期刊：
Applied Mathematics and Computation,2015年266:539-559 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.
关键词：
Brownian motion;Stochastic differential equation;Generalized Ito's formula;Markov chain;Ratio-dependent prey-predator model
摘要：
In this paper, we investigate the stochastic permanence and extinction of a stochastic ratiodependent prey-predator model controlled by a Markov chain. In the permanent case we estimate the superior limit and the inferior limit of the average in time of the sample path of the solution. The boundaries are related to the stationary probability distribution of the Markov chain and the parameters of the subsystems. Finally, we illustrate our main results by two examples and some numerical experiments. (C) 2015 Elsevier Inc. All rights reserved.
关键词：
improved Tabu search;time window constraints.;Improved ant colony optimization;vehicle routing problem;simultaneous pickups and deliveries
摘要：
A mixed integer programming mathematical formulation of vehicle routing problem with simultaneous pickups and deliveries, and time window constraints (VRP-SPDTW) is presented in this paper. The proposed model aims at minimizing the vehicle number and the overall travel cost. A novel two-stage hybrid metaheuristic method for VRP-SDPTW is also proposed. The first stage adopts improved ant colony optimization (IACO) to determine the minimum number of used vehicles. The second stage employs improved Tabu search to optimize the total travel cost, in which the initial solutions are obtained by IACO in the first stage. Experimental results demonstrate the effectiveness of the proposed metaheuristic method.
期刊：
Complex Variables and Elliptic Equations,2013年58(12):1647-1653 ISSN：1747-6933
通讯作者：
Ponnusamy, Saminathan
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.
通讯机构：
[Ponnusamy, Saminathan] I;Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India.
摘要：
The convolution of two univalent harmonic mappings of the unit disc onto convex domains is not necessarily univalent. Dorff, Nowak and Wołoszkiewicz formulated an open problem concerning the convolution of two right half-plane mappings when one of them is fixed. In this article we solve this open problem.
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Chennai Ctr SETS, Indian Stat Inst, MGR Knowledge City, Madras 600113, Tamil Nadu, India.;[Rasila, Antti] Aalto Univ, Dept Math & Syst Anal, Aalto 00076, Finland.
关键词：
Majorant;Bloch space;Hardy space;Lipschitz space
摘要：
In this paper, we establish a Bloch-type growth theorem for generalized Bloch-type spaces and discuss relationships between Dirichlet-type spaces and Hardy-type spaces on certain classes of complex-valued functions. Then we present some applications to non-homogeneous Yukawa PDEs. We also consider some properties of the Lipschitz-type spaces on certain classes of complex-valued functions. Finally, we will study a class of composition operators on these spaces.
作者机构：
[Yang, Liu] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421008, Hunan, Peoples R China.;[Ouyang, Zigen; Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liu, Zhisu] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Multiplicity;Kirchhoff type equation;Critical growth
摘要：
In this paper, we study the following Kirchhoff type equation with critical growth {-(a + b integral(Omega) vertical bar del u vertical bar(2)dx) del u = lambda u + mu vertical bar u vertical bar(2)u + vertical bar u vertical bar(4)u in Omega, u = 0 on partial derivative Omega, where a > 0, b >= 0 and Omega is a smooth bounded domain in R-3. When the real parameter mu is larger than some positive constant, we investigate the multiplicity of nontrivial solutions for the above problem with parameter lambda belonging to a left neighborhood of the Dirichlet eigenvalue of the Laplacian operator -Delta. (C) 2016 Elsevier Ltd. All rights reserved.
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Su, Zhenhua] Huaihua Univ, Dept Math, Huaihua 418008, Hunan, Peoples R China.
通讯机构：
[Chen, Shaolin] H;Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.
会议名称：
International Conference Geometric Function Theory
会议时间：
OCT 23-24, 2013
会议地点：
Univ Belgrade, Fac Math, Belgrade, SERBIA
会议主办单位：
Univ Belgrade, Fac Math
关键词：
Hardy-Littlewood type theorem;majorant;hyperbolic harmonic function
摘要：
In this paper, we first show that a result of Girela et al. on analytic functions can be extended to hyperbolic-harmonic functions, and then we establish Hardy-Littlewood-type theorems on hyperbolic harmonic functions.
摘要：
We prove Schwarz-Pick type estimates and coefficient estimates for a class of functions induced by the elliptic partial differential operators. Then we apply these results to obtain a Landau type theorem. (C) 2015 Elsevier Inc. All rights reserved.
摘要：
In the article, the variational iteration algorithm LFVIA-II is implemented to solve the diffusion equation occurring in non-differentiable heat transfer. The operators take in sense of the local fractional operators. The obtained results show the fractal behaviors of heat transfer with non-differentiability.
作者机构：
[Tong, Xiaojiao] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421002, Peoples R China.;[Liu, Chunping] Hebei Extra High Voltage Branch, Shijiazhuang 050070, Peoples R China.;[Luo, Xiao] Hong Kong Polytech Univ, Dept Elect Engn, Kowloon, Hong Kong, Peoples R China.;[Zhou, Renjun] Changsha Univ Sci & Technol, Sch Elect & Informat Engn, Changsha 410014, Hunan, Peoples R China.
通讯机构：
[Tong, Xiaojiao] H;Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421002, Peoples R China.
会议名称：
3rd International Symposium on Optimization and Systems Biology
会议时间：
SEP 20-22, 2009
会议地点：
Chinese Acad Sci, Zhangjiajie, PEOPLES R CHINA
会议主办单位：
Chinese Acad Sci
关键词：
Available transfer capability (ATC);smoothing newton method;static security;wind generation
摘要：
The approach of available transfer capability (denoted as ATC) incorporating wind generation has been paid very high attention since the development of wind generation. Based on the maximum function, this paper presents an ATC model. The characteristic of the new model is twofold. First, it considers wind turbines connected to power system and static security of power system simultaneously. Second, it is a system of semismooth equations and can be solved easily. By using the smoothing strategy, a smoothing Newton method is adopted for solving the proposed new ATC model. Numerical simulation results of the IEEE 30-bus and 118-bus system show that the new model and algorithm are feasible and effective. The impact of wind turbines connected to power system on ATC is also analyzed.
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.
作者：
Abu Muhanna, Yusuf*;Li, Liulan;Ponnusamy, Saminathan
期刊：
Archiv der Mathematik,2014年103(6):461-471 ISSN：0003-889X
通讯作者：
Abu Muhanna, Yusuf
作者机构：
[Abu Muhanna, Yusuf] Amer Univ Sharjah, Dept Math, Sharjah 26666, U Arab Emirates.;[Li, Liulan] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] SETS, Indian Stat Inst, Chennai Ctr, Madras 600113, Tamil Nadu, India.
通讯机构：
[Abu Muhanna, Yusuf] A;Amer Univ Sharjah, Dept Math, Sharjah 26666, U Arab Emirates.
关键词：
Univalent;Convex;Starlike;Close-to-convex;Extreme points;Hayman index;Arclength;Zalcman functional;and Harmonic function
摘要：
Lawrence Zalcman's conjecture states that if is analytic and univalent in the unit disk , then for each , with equality only for the Koebe function and its rotations. This conjecture remains open although it has been verified for a few geometric subclasses of the class of univalent analytic functions. In this paper, we consider this problem for the family of normalized functions f analytic and univalent in the unit disk |z| < 1 satisfying the condition Functions satisfying this condition are known to be convex in some direction (and hence close-to-convex and univalent) in |z| < 1. A few other related basic results and remarks about the Hayman index of functions in this family are also presented.
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;Starlike and univalent harmonic mappings;Partial sum
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：
Journal of Mathematical Analysis and Applications,2013年408(2):589-596 ISSN：0022-247X
通讯作者：
Ponnusamy, Saminathan
作者机构：
[Li, Liulan] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Stat Inst, Chennai Ctr, Soc Elect Transact & Secur, MGR Knowledge City, Madras 600113, Tamil Nadu, India.;[Ponnusamy, Saminathan] Indian Stat Inst, Chennai Ctr, Soc Elect Transact & Secur, MGR Knowledge City, CIT Campus, Madras 600113, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] I;Indian Stat Inst, Chennai Ctr, Soc Elect Transact & Secur, MGR Knowledge City, CIT Campus, Madras 600113, Tamil Nadu, India.
关键词：
Harmonic mappings;Partial sum;Univalent;Convex;Starlike and close-to-convex mappings
摘要：
One of the classical results from Szego shows that if h(z) = z + Sigma(infinity)(n=2) a(n)z(n) is analytic and univalent in the unit disk D := {z is an element of C: vertical bar Z vertical bar < 1), then the 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. The exact (largest) radius of the univalence r(n) of s(n) (h) remains an open problem. On the other hand, not much is known in the case of harmonic univalent functions. It is then natural to consider the class P-H(0) of normalized harmonic mappings f = h + (g) over bar in the unit disk D satisfying the condition Re h' (z) > vertical bar g'(z)vertical bar for z is an element of D, where g'(0) = 0. Functions in P-H(0) are known to be univalent and close-to-convex in D. In this paper, we first show that each f is an element of P-H(0) is convex in the disk vertical bar z vertical bar < root 2 - 1, and then determine the value of r so that the partial sums off f is an element of P-H(0) are convex in vertical bar z vertical bar < r. (C) 2013 Elsevier Inc. All rights reserved.
作者机构：
[Tong, Xiaojiao] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421002, Peoples R China.;[Wu, Felix] 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 & Comp Sci, Hengyang 421002, Peoples R China.
关键词：
reward-risk measure;performance ratio;min-max optimization;CVaR measure;allocation of generation asset
摘要：
In this article, we study reward–risk ratio models under partially known message of random variables, which is called robust (worst-case) performance ratio problem. Based on the positive homogenous and concave/convex measures of reward and risk, respectively, the new robust ratio model is reduced equivalently to convex optimization problems with a min–max optimization framework. Under some specially partial distribution situation, the convex optimization problem is converted into simple framework involving the expectation reward measure and conditional value-at-risk measure. Compared with the existing reward–risk portfolio research, the proposed ratio model has two characteristics. First, the addressed problem combines with two different aspects. One is to consider an incomplete information case in real-life uncertainty. The other is to focus on the performance ratio optimization problem, which can realize the best balance between the reward and risk. Second, the complicated optimization model is transferred into a simple convex optimization problem by the optimal dual theorem. This indeed improves the usability of models. The generation asset allocation in power systems is presented to validate the new models.
