期刊：
IAENG International Journal of Applied Mathematics,2016年46(3):298-304 ISSN：1992-9978
通讯作者：
Zhang, Qianhong(zqianhong68@163.com)
作者机构：
[Liu, Jingzhong] School of Mathematics Physics and Energy Engineering, Hunan Institute of Technology, Hengyang, Hunan, 421002, China;[Luo, Zhenguo] School of Mathematics and Statistics, Hengyang Normal University, Hengyang, Hunan, 421002, China;[Zhang, Qianhong] School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou, 550025, China
通讯机构：
[Zhang, Q.] S;School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou, China
摘要：
By employing continuation theorem of the coincidence degree, and inequality technique, some sufficient conditions are established for the existence of periodic solution and global exponential stability of fuzzy cellular neural networks with time-varying delays. These results have important leading significance in the design and applications of globally stable neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.
期刊：
International Journal of Dynamical Systems and Differential Equations,2015年5(4):336-353 ISSN：1752-3583
通讯作者：
Zhang, Qianhong(zqianhong68@163.com)
作者机构：
[Qianhong Zhang] Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, Guizhou, China;[Jingzhong Liu] Department of Mathematics and Physics, Hunan Institute of Technology, Hengyang, Hunan, China;[Zhenguo Luo] Department of Mathematics, Hengyang Normal University, Hengyang, Hunan, China;[Yuanfu Shao] School of Science, Guilin University of Technology, Guilin, Guangxi, China
通讯机构：
Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, Guizhou, China
摘要：
This paper is concerned with the existence, the boundedness and the asymptotic behaviour of the positive solutions of a second-order fuzzy nonlinear difference equations. The parameter and initial values of system are positive fuzzy numbers. Finally an example is given to illustrate the effectiveness of the results obtained.
关键词：
rho*-mixing sequences of random variables;Marcinkiewicz strong laws;Weighted sums
摘要：
Some strong laws are established for linear statistics that are weighted sums of, where {Xn; n 1} is a sequence of ρ∗-mixing random variables, and {ani; 1 i n, n 1} is an array of real numbers. The results obtained extend and generalize the corresponding results of Guanghui Cai (Anais da Academia Brasileira de Cincias, 78(4):615-621, 2006) for identically distributed ρ∗-mixing sequences of random variables.
摘要：
In this paper, the global stability has been investigated for a novel class of competitive neural networks with mixed time delays and discontinuous activations. Without presuming the boundedness of activation functions, we draw two set of sufficient conditions ensuring the existence, uniqueness of the equilibrium, global exponential asymptotic stability of the solution and the associated output of the solution converging to the output equilibrium point in measure, by linear matrix inequality, M-matrix, Leray-Schauder alternative theorem in multivalued analysis, general Lyapunov method, topological degree theory of set-valued map. Meanwhile, we present a result on the global convergence in finite time of given neural networks. The results in the literature are generalized and significantly improved. Finally, one example and simulations are presented to demonstrate the effectiveness of the theoretical results. In this paper, the global stability has been investigated for a novel class of competitive neural networks with mixed time delays and discontinuous activations. Without presuming the boundedness of activation functions, we draw two set of sufficient conditions ensuring the existence, uniqueness of the equilibrium, global exponential asymptotic stability of the solution and the associated output of the solution converging to the output equilibrium point in measure, by linear matrix inequality, M-matrix, Leray-Schauder alternative theorem in multivalued analysis, general Lyapunov method, topological degree theory of set-valued map. Meanwhile, we present a result on the global convergence in finite time of given neural networks. The results in the literature are generalized and significantly improved. Finally, one example and simulations are presented to demonstrate the effectiveness of the theoretical results.
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Stat Inst, Chennai Ctr, SETS, MGR Knowledge City, Chennai 600113, Tamil Nadu, India.;[Rasila, Antti] Aalto Univ, Dept Math & Syst Anal, FI-00076 Aalto, Finland.;[Rasila, Antti] Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.
通讯机构：
[Rasila, Antti] A;Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.
关键词：
Harmonic and Bloch mappings;Quasiconformal mappings;Hardy and Lipschitz spaces;Length;Area function
摘要：
In this paper, we give bounds for length and area distortion for harmonic K-quasiconformal mappings, and investigate certain Lipschitz-type spaces on harmonic mappings.
期刊：
Applied Mathematics and Computation,2015年266(C):539-559 ISSN：0096-3003
通讯作者：
Li, Xiaoyue
作者机构：
[Ouyang, Mengqian] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Peoples R China.;[Li, Xiaoyue; Ouyang, Mengqian] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China.
通讯机构：
[Li, Xiaoyue] N;NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China.
摘要：
In this paper, we consider initial-boundary value problem of Euler–Bernoulli viscoelastic equation with a delay term in the internal feedbacks. Namely, we study the following equation
$$u_{tt}(x,t)+ \Delta^2 u(x,t)-\int\limits_0^t g(t-s)\Delta^2 u(x,s){\rm d}s+\mu_1u_t(x,t)+\mu_2 u_t(x,t-\tau)=0 $$
together with some suitable initial data and boundary conditions in
$${\Omega\times (0,+\infty)}$$
. For arbitrary real numbers μ
1 and μ
2, we prove that the above-mentioned model has a unique global solution under suitable assumptions on the relaxation function g. Moreover, under some restrictions on μ
1 and μ
2, exponential decay results of the energy for the concerned problem are obtained via an appropriate Lyapunov function.
摘要：
In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation
$$u_{tt}(x, t) - \Delta {u}(x, t) + \int_{0}^{t} g(t - s)\,\Delta {u}(x, s){\rm d}s + \mu_{1} u_{t}(x, t) + \mu_{2} u_{t}(x, t -\tau) = 0$$
together with initial-boundary conditions of Dirichlet type in Ω × (0, + ∞) and prove that for arbitrary real numbers μ
1 and μ
2, the above-mentioned problem has a unique global solution under suitable assumptions on the kernel g. This improve the results of the previous literature such as Nicaise and Pignotti (SIAM J. Control Optim 45:1561–1585, 2006) and Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065–1082, 2011) by removing the restriction imposed on μ
1 and μ
2. Furthermore, we also get an exponential decay results for the energy of the concerned problem in the case μ
1 = 0 which solves an open problem proposed by Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065–1082, 2011).
期刊：
Journal of Applied Mathematics and Computing,2013年42(1-2):89-102 ISSN：1598-5865
通讯作者：
Yang, L.(yangliu19731974@yahoo.com.cn)
作者机构：
[Yang, Liu; Luo, Liping; Luo, Zhenguo] Department of Mathematics and Computing Sciences, Hengyang Normal University, Hengyang, People’s Republic of China;[Chen, Haibo] Department of Mathematics, Central South University, Changsha, People’s Republic of China
通讯机构：
[Liu Yang] D;Department of Mathematics and Computing Sciences, Hengyang Normal University, Hengyang, People’s Republic of China
摘要：
In this paper, we investigate the positive solutions for a class of nonlinear q-fractional boundary value problem. We not only obtain the existence and uniqueness of positive solutions, but also establish the iterative schemes for approximating the solutions, which is benefit for computation and application.
作者机构：
[Li, Liulan] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India.;[Ponnusamy, Saminathan] SETS, Chennai Ctr, Indian Stat Inst, CIT Campus, Madras 600113, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] S;SETS, Chennai Ctr, Indian Stat Inst, CIT Campus, Madras 600113, Tamil Nadu, India.
关键词：
Close-to-convex;Convex;Partial sum;Starlike and univalent harmonic mappings
摘要：
If S denotes the class of functions h(z) = z + Sigma(infinity)(n=2) a(n)Z(n) which are analytic and univalent in the unit disk vertical bar z vertical bar < 1, then the classical result of Szego shows that every section s(n)(h)(z) = Sigma(n)(k=1) a(k)z(k) of h is univalent in vertical bar z vertical bar < 1/4. Exact (largest) radius of univalence r(n) of s(n)(h) remains an open problem, although the corresponding results for sections of various geometric subclasses of S have been obtained which include those h is an element of S for which Re h'(z) > 0 holds in the unit disk. However, no attempt has been made to derive harmonic analog of these results. The central object in this case is the class S-H(0) of sense-preserving harmonic univalent mappings f = h+(g) over bar defined on the unit disk, normalized so that h(0) = g(0) = h'(0) - 1 = g'(0) = 0. Our primary objective in this paper is to solve the univalency of every section of a harmonic function in the class P-H(0)(alpha), where P-H(0)(alpha) denotes the class of normalized univalent harmonic mapping f = h+(g) over bar in the unit disk vertical bar z vertical bar < 1 satisfying the condition Re(h'(z) - alpha) > vertical bar g'(z)vertical bar for vertical bar z vertical bar < 1, where g'(0) = 0 and 0 <= alpha < 1. In this paper, we first present sharp bounds for the moduli of the coefficients a(n), b(n) of f is an element of P-H(0)(alpha) and then determine the value of r so that the partial sums of f is an element of P-H(0) are close-to-convex in vertical bar z vertical bar < r. (C) 2013 Elsevier Ltd. All rights reserved.
期刊：
International Journal of Applied Mathematics & Statistics,2013年47(17):408-415 ISSN：0973-1377
通讯作者：
Li, L.
作者机构：
[Rui Xiao] Department of Electronic Science, Huizhou University, Huizhou 516067, Guangdong, China;[Long Li] College of Computer, National University of Defense Technology, Changsha 410005, Hunan, China;[Guohui Zhang; Long Li] Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang 421008, Hunan, China
通讯机构：
[Li, L.] C;College of Computer, , Changsha 410005, Hunan, China
作者机构：
[Huang, Lihong; Wang, Yanqun] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.;[Wang, Yanqun] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421008, Hunan, Peoples R China.;[Huang, Lihong] Hunan Womens Univ, Changsha 410004, Hunan, Peoples R China.
通讯机构：
[Huang, Lihong] H;Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.
关键词：
Discontinuous activation;Generalized Lyapunov-like approach;Global exponential asymptotic stability;Leray-Schauder alternative theorem;Mixed time delays
摘要：
In this paper, we investigate the dynamical behaviors of a novel class of Cohen-Grossberg neural networks with not only mixed time delays, i.e., time varying delays and distributed delays, but also discontinuous activations, which may be unbounded or nonmonotonic. Some sufficient conditions are derived to ensure the existence, uniqueness of the equilibrium, global exponential asymptotic stability of the solution and the associated output of the solution converging to the output equilibrium point in measure by using the Leray-Schauder alternative theorem in multivalued analysis, matrix theory and generalized Lyapunov-like approach. Some recent results in the literature are generalized and significantly improved. One example is provided to demonstrate the effectiveness of the theoretical results. (C) 2013 Elsevier B.V. All rights reserved.
摘要：
The control problem in ultrasound therapy is to destroy the tumor tissue while not harming the intervening healthy tissue with a desired temperature elevation. The objective of this research is to present a robust and feasible method to control the temperature distribution and the temperature elevation in treatment region within the prescribed time, which can improve the curative effect and decrease the treatment time for heating large tumor (>= 2.0 cm in diameter). An adaptive self-tuning-regulator (STR) controller has been introduced into this control method by adding a time factor with a recursive algorithm, and the speed of sound and absorption coefficient of the medium is considered as a function of temperature during heating. The presented control method is tested for a self-focused concave spherical transducer (0.5 MHz, 9 cm aperture, 8.0 cm focal length) through numerical simulations with three control temperatures of 43 degrees C, 50 degrees C and 55 degrees C. The results suggest that this control system has adaptive ability for variable parameters and has a rapid response to the temperature and acoustic power output in the prescribed time for the hyperthermia interest. There is no overshoot during temperature elevation and no oscillation after reaching the desired temperatures. It is found that the same results can be obtained for different frequencies and temperature elevations. This method can obtain an ellipsoid-shaped ablation region, which is meaningful for the treatment of large tumor. (C) 2012 Elsevier B.V. All rights reserved.
关键词：
Nonlinear programming;Optimal power flow with transient stability constraint;Clearing time of faults;Generalized semi-infinite programming
摘要：
This paper presents a new nonlinear programming problem arising in the control of power systems, called optimal power flow with transient stability constraint and variable clearing time of faults and abbreviated as OTS-VT. The OTS-VT model is converted into a implicit generalized semi-infinite programming (GSIP) problem. According to the special box structure of the reformulated GSIP, a solution method based on bi-level optimization is proposed. The research in this paper has two contributions. Firstly, it generalizes the OTS study to general optimal power flow with transient stability problems. From the viewpoint of practical applications, the proposed research can improve the decision-making ability in power system operations. Secondly, the reformulation of OTS-VT also provides a new background and a type of GSIP in the research of mathematical problems. Numerical results for two chosen power systems show that the methodology presented in this paper is effective and promising.
期刊：
Journal of Theoretical and Applied Information Technology,2012年46(1):114-119 ISSN：1817-3195
通讯作者：
Li, L.
作者机构：
[Xu, Tian; Li, Long] Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang, 421008, China;[Yang, Jie] School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China;[Liu, Yan] Department of Applied Mathematics, Dalian Polytechnic University, Dalian, 116034, China
通讯机构：
Department of Mathematics and Computational Science, Hengyang Normal University, China
摘要：
In the training of feedforward neural networks, it is usually suggested that the initial weights should be small in magnitude in order to prevent premature saturation. The aim of this paper is to point out the other side of the story: In some cases, the gradient of the error functions is zero not only for infinitely large weights but also for zero weights. Slow convergence in the beginning of the training procedure is often the result of sufficiently small initial weights. Therefore, we suggest that, in these cases, the initial values of the weights should be neither too large, nor too small. For instance, a typical range of choices of the initial weights might be something like (−0.4,−0.1) ∪ (0.1, 0.4), rather than (−0.1, 0.1) as suggested by the usual strategy. Our theory that medium size weights should be used has also been extended to a few commonly used transfer functions and error functions. Numerical experiments are carried out to support our theoretical findings.
作者：
Tong, Xiaojiao*;Qi, Liqun;Wu, Soon-Yi;Wu, Felix F.
期刊：
Computational Optimization and Applications,2012年51(1):175-197 ISSN：0926-6003
通讯作者：
Tong, Xiaojiao
作者机构：
[Tong, Xiaojiao] Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.;[Qi, Liqun] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China.;[Wu, Soon-Yi] Natl Cheng Kung Univ, Dept Math, Natl Ctr Theoret Sci, Tainan 70101, Taiwan.;[Wu, Felix F.] Univ Hong Kong, Dept Elect & Elect Engn, Hong Kong, Hong Kong, Peoples R China.
通讯机构：
[Tong, Xiaojiao] H;Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.
关键词：
Power systems;Stability constraint;Nonlinear programs;Smoothing SQP method;Convergence
摘要：
In this paper, A class of third-order nonlinear neutral damped functional differential equations with distributed deviating arguments are studied. By using a generalized Riccati transformation and Kamenev-type or Philos-type integral averaging technique,we establish some new sufficient conditions which insure that any solution of this equation oscillates or converges to zero.
