G, its first and second Zagreb coindices are defined as the sum of degree sum of of nonadjacent vertex pairs and the sum of degree product of nonadjacent vertices pairs, respectively. Motivated by the work in [1], we study Zagreb coindices of a new kind of composite graph, namely, double graph. For any given nontrivial graph, explicit formulas are given for the Zagreb coindices of its double graph and k-iterated double graph, respectively.
摘要：
In this paper, sharp bounds for cyclic sums of the ratio of the exradius to the sides of a triangle are established depending on the circumradius and inradius of the triangle. The best possible parameters for the expressions of bounds are derived. Moreover, an alternative bound for the ratio of the exradius to the sides of triangle, expressed by trigonometric functions, is also considered.
期刊：
Ars Combinatoria,2015年122:79-88 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.;[Liu, Weijun] Cent S Univ, Coll Math, Changsha 410075, 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：
For a graph G = (V, E), the Schultz index of G is defined as {equation presented} where dG{u) (or d(u)) is {equation presented} the degree of the vertex u in G, and do{u, v) is the distance between u and v in G. In this paper, we investigate the Schultz index of tricyclic graphs. The n-tricyclic graphs with the minimum Schultz index are determined.
期刊：
JOURNAL OF MATHEMATICAL INEQUALITIES,2015年9(2):331-343 ISSN：1846-579X
通讯作者：
Yang, Zhen-Hang
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：
[Yang, Zhen-Hang] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
Exponential-geometric mean;First Seiffert mean;Identric mean;Logarithmic mean;Neuman-Sándor mean;Power-exponential mean
摘要：
Let p is an element of R, M be a bivariate mean, and M-p be defined by M-p(a, b) = M-1/p(a(p), b(p)) (p not equal 0) and M-0(a, b) = lim(p -> 0)M(p)(a, b). In this paper, we prove that the sharp inequalities L-2(a, b) < P(a, b) < NS1/2(a, b) < He(a, b) < A(2/3)(a, b) < I(a, b) < Z(1/3)(a, b) < Y-1/2(a, b) hold for all a, b > 0 with a not equal b, where L(a, b) = (a- b)/(loga - logb), P(a, b) = (a - b)/[2arcsin((a- b)/(a + b))], NS(a, b) =(a- b)/[2arcsinh ((a- b)/(a + b))], He(a, b) =(a + root ab+ b)/3, A(a, b) = (a + b)/2, I(a, b) = 1/e(a(a)/b(b))(1/)((a-b)), Z(a, b) = a(a/(a+b)) b(b/(a+b)) and Y(a, b) = I(a, b) e(1-ab/L2(a, b)) are respectively the logarithmic, first Seiffert, Neuman-Sandor, Heronian, arithmetic, identric, power-exponential and exponential-geometric means of a and b.
期刊：
Journal of Function Spaces,2015年2015 ISSN：2314-8896
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.
摘要：
We present the best possible parameters p, q is an element of (0, infinity) such that the double inequality (1/3 P-2) cosh(px) + 1 - 1/3p(2) < sinh(x)/x < (1/3q(2)) cosh(qx) + 1 - 1/3q(2) 2 holds for all x is an element of (0, infinity). As applications, some new inequalities for certain special function and bivariate means are found.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2015年2015(1):1-9 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Li, Jun-Feng] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Qian, Wei-Mao] Huzhou Broadcast & TV Univ, Sch Distance Educ, Huzhou 313000, 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：
Toader mean;arithmetic mean;quadratic mean;Neuman mean
摘要：
In this paper, we present the best possible parameters
$\alpha, \beta \in\mathbb{R}$
and
$\lambda, \mu\in(1/2, 1)$
such that the double inequalities
$\alpha N_{AQ}(a,b)+(1-\alpha)A(a,b)< T^{\ast}(a,b)<\beta N_{AQ}(a,b)+(1-\beta)A(a,b)$
,
$Q[\lambda a+(1-\lambda)b, \lambda b+(1-\lambda)a]< T^{\ast}(a,b)< Q[\mu a+(1-\mu)b, \mu b+(1-\mu)a] $
hold for all
$a, b>0$
with
$a\neq b$
, where
$T^{\ast}(a,b)$
,
$A(a,b)$
,
$Q(a,b)$
and
$N_{QA}(a,b)$
are the Toader, arithmetic, quadratic, and Neuman means of a and b, respectively.
摘要：
Strictly Schur convexity, Schur multiplicative convexity and Schur harmonic convexity are investigated for the elliptic Neuman mean. As applications, several sharp bounds for the arithmetic, geometric and harmonic means in terms of the elliptic Neuman mean are presented.
期刊：
Journal of Mathematical Analysis and Applications,2015年427(2):646-668 ISSN：0022-247X
通讯作者：
Han, Jiangfeng
作者机构：
[Han, Jiangfeng; Migorski, Stanislaw] Jagiellonian Univ, Inst Comp Sci, Fac Math & Comp Sci, PL-30348 Krakow, Poland.;[Li, Yunxiang] Hunan City Univ, Dept Math, Yiyang 413000, Hunan, Peoples R China.;[Han, Jiangfeng] Jagiellonian Univ, Inst Comp Sci, Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland.
通讯机构：
[Han, Jiangfeng] J;Jagiellonian Univ, Inst Comp Sci, Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland.
关键词：
Variational-hemivariational inequality;Clarke subdifferential;Existence and uniqueness;Viscoelastic materials;Quasistatic;Fixed point theorem
摘要：
The goal of this paper is to study a mathematical model which describes the adhesive contact between a deformable body and a foundation. The body consists of a viscoelastic material with long memory and the process is assumed to be quasistatic. The adhesive contact condition on the normal plane is modeled by a version of normal compliance condition with unilateral constraint in which adhesion is taken into account, the adhesive contact condition on the tangential plane is described by an adhesive Clarke subdifferential condition, and the evolution of the bonding field is described by an ordinary differential equation. We derive the variational formulation of this problem which is a system of a variational-hemivariational inequality for the displacement field and an ordinary differential equation for the bonding field. Then, we obtain existence and uniqueness results on abstract inclusions and abstract variational-hemivariational inequalities. Finally, we apply the abstract results to prove the existence of a unique weak solution to the contact problem. (C) 2015 Elsevier Inc. All rights reserved.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2015年2015(1):1-10 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Zhou, Shuang-Shuang; Zhang, Xiao-Hui] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Qian, Wei-Mao] Huzhou Broadcast & TV Univ, Sch Distance Educ, Huzhou 313000, 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：
power-type Heronian mean;Sandor mean;Yang mean
摘要：
We prove that the double inequalities
$H_{\alpha}(a, b) < X(a, b)<H_{\beta}(a, b)$
and
$H_{\lambda}(a, b)< U(a, b)<H_{\mu}(a, b)$
hold for all
$a, b>0$
with
$a\neq b$
if and only if
$\alpha\leq1/2$
,
$\beta\geq\log3/(1+\log2)=0.6488\cdots$
,
$\lambda\leq2\log3/(2\log\pi-\log2) =1.3764\cdots$
, and
$\mu\geq2$
, where
$H_{p}(a, b)$
,
$X(a, b)$
, and
$U(a, b)$
are, respectively, the pth power-type Heronian mean, Sándor mean, and Yang mean of a and b.
作者机构：
[Zhou, Shuangshuang] Hunan City Univ, Sch Math & Computat Sci, Yiyang, Peoples R China.;[Zheng, Sining; Zhou, Shuangshuang] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.
通讯机构：
[Zheng, Sining] D;Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.
关键词：
degenerate parabolic equation;global solution;gradient term;large time behavior
摘要：
In this paper, we investigate positive solutions of the degenerate parabolic equation not in divergence form: ut = u(p) Delta u + u(q) |del u|(2) - u(r), subject to null Dirichlet boundary condition. We study the existence of global solutions and the large time behavior for them. The main effort is paid to obtain uniform asymptotic profiles for decay solutions, under various dominations of the nonlinear diffusion or absorption. It is shown that the large time property of the solution u behaves just like (1+(r-1)t)(-1/r- 1) if the decay is governed by the nonlinear absorption with 1 < r < p+1. Otherwise, the asymptotic profiles would possess the form of (1 + pt)W-1/p, with W solving various homogeneous Dirichlet elliptic equations: (i) -Delta W = W1-p - W if r = p + 1 < q + 2; (ii) -Delta W = W1-p - W + W-1 |del W|(2) if r > p + 1 = q + 2; and (iii) -Delta W = W1-p if r, q + 2 > p + 1.
期刊：
Journal of Mathematical Analysis and Applications,2015年428(1):587-604 ISSN：0022-247X
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.;[Wang, Miao-Kun] Huzhou Univ, Dept Math, Huzhou 813000, 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：
Quotient of power series;Piecewise monotonicity;Hypergeometric function;Leaden inequality
摘要：
In this paper, we present the necessary and sufficient condition for the monotonicity of the quotient of power series. As applications, some gaps and misquotations in certain published articles are pointed out and corrected, and some known results involving the Landen inequalities for zero-balanced hypergeometric functions are Improved. (C) 2015 Elsevier Inc. All rights reserved.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2015年2015(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.;[Zhao, Tie-Hong] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, 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：
complete elliptic integral;generalized convexity;Lehmer mean
摘要：
In this paper, the authors present necessary and sufficient conditions for the complete elliptic integrals of the first and second kind to be convex or concave with respect to the Lehmer mean.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2015年2015(1):1-19 ISSN：1029-242X
通讯作者：
Yang, Zhen-Hang
作者机构：
[Yang, Zhen-Hang] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Chu, Yu-Ming] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China.
通讯机构：
[Yang, Zhen-Hang] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
Cusa type inequality;Lazarević inequality;Schwab-Borchardt mean;hyperbolic function
摘要：
In the article, we establish several Lazarević and Cusa type inequalities involving the hyperbolic sine and cosine functions with two parameters. As applications, we find some new bounds for certain bivariate means. MSC: 26D05, 26D07, 33B10, 26E60.
期刊：
Ars Combinatoria,2015年122:379-397 ISSN：0381-7032
通讯作者：
Chen, Shubo
作者机构：
[Chen, Shubo] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.;[Liu, Weijun; Chen, Shubo] Cent South Univ, Coll Math & Stat, Changsha 410075, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
摘要：
For a graph G = (V, E), the modified Schultz index of G is defined as S∗(G) = σ (dG(u).dG(v))dG(u, v) where dG{u) (or d(u)) is {u,u}CV(G) the degree of the vertex u in G, and dG(u, v) is the distance between u and v. The first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. In this paper, we present a unified approach to investigate the modified Schultz index and Zagreb indices of tricyclicgraphs. The tricyclic graph with n vertices having minimum modified Schultz index and maximum Zagreb indicesare determined.
摘要：
This article concerns with a class of evolutionary hemivariational inequalities in the framework of evolution triple. Based on the Rothe method, monotonicity-compactness technique and the properties of Clarke's generalized derivative and gradient, the existence and convergence theorems to these problems are established. The main idea in the proof is using the time difference to construct the approximate problems. The work generalizes the existence results on evolution inclusions and hemivariational inequalities of second order.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2015年2015(1):1-11 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：
logarithmic mean;Yang mean;first Seiffert mean;Neuman-Sandor mean;Sandor-Yang mean
摘要：
In this paper, we present the sharp bounds of the ratios
$U(a,b)/L_{4}(a,b)$
,
$P_{2}(a,b)/U(a,b)$
,
$NS(a,b)/P_{2}(a,b)$
and
$B(a,b)/NS(a,b)$
for all
$a, b>0$
with
$a\neq b$
, where
$L_{4}(a,b)=[(b^{4}-a^{4})/(4(\log b-\log a))]^{1/4}$
,
$U(a,b)=(b-a)/[\sqrt{2}\arctan((b-a)/\sqrt{2ab})]$
,
$P_{2}(a,b)=[(b^{2}-a^{2})/(2\arcsin ((b^{2}-a^{2})/(b^{2}+a^{2})))]^{1/2}$
,
$NS(a,b)=(b-a)/[2\sinh ^{-1}((b-a)/(b+a))]$
,
$B(a,b)=Q(a,b)e^{A(a,b)/T(a,b)-1}$
,
$A(a,b)=(a+b)/2$
,
$Q(a,b)=\sqrt{(a^{2}+b^{2})/2}$
, and
$T(a,b)=(a-b)/[2\arctan((a-b)/(a+b))]$
.
