作者机构：
[Wang, Miao-Kun] Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.;[Chu, Yu-Ming] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China.;[Zhang, Wen] Icahn Sch Med Mt Sinai, Friedman Brain Inst, New York, NY 10029 USA.
关键词：
Convex function;Csiszár divergence;Jensen’s inequality;s-convex function
摘要：
In the article, we establish an inequality for Csiszár divergence associated with s-convex functions, present several inequalities for Kullback–Leibler, Renyi, Hellinger, Chi-square, Jeffery’s, and variational distance divergences by using particular s-convex functions in the Csiszár divergence. We also provide new bounds for Bhattacharyya divergence.
期刊：
Applied Mathematics and Computation,2019年348:552-564 ISSN：0096-3003
通讯作者：
Chu, Yu-Ming
作者机构：
[Yang, Zhen-Hang] Hunan City Univ, Coll 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.;[Chu, Yu-Ming] Huzhou Univ, Dept Math, Hzhou 313000, Peoples R China.;[Zhang, Wen] Icahn Sch Med Mt Sinai, Friedman Brain Inst, New York, NY 10029 USA.
摘要：
In the article, we prove that the double inequality pi/2J(r') - 51 pi-160/160 r(16) < epsilon(r) < pi/2(r') - 5 pi/3x2(31 )r(16) holds for all r is an element of (0, 1), where epsilon(r) = integral( pi/2)(0)root 1-r(2)sin(2)(t)dt is the complete elliptic integral of the second kind, r' = (1 - r(2))(1/2) and J(r) = 51r(2) + 20r root r + 50r + 20 root r + 51/16(5r + 2 root r + 5). (C) 2018 Elsevier Inc. All rights reserved.
摘要：
We establish a Hermite-Hadamard type identity and several new Hermite-Hadamard type inequalities for conformable fractional integrals and present their applications to special bivariate means.
关键词：
Green's function;Hermite-Hadamard inequality;convex function
摘要：
In the article, we establish the left Riemann-Liouville fractional Hermite-Hadamard type inequalities and the generalized Hermite-Hadamard type inequalities by using Green's function and Jensen's inequality, and present several new Hermite-Hadamard type inequalities for a class of convex as well as monotone functions.
摘要：
Kernel partial least squares (KPLS) has become popular techniques for chemical and biological modeling, which is a nonlinear extension of linear PLS. Training samples are transformed into a feature space via a nonlinear mapping, and then PLS algorithm can be carried out in the feature space. However, one of the main limitations of KPLS is that each feature is given the same importance in the kernel matrix, thus explaining the poor performance of KPLS for data with many irrelevant features. In this study, we provide a new strategy incorporated variable importance into KPLS, which is termed as the WKPLS approach. The WKPLS approach by modifying the kernel matrix provides a feasible way to differentiate between the true and noise variables. On the basis of the fact that the regression coefficients of the PLS model reflect the importance of variables, we firstly obtain the normalized regression coefficients by establishing the PLS model with all the variables. Then, Variable importance is incorporated into primary kernel. The performance of WKPLS is investigated with one simulated dataset and two structure–activity relationship (SAR) datasets. Compared with standard linear kernel PLS and Gaussian kernel PLS, The results show that WKPLS yields superior prediction performances to standard KPLS. WKPLS could be considered as a good mechanism by introducing extra information to improve the performance of KPLS for modeling SAR.
关键词：
Ostrowski inequality;Conformable derivative;Conformable integral;Arithmetic mean;Generalized logarithmic mean
摘要：
In the article, we establish several Ostrowski type inequalities involving the conformable fractional integrals. As applications, we find new inequalities for the arithmetic and generalized logarithmic means.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Coll Math, Yiyang 413000, Hunan, Peoples R China.;Hunan Univ, Coll Math, Changsha 410082, Hunan, Peoples R China.
摘要：
In this paper, we study a new graph invariant named Resistance-Harary index, defined as RH(G) = Sigma({u,v}subset of v(G)) 1/r(G)(u,v) where r(G)(u, v) is the resistance distance between vertices u and v of a connected graph G. We establish that S-n(3) and P-n(3). are the graphs with the maximal and minimal Resistance-Harary index among all unicyclic graphs on n vertices, respectively.
期刊：
Agro Food Industry Hi-Tech,2017年28(1):145-147 ISSN：1722-6996
通讯作者：
Xiong, Peiying
作者机构：
[Dai, Anding; Xiong, Peiying] Hunan City Univ, Coll Math & Comp Sci, Yiyang, Hunan, Peoples R China.
通讯机构：
[Xiong, Peiying] H;Hunan City Univ, Coll Math & Comp Sci, Yiyang, Hunan, Peoples R China.
关键词：
Fuzzy and discrete;Impulse;Kinetics;Neural network;Stochastic;Time-varying delay
摘要：
In order to figure out the influence of time-varying delays and impulse on the stability of stochastic and discrete neural network, and supplement the results of kinetics study on stochastic and discrete neural network, the analysis about the dynamic system of stochastic and discrete neural network is carried out in this thesis based on the stochastic and discrete neural network with time-varying delays and impulse and theories of kinetics study. Besides, methods such as differential inequality, matrix and numerical simulation are adopted herein to further study the stability of stochastic and discrete neural network with time-varying delays and impulse. And it has been found through kinetics study that the stably stochastic and discrete neural network with time-varying delays and impulse becomes not stable after introducing time-varying delays and impulse, and the instability is quite unstable.
期刊：
Chemometrics and Intelligent Laboratory Systems,2017年168:107-113 ISSN：0169-7439
通讯作者：
Huang, Xin
作者机构：
[Huang, Xin] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.;[Xia, Li] Hunan City Univ, Sch Chem & Environm Engn, Yiyang 413000, Peoples R China.;[Huang, Xin] State Stat Bur, Key Lab Stat Informat Technol & Data Min, Beijing 100826, Peoples R China.
通讯机构：
[Huang, Xin] H;Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
摘要：
In this paper, not only some novel sufficient criteria for stability of discrete delay neural networks but also a new discriminant method for self synchronization of Hopfield neural networks are considered. Some novel stability criteria for discrete delay neural networks are obtained if the time average of the difference for two coefficients on some fixed lengths is lower bounded by some positive numbers. Moreover, a new discrete Halanay inequality is given, which extends the existing results. Based on the Halanay inequality, a novel sufficient criterion on self synchronization of Hopfield neural networks with time delay is obtained. Two numerical examples are given to demonstrate the effectiveness of proposed methods.
摘要：
In order to figure out influences of variable delay on stability of discrete fuzzy neural network loop and supplement achievements of kinetic study on discrete fuzzy neural network system, the author has the in-depth study on kinetic system of discrete fuzzy neural network loop on the basis of variable delay and discrete fuzzy neural network theory. Moreover, with mathematical model, matrix analysis and numerical simulation, the author explores index stability and correctness of discrete fuzzy neural network loop with variable delay. Findings of kinetic study show that after introducing variable delay, stable standards of discrete fuzzy neural network loop system have the larger time-lag dependence and it has the stronger conservatism.
作者机构：
[Huang, Xin; Luo, Yi-Ping] Hunan City Univ, Dept Math, Yiyang 413000, Peoples R China.;[Huang, Xin] State Stat Bur, Key Lab Stat Informat Technol & Data Min, Beijing 100826, Peoples R China.;[Xu, Qing-Song] Cent S Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China.;[Liang, Yi-Zeng] Cent S Univ, Res Ctr Modernizat Tradit Chinese Med, Changsha 410083, Hunan, Peoples R China.
通讯机构：
[Huang, Xin] H;[Huang, Xin] S;Hunan City Univ, Dept Math, Yiyang 413000, Peoples R China.;State Stat Bur, Key Lab Stat Informat Technol & Data Min, Beijing 100826, Peoples R China.
摘要：
In the article, we prove that the double inequalities
$$ \frac{\sqrt{\pi}e^{-x}}{\sqrt{2(x+a)}}< K_{0}(x)< \frac{\sqrt{\pi }e^{-x}}{\sqrt{2(x+b)}},\qquad 1+ \frac{1}{2(x+a)}< \frac {K_{1}(x)}{K_{0}(x)}< 1+\frac{1}{2(x+b)} $$
hold for all
$x>0$
if and only if
$a\geq1/4$
and
$b=0$
if
$a, b\in[0, \infty)$
, where
$K_{\nu}(x)$
is the modified Bessel function of the second kind. As applications, we provide bounds for
$K_{n+1}(x)/K_{n}(x)$
with
$n\in\mathbb{N}$
and present the necessary and sufficient condition such that the function
$x\mapsto\sqrt {x+p}e^{x}K_{0}(x)$
is strictly increasing (decreasing) on
$(0, \infty)$
.
期刊：
Journal of Nonlinear Sciences and Applications,2017年10(3):929-936 ISSN：2008-1898
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, Xiao-Hui] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, 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：
Gaussian hypergeometric function;complete elliptic integral;Stolarsky mean
摘要：
In the article, we prove that the double inequality 25/16 < epsilon(r)/S-5/2,S-2 (1, r ') < pi/2, holds for all r is an element of(0, 1) with the best possible constants 25/16 and pi/2, where r ' = (1 - r(2))(1/2),epsilon(r) = integral(pi/2)(0) root 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. (C) 2017 All rights reserved.
