期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2016年2016(1):1-9 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Yang, Zhen-Hang; Li, Jun-Feng] 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：
power mean;second Yang mean;arithmetic mean;quadratic mean;geometric mean;Lehmer mean;first Seiffert mean;logarithmic mean
摘要：
In this paper, we present the best possible parameters p and q such that the double inequality
$$ M_{p}(a,b)< V(a,b)< M_{q}(a,b) $$
holds for all
$a, b>0$
with
$a\neq b$
, where
$M_{r}(a,b)=[(a^{r}+b^{r})/2]^{1/r}$
(
$r\neq0$
) and
$M_{0}(a,b)= \sqrt {ab}$
is the rth power mean and
$V(a,b)=(a-b)/[\sqrt{2}\sinh^{-1}((a-b)/\sqrt{2ab})]$
is the second Yang mean.
期刊：
Journal of Combinatorial Optimization,2016年31(1):327-332 ISSN：1382-6905
通讯作者：
Chen, Shubo
作者机构：
[Chen, Shubo] Hunan City Univ, Coll Math, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Coll Math, Yiyang 413000, Hunan, Peoples R China.
关键词：
Gutman index;Degree distance;Extremal graph
摘要：
The Gutman index (also known as Schultz index of the second kind) of a graph
$$G$$
is defined as
$$Gut(G)=\sum \nolimits _{u,v\in V(G)}d(u)d(v)d(u, v)$$
. A graph
$$G$$
is called a cactus if each block of
$$G$$
is either an edge or a cycle. Denote by
$$\mathcal {C}(n, k)$$
the set of connected cacti possessing
$$n$$
vertices and
$$k$$
cycles. In this paper, we give the first three smallest Gutman indices among graphs in
$$\mathcal {C}(n, k)$$
, the corresponding extremal graphs are characterized as well.
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：
Arithmetic mean;Power mean;Quadratic mean;Seiffert mean;Śandor-Yang mean
摘要：
In this paper, we prove that the double inequality $M_{p}(a,b)<B(a,b)<M_{q}(a,b)% holds for all $a, b>0$ with $a\neq b$ if and only if $p\leq 4\log 2/(4+2\log 2-\pi)=1.2351\cdots$ and $q\geq 4/3$, where $% M_{r}(a,b)=[(a^{r}+b^{r})/2]^{1/r}$ $(r\neq 0)$ and $M_{0}(a,b)=\sqrt{ab}$ is the $r$th power mean, $B(a,b)=Q(a,b)e^{A(a,b)/T(a,b)-1}$ is the S\'{a}% ndor-Yang mean, $A(a,b)=(a+b)/2$, $Q(a,b)=\sqrt{(a^{2}+b^{2})/2}$ and $% T(a,b)=(a-b)/[2\arctan((a-b)/(a+b))]$.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2016年2016(1):1-10 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.;[Yang, Zhen-Hang] State Grid Zhejiang Elect Power Res Inst, Customer Serv Ctr, Hangzhou 310009, Zhejiang, 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：
In this paper, we present the monotonicity and absolute monotonicity properties for the two-parameter hyperbolic and trigonometric functions. As applications, we find several complete monotonicity properties for the functions involving the gamma function and provide the bounds for the error function.
摘要：
Considering the lack of the research on the relationship between HR flexibility and scheduling effect, a resource-competency matrix-based method was proposed in order to reveal the quantitative relationship between them. Meanwhile, a job shop scheduling model with HR flexibility was established and the improved genetic algorithm was used to solve the model. A case analysis demonstrated significant impact of HR flexibility on the scheduling effect, which provided valuable guidance for building flexible manufacturing systems.
期刊：
Journal of Mathematical Analysis and Applications,2016年438(2):875-888 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.;[Zhang, Wen] Yeshiva Univ, Albert Einstein Coll Med, New York, NY 10033 USA.
通讯机构：
[Chu, Yu-Ming] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
Gaussian hypergeometric function;Complete elliptic integral;Stolarsky mean
摘要：
In this paper, we prove that the double inequality
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2016年2016(1):1-9 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Sun, Hui] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Yang, Zhen-Hang] State Grid Zhejiang Elect Power Res Inst, Dept Sci & Technol, Hangzhou 310009, 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：
Wilker-type inequality;sine function;tangent function;necessary and sufficient condition
摘要：
In the article, we provide the necessary and sufficient conditions for the parameters α and β such that the generalized Wilker-type inequality
$$ \frac{2\beta}{\alpha+2\beta} \biggl(\frac{\sin x}{x} \biggr)^{\alpha}+ \frac{\alpha}{\alpha+2\beta} \biggl(\frac{\tan x}{x} \biggr)^{\beta}-1>(< )0 $$
holds for all
$x\in(0, \pi/2)$
.
期刊：
Ars Combinatoria,2016年127:315-327 ISSN：0381-7032
通讯作者：
Chen, Shubo
作者机构：
[Yang, Jianguang; Chen, Shubo] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, 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：
The resistance distance between two vertices of a connected graph G is defined as the effective resistance between them in the corresponding electrical network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index of K f(G) is the sum of resistance distances between all pairs of vertices of the graph G. In this paper, we'll determine the tricyclic graphs with the smallest and the second smallest Kirchhoff indices.
期刊：
Journal of Function Spaces,2016年2016:1-7 ISSN：2314-8896
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Song, Ying-Qing] 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.
摘要：
We present the best possible parameters α 1 , α 2 , β 1 , β 2 ∈ R and α 3 , β 3 ∈ ( 1 / 2,1 ) such that the double inequalities α 1 A ( a , b ) + ( 1 - α 1 ) C ( a , b ) < N Q A ( a , b ) < β 1 A ( a , b ) + ( 1 - β 1 ) C ( a , b ) , A α 2 ( a , b ) C 1 - α 2 ( a , b ) < N Q A ( a , b ) < A β 2 ( a , b ) C 1 - β 2 ( a , b ) , and C [ α 3 a + ( 1 - α 3 ) b , α 3 b + ( 1 - α 3 ) a ] < N Q A ( a , b ) < C [ β 3 a + ( 1 - β 3 ) b , β 3 b + ( 1 - β 3 ) a ] hold for all a , b > 0 with a ≠ b and give several sharp inequalities involving the hyperbolic and inverse hyperbolic functions. Here, N ( a , b ) , A ( a , b ) , Q ( a , b ) , and C ( a , b ) are, respectively, the Neuman, arithmetic, quadratic, and centroidal means of a and b , and N Q A ( a , b ) = N [ Q ( a , b ) , A ( a , b ) ] .
期刊：
Advances in Difference Equations,2016年2016(1):1-18 ISSN：1687-1847
通讯作者：
Liu, Xin-Ge
作者机构：
[Liu, Xin-Ge; Shu, Yan-Jun; Qiu, Sai-Bing] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.;[Qiu, Sai-Bing] Hunan City Univ, Coll Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Liu, Xin-Ge] C;Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.
关键词：
state estimation;discrete-time;leakage delay;stability
摘要：
We investigate state estimation for a class of discrete-time recurrent neural networks with leakage delay and time-varying delay. The design method for the state estimator to estimate the neuron states through available output measurements is given. A novel delay-dependent sufficient condition is obtained for the existence of state estimator such that the estimation error system is globally asymptotically stable. Based a novel double summation inequality and reciprocally convex approach, an improved stability criterion is obtained for the error-state system. Two numerical examples are given to demonstrate the effectiveness of the proposed design methods. The simulation results show that the leakage delay has a destabilizing influence on a neural network system.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2016年2016(1):1-10 ISSN：1029-242X
通讯作者：
Zhao, Tie-Hong
作者机构：
[Zhao, Tie-Hong] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China.;[Qian, Wei-Mao] Huzhou Broadcast & TV Univ, Sch Distance Educ, Huzhou 313000, Peoples R China.;[Song, Ying-Qing] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Zhao, Tie-Hong] H;Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China.
关键词：
Schwab-Borchardt mean;arithmetic mean;quadratic mean;Neuman-Sandor mean;second Seiffert mean;Sandor-type mean;power mean
摘要：
In the article, we prove that the double inequalities
$M_{\alpha }(a,b)< S_{QA}(a,b)< M_{\beta}(a,b)$
and
$M_{\lambda }(a,b)< S_{AQ}(a,b)< M_{\mu}(a,b)$
hold for all
$a, b>0$
with
$a\neq b$
if and only if
$\alpha\leq\log 2/[1+\log2-\sqrt{2}\log(1+\sqrt{2})]=1.5517\ldots$
,
$\beta\geq5/3$
,
$\lambda\leq4\log2/[4+2\log2-\pi]=1.2351\ldots$
and
$\mu\geq4/3$
, where
$S_{QA}(a,b)=A(a,b)e^{Q(a,b)/M(a,b)-1}$
and
$S_{AQ}(a,b)=Q(a,b)e^{A(a,b)/T(a,b)-1}$
are the Sándor-type means,
$A(a,b)=(a+b)/2$
,
$Q(a,b)=\sqrt{(a^{2}+b^{2})/2}$
,
$T(a,b)=(a-b)/[2\arctan((a-b)/(a+b))]$
, and
$M(a,b)=(a-b)/[2\sinh ^{-1}((a-b)/(a+b))]$
are, respectively, the arithmetic, quadratic, second Seiffert, and Neuman-Sándor means.
关键词：
Toader mean;arithmetic mean;quadratic mean;contraharmonic mean;complete elliptic integral
摘要：
In this paper, we present the best possible Toader mean bounds of arithmetic and quadratic means by the one-parameter quadratic and contraharmonic means. As applications in engineering and technology, we find new bounds for the complete elliptic integral of the second kind. (C) 2016 All rights reserved.
作者机构：
[Chu, Yu-Ming; Song, Ying-Qing; Yang, ZH; Chu, YM; Song, YQ; Yang, Zhen-Hang] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Yang, ZH; Chu, YM; Song, YQ] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
Toader-Qi mean;logarithmic mean;identric mean;modified Bessel function
摘要：
In the article, we prove that the double inequality lambda root L(a,b)I(a,b) < TQ(a,b) < mu root L(a,b)I(a,b) holds for all a,b > 0 with a not equal b if and only if lambda <= root e/pi and mu >= 1, and give an affirmative answer to the conjecture proposed by Yang in [39], where L(a,b) = (b-a)/(logb-loga), I(a,b) = (b(b)/a(a))(1/(b-a))/e and TQ(a,b) = 2/pi integral(pi/2)(0) a(cos2 theta)b(sin2 theta) d theta are respectively the logarithmic, identric and Toader-Qi means of a and b.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2016年2016(1):1-10 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.;[Yang, Zhen-Hang] State Grid Zhejiang Elect Power Res Inst, Customer Serv Ctr, Hangzhou 310009, Zhejiang, Peoples R China.;[Zhang, Wen] Yeshiva Univ, Albert Einstein Coll Med, New York, NY 10033 USA.
通讯机构：
[Chu, Yu-Ming] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
incomplete gamma function;gamma function;psi function
摘要：
In the article, we deal with the monotonicity of the function
$x\rightarrow[ (x^{p}+a )^{1/p}-x]/I_{p}(x)$
on the interval
$(0, \infty)$
for
$p>1$
and
$a>0$
, and present the necessary and sufficient condition such that the double inequality
$[ (x^{p}+a )^{1/p}-x]/a< I_{p}(x)<[ (x^{p}+b )^{1/p}-x]/b$
for all
$x>0$
and
$p>1$
, where
$I_{p}(x)=e^{x^{p}}\int_{x}^{\infty}e^{-t^{p}}\,dt$
is the incomplete gamma function.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2016年2016(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.;[Yang, Zhen-Hang] State Grid Zhejiang Elect Power Res Inst, Customer Serv Ctr, Hangzhou 310009, 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：
error function;monotonicity;bound
摘要：
In the article, we present the necessary and sufficient condition for the parameter p on the interval
$(7/5, \infty)$
such that the function
$x\rightarrow\operatorname{erf}(x)/B_{p}(x)$
is strictly increasing (decreasing) on
$(0, \infty)$
, and find the best possible parameters p, q on the interval
$(7/5, \infty)$
such that the double inequality
$B_{p}(x)<\operatorname{erf}(x)<B_{q}(x)$
holds for all
$x>0$
, where
$\operatorname{erf}(x)=2\int_{0}^{x}e^{-t^{2}}\,dt/\sqrt{\pi}$
is the error function,
$B_{p}(x)=\sqrt{1-\lambda(p)e^{-px^{2}}-[1-\lambda(p)]e^{-\mu(p)x^{2}}}$
,
$\lambda(p)=16(5p-7)/[(15p^{2}-40p+28)(45p^{2}-60p-4)]$
and
$\mu(p)=4(5p-7)/[5(3p-4)]$
.
期刊：
JOURNAL OF MATHEMATICAL INEQUALITIES,2016年10(2):423-432 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：
Jordan inequality;cosine function;sine integral;Catalan constant;Schwab-Borchardt
摘要：
We present the best possible parameters p, q is an element of(0,1] such that the double inequality (1)(3p2) cos(px) + 1 (1)(3p2) < (sin(x))(x) < (1)(3q2) cos(qx) + 1 (1)(3q2) holds for all x is an element of(0, pi/2). As applications, some new inequalities for the sine integral, Catalan constant and Schwab-Borchardt mean are found.
期刊：
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY,2016年75(1):157-168 ISSN：0340-6253
通讯作者：
Chen, Shubo
作者机构：
[Chen, Qiao; Cai, Xia; Guo, Zhijun; Chen, Shubo] Hunan City Univ, Coll Math, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Coll Math, Yiyang 413000, Hunan, Peoples R China.
摘要：
The resistance distance r(u, v) between two vertices u, v of a connected graph G is defined as the effective resistance between them in the corresponding elec-trical network constructed from G by replacing each edge of G with a unit resis-tor. Let G be a connected graph, the degree resistance distance of G is defined as DR(G) = P-u,v-°°V (G)[d(u) + d(v)]r(u, v), where d(u) is the degree of the vertex u. In this paper, we firstly characterize n-vertex unicyclic graphs with given girth having maximum and second maximum degree resistance distance, then give n-vertex unicyclic graphs with the maximum and second maximum degree resistance distance. of G is defined as u) + d(v)]r(u, v), where d(u) is the degree of the vertex u. In this paper, we firstly characterize n-vertex unicyclic graphs with given girth having maximum and second maximum degree resistance distance, then give n-vertex unicyclic graphs with the maximum and second maximum degree resistance distance.
期刊：
Journal of Function Spaces,2016年2016:1-6 ISSN：2314-8896
通讯作者：
Chu, Yu-Ming
作者机构：
[Wang, Hua] Natl Univ Def Technol, Dept Math & Syst Sci, Changsha 410073, Hunan, Peoples R China.;[Wang, Hua] Changsha Univ Sci & Technol, Dept Math, Changsha 410014, Hunan, Peoples R China.;[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.
摘要：
We present the best possible parameters alpha(1), beta(1), alpha(2), beta(2) is an element of R and alpha(3), beta(3) is an element of (1/2, 1) such that the double inequalities Q(alpha 1) (a, b)A(1-alpha 1) (a, b) < AG [A(a, b), Q(a, b)] < Q(beta 1)(a, b) A(1-beta 1) (a, b), alpha(2)Q(a, b) + (1 - alpha(2)) A(a, b) < AG[A(a, b), Q(a, b)] < beta(2)Q (a, b) + (1 - beta(2)) A (a, b), Q[alpha(3)a + (1 - alpha(3))b, alpha(3)b + (1 - alpha(3))a] < AG [A(a, b), Q(a, b)] < Q[beta(3)a + (1 - beta(3))b, beta(3)b + (1 - beta(3))a] hold for all a, b > 0 with a not equal b, where A(a, b), Q(a, b), and AG(a, b) are the arithmetic, quadratic, and Gauss arithmetic-geometric means of a and b, respectively. As applications, we find several new bounds for the complete elliptic integrals of the first and second kind.
