期刊：
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS,2017年32(3):2295-2308 ISSN：1064-1246
通讯作者：
Wang, Jian-Qiang
作者机构：
[Wang, Meng-Xian; Wang, Jian-Qiang] Cent S Univ, Sch Business, Changsha 410083, Hunan, Peoples R China.;[Wang, Meng-Xian] Hunan City Univ, Sch Math & Computat Sci, Yiyang, Peoples R China.;[Wang, Jian-Qiang] Key Lab Hunan Prov Mobile Business Intelligence, Changsha, Hunan, Peoples R China.;[Wang, Jian-Qiang] Mobile E Business Collaborat Innovat Ctr Hunan Pr, Changsha, Hunan, Peoples R China.
通讯机构：
[Wang, Jian-Qiang] C;Cent S Univ, Sch Business, Changsha 410083, Hunan, Peoples R China.
摘要：
Anomaly detection is an important task for applications involving Big Data. Comparing with traditional method, anomaly detection in Big Data confronts growing amounts of data with high dimensionality and complex structures, which require more real-time analysis. This paper presents a fuzzy input-output system for anomalous data using electronic consumer records (ECR), a trapezium-cloud-map-filtration (TCMF) framework and a value mining model. ECRs are used to add or remove criteria based on consumers' consumption. In addition, MapReduce framework and trapezium clouds generated from each subsample are aggregated by using the aggregated trapezium cloud as a filter for each subsample. Then, a fuzzy logic-based value mining model is proposed based on Takagi-Sugeno model (T-S model) and trapezium clouds. This paper establishes a system that can improve decision-making accuracy by filtering large-scale data, and an illustrative example using a hotel booking situation is presented to verify the validity and feasibility of the proposed model. Finally, a comparative analysis is conducted between the proposed approach and existing methods.
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 electrical network, constructed from G by replacing each edge of G with a unit resistor. The degree resistance distance of G is defined as D-R(G) = Sigma({u, v}subset of) (V(G)) (d(u) + d(upsilon)) r(u, v), where d(u) is the degree of the vertex u. Let G(n,m) be the set of connected graphs with order n and m edges. In this paper, we'll determine the extremal graphs among G(n,m) with the minimum degree resistance distance.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2017年2017(1):1-10 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Zhao, Tie-Hong] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Zhang, Wen] Icahn Sch Med Mt Sinai, Friedman Brain Inst, 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：
arithmetic mean;Toader mean;quadratic mean;complete elliptic integral
摘要：
In this paper, we present the best possible parameters
$\alpha(r)$
and
$\beta(r)$
such that the double inequality
$$\begin{aligned} \bigl[\alpha(r)A^{r}(a,b)+ \bigl(1-\alpha(r) \bigr)Q^{r}(a,b) \bigr]^{1/r} < & TD \bigl[A(a,b), Q(a,b) \bigr] \\ < & \bigl[\beta(r)A^{r}(a,b)+ \bigl(1-\beta(r) \bigr)Q^{r}(a,b) \bigr]^{1/r} \end{aligned}$$
holds for all
$r\leq 1$
and
$a, b>0$
with
$a\neq b$
, and we provide new bounds for the complete elliptic integral
$\mathcal{E}(r)=\int_{0}^{\pi/2}(1-r^{2}\sin^{2}\theta)^{1/2}\,d\theta$
$(r\in (0, \sqrt{2}/2))$
of the second kind, where
$TD(a,b)=\frac{2}{\pi}\int_{0}^{\pi/2}\sqrt{a^{2}\cos^{2}\theta+b^{2}\sin^{2}\theta}\,d\theta$
,
$A(a,b)=(a+b)/2$
and
$Q(a,b)=\sqrt{(a^{2}+b^{2})/2}$
are the Toader, arithmetic, and quadratic means of a and b, respectively.
摘要：
In this paper, we discover two novel integral identities for twice differentiable functions. Under the utility of these identities, we establish some generalized inequalities for classical integrals and Riemann-Liouville fractional integrals of the Hermite-Hadamard type via functions whose derivatives absolute values are MT-convex. At the end, we present applications for special means and several error approximations for the trapezoidal formula. (C) 2016 All rights reserved.
期刊：
Journal of Nonlinear Sciences and Applications,2016年9(5):2031-2038 ISSN：2008-1898
通讯作者：
Chu, Yu-Ming
作者机构：
[Xia, Fang-Li; Chu, Yu-Ming; Chen, Shu-Bo] 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：
Neuman mean;Schwab-Borchardt mean;harmonic mean;geometric mean;arithmetic mean;quadratic mean;contra-harmonic mean
摘要：
In the article, we present the sharp bounds for the Neuman mean N-AG(a, b), N-GA(a, b), N-QA(a, b) and N-AQ(a, b) in terms of the convex combinations of the arithmetic and one-parameter harmonic and contraharmonic means. As applications, we find several sharp inequalities for the first Seiffert, second Seiffert, Neuman-Sandor and logarithmic means. (C) 2016 All rights reserved.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2016年2016(1):1-13 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Hong-Hu] Changsha Univ Sci & Technol, Sch Civil Engn & Architecture, Changsha 410114, Hunan, Peoples R China.;[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.
摘要：
In the article, we present certain
$p, q\in\mathbb{R}$
such that the Wilker-type inequalities
$$\begin{aligned}& \frac{2q}{p+2q} \biggl(\frac{\sin x}{x} \biggr)^{p}+ \frac{p}{p+2q} \biggl(\frac{\tan x}{x} \biggr)^{q}>(< )1\quad \mbox{and}\\& \biggl(\frac{\pi}{2} \biggr)^{p} \biggl(\frac{\sin x}{x} \biggr)^{p}+ \biggl[1- \biggl(\frac{\pi}{2} \biggr)^{p} \biggr] \biggl(\frac{\tan x}{x} \biggr)^{q}>(< )1 \end{aligned}$$
hold for all
$x\in(0, \pi/2)$
.
期刊：
BOUNDARY VALUE PROBLEMS,2016年2016(1):1-19 ISSN：1687-2770
通讯作者：
Zhou, Shuangshuang
作者机构：
[Zhou, Shuangshuang; Tang, Xianhua] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.;[Zhou, Shuangshuang] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Yang, Chunxiao] Xian Univ Architecture & Technol, Sch Sci, Xian 710055, Peoples R China.
通讯机构：
[Zhou, Shuangshuang] C;[Zhou, Shuangshuang] H;Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
doubly degenerate parabolic;not in divergence form;blow-up;global solution;gradient term
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; Chu, Hong-Hu] 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.
摘要：
In the article, we establish several inequalities for the Ramanujan constant function
$R(x)=-2\gamma-\psi(x)-\psi(1-x)$
on the interval
$(0, 1/2]$
, where
$\psi(x)$
is the classical psi function and
$\gamma=0.577215\cdots$
is the Euler-Mascheroni constant.
期刊：
Mathematical Problems in Engineering,2016年2016:1-5 ISSN：1024-123X
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; Zhang, Xiao-Hui] 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 prove that the double inequality J α ( a , b ) < U ( a , b ) < J β ( a , b ) holds for all a , b > 0 with a ≠ b if and only if α ≤ 2 / ( π - 2 ) = 0.8187 ⋯ and β ≥ 3 / 2 , where U ( a , b ) = ( a - b ) / [ 2 arctan ( ( a - b ) / 2 a b ) ] , and J p ( a , b ) = p ( a p + 1 - b p + 1 ) / [ ( p + 1 ) ( a p - b p ) ] ( p ≠ 0 , - 1 ) , J 0 ( a , b ) = ( a - b ) / ( log a - log b ) , and J - 1 ( a , b ) = a b ( log a - log b ) / ( a - b ) are the Yang and p th one-parameter means of a and b , respectively.
期刊：
Ars Combinatoria,2016年124:183-192 ISSN：0381-7032
通讯作者：
Chen, Shubo
作者机构：
[Chen, Shubo] Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
摘要：
Let G be a cactus, which all of blocks of G are either edges or cycles. Denote W(n,r) the set of cactuses of order n and with r cycles. In this paper, we present a unified approach to the extremal cactuses, for Schultz and the modified Schultz indices.
摘要：
In this paper, the adaptive exponential synchronization problem of neutral-type coupled neural networks with Markovian switching parameters is investigated. The switching parameters are modeled as a continuous time, finite state Markov chain. Based on Lyapunov stability theory, stochastic analysis and matrix theory, some sufficient conditions for exponential synchronization in mean square are derived. The adaptive controllers are added to part of nodes, and the adaptive laws are depend on Markov chain and error states. Two numerical examples are exhibited to illustrate the validity of the theoretical results. Through the comparison of average value of synchronization control cost and synchronization time, we verify that control different nodes may be more effectively to achieve synchronization than control fixed nodes when the network topology is switching by a Markov chain.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2016年2016(1):1-21 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：
modified Bessel function;Toader-Qi mean;logarithmic mean;identric mean
摘要：
In the article, we present several sharp bounds for the modified Bessel function of the first kind
$I_{0}(t)=\sum_{n=0}^{\infty}\frac{t^{2n}}{2^{2n}(n!)^{2}}$
and the Toader-Qi mean
$TQ(a,b)=\frac{2}{\pi}\int_{0}^{\pi/2}a^{\cos^{2}\theta }b^{\sin^{2}\theta}\,d\theta$
for all
$t>0$
and
$a, b>0$
with
$a\neq b$
.
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.;[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：
complete elliptic integral;Stolarsky mean;Toader mean;Toader-Qi mean
摘要：
In the article, we prove that the function
$r\mapsto \mathcal{E}(r)/S_{9/2-p, p}(1, r')$
is strictly increasing on
$(0, 1)$
for
$p\leq7/4$
and strictly decreasing on
$(0, 1)$
for
$p\in [2, 9/4]$
, where
$r'=\sqrt{1-r^{2}}$
,
$\mathcal{E}(r)=\int_{0}^{\pi/2}\sqrt{1-r^{2}\sin^{2}(t)}\,dt$
is the complete elliptic integral of the second kind, and
$S_{p, q}(a, b)=[q(a^{p}-b^{p})/(p(a^{q}-b^{q}))]^{1/(p-q)}$
is the Stolarsky mean of a and b. As applications, we present several new bounds for
$\mathcal{E}(r)$
, the Toader mean
${T}(a,b)=(2/\pi)\int_{0}^{\pi/2}\sqrt{a^{2}\cos^{2}t+b^{2}\sin^{2}t}\,dt$
, and the Toader-Qi mean
$\operatorname{TQ}(a,b)=(2/\pi)\int_{0}^{\pi/2}a^{\cos^{2}\theta}b^{\sin^{2}\theta }d\theta$
.
期刊：
JOURNAL OF MATHEMATICAL INEQUALITIES,2016年10(2):301-312 ISSN：1846-579X
通讯作者：
Guo, Zhi-Jun
作者机构：
[Chu, Yu-Ming; Song, Ying-Qing; Zhang, Yan; Guo, Zhi-Jun] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Guo, Zhi-Jun] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
Arithmetic mean;Geometric mean;Neuman mean;Quadratic mean;Schwab-Borchardt mean
摘要：
In this paper, we find the greatest values alpha(1), alpha(2), alpha(3), alpha(4), alpha(5), alpha(6), alpha(7), alpha(8) and the least values beta(1), beta(2), beta(3), beta(4), beta(5), beta(6), beta(7), beta(8) such that the double inequlities A alpha(1)(a, b)G(1-alpha 1) (a, b) < N-GA(a, b) < A(beta 1) (a, b)G(1-beta 1) (a, b), alpha(2)/G(a, b) + 1 - alpha(2)/A(a, b) < 1/N-GA (a, b) < beta(2)/G(a, b) + 1 - beta(2)/A(a, b), A alpha 3 (a, b) G(1-alpha 3) (a, b) < N-AG (a, b) < A(beta 3) (a, b)G(1-beta 3) (a, b), alpha(4)/G(a, b) + 1 - alpha(4)/A(a, b) < 1/N-GA(a, b) < beta 4/G(a, b) + 1 - beta(4)/A(a, b), Q(alpha 5) (a, b)A(1-alpha 5) (a, b) < N-AQ (a, b) < Q(beta 5) (a, b)A(1-beta 5) (a, b), alpha(6)/A (a, b) + 1 - alpha(6)/Q (a, b) < 1/N-AQ (a, b) < beta(6)/A(a, b) + 1 - beta(6)/Q(a, b), Q(alpha 7) (a, b)A(1 - alpha 7) (a, b) < N-QA (a, b) < Q beta(7) (a, b)A(1 -beta 7) (a, b), alpha(8)/A(a, b) + 1 - alpha(8)/Q(a, b) < 1/N-QA(a, b) < beta(8)/A(a, b) + 1 - beta(8)/Q(a, b) hold for all a,b > 0 with a not equal b, where G, A and Q are respectively the geometric, arithmetic and quadratic mean, and N-GA, N-AG, N-AQ AND N-QA are the Neuman means derived from the Schwab-Borchardt mean.
摘要：
In this paper, we give several improvements of Mitrinovic-Adamovic's inequality and Lazarevic's inequality. Our results show some interesting relationships between Mitrinovic-Adamovic's inequality and Lazarevic's inequality. At the end of the paper, the improved Lazarevic's inequality is applied to the sharpening of Wilker-type inequalities for hyperbolic functions. (C) 2016 All rights reserved.
摘要：
We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is assumed to be quasistatic and the material behaviour is described by a viscoelastic constitutive law with damage. The friction and contact are modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is a coupled system of a hemivariational inequality for the velocity and a parabolic variational inequality for the damage field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of time-dependent stationary inclusions and a fixed point theorem.
期刊：
Journal of Function Spaces,2016年2016 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 prove that the inequality TQ(a,b) > L-p(a,b) holds for all a,b > 0 with a not equal b if and only if p <= 3/2, where TQ(a,b) = (2/pi) integral(pi/2)(0) a(cos2 theta)bsin(2 theta)d theta, L-p(a,b) - inverted right perpendicular(bp - ap)/(p(b - a))inverted left perpendicular(1/p) (p not equal 0), and L-0(a,b) = root ab are, respectively, the Toader-Qi and p-order logarithmic means of a and b. As applications, we find two fine inequalities chains for certain bivariate means.
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 discuss the monotonicity properties of the function
$x\rightarrow (1-e^{-ax^{p}} )^{1/p}/\int_{0}^{x}e^{-t^{p}}\,dt$
for
$a, p>0$
with
$p\neq1$
on
$(0, \infty)$
and prove that the double inequality
$\Gamma(1+1/p) (1-e^{-a x^{p}} )^{1/p} <\int_{0}^{x}e^{-t^{p}}\,dt<\Gamma(1+1/p) (1-e^{-b x^{p}} )^{1/p}$
holds for all
$x>0$
if and only if
$a\leq\min\{1, \Gamma^{-p}(1+1/p)\}$
and
$b\geq\max\{1, \Gamma^{-p}(1+1/p)\}$
.
