ON ALZER'S INEQUALITY AND ITS GENERALIZED FORMS
作者：
Liao, Jiding* ;Guan, Kaizhong
期刊：
JOURNAL OF MATHEMATICAL INEQUALITIES ,2010年4(2):161-170 ISSN：1846-579X
通讯作者：
Liao, Jiding
作者机构：
[Liao, Jiding] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.;[Guan, Kaizhong] Univ S China, Dept Math, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liao, Jiding] C;Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.
摘要：
By using the theory of multiplicatively convex functions, we present some general forms of Alzer's inequality. As consequence, some relevant results in the literature are recovered and an open problem by J. S. Ume [12] is also solved.
语种：
英文
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CONTROLLABILITY FOR A PARABOLIC EQUAON WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT
作者：
Xu Youjun* ;Liu Zhenhai
期刊：
数学物理学报(英文版) ,2010年30(5):1593-1604 ISSN：0252-9602
通讯作者：
Xu Youjun
作者机构：
[Xu Youjun] Univ S China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Liu Zhenhai] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.
通讯机构：
[Xu Youjun] U;Univ S China, Sch Math & Phys, Hengyang 421001, Peoples R China.
关键词：
controllability;Kakutani fixed-point theorem;nonlinear gradient term
摘要：
In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN. The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem. © 2010 Wuhan Institute of Physics and Mathematics.
语种：
英文
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Dynamical properties in a fourth-order nonlinear difference equation
作者：
Chen, Yunxin* ;Li, Xianyi
期刊：
Advances in Difference Equations ,2010年2010(1):1-9 ISSN：1687-1847
通讯作者：
Chen, Yunxin
作者机构：
[Chen, Yunxin] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Li, Xianyi] Shenzhen Univ, Coll Math & Computat Sci, Shenzhen 518060, Guangdong, Peoples R China.
通讯机构：
[Chen, Yunxin] U;Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Functional Equation;Equilibrium Point;Nontrivial Solution;Clear Picture;Stable Result
摘要：
The rule of trajectory structure for fourth-order nonlinear difference equation xn+1 = (xan-2 + xn-3) / (xxan-2 + xn-3), n=0,1,2, where a [ 0,1) and the initial values x-3, x-2, x-1, x 0[ 0,λ;), is described clearly out in this paper. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is 4+, 3-, 1+, 2-, 2+, 1-, 1+, 1- in a period. By utilizing this rule its positive equilibrium point is verified to be globally asymptotically stable. Copyright © 2010 Y. Chen and X. Li.
语种：
英文
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组织细胞DNA降解与死亡时间的相关性的显微拉曼光谱分析
作者：
Xiong Ping;Guo Ping* ;Zhang Jing
期刊：
光谱学与光谱分析 ,2010年30(6):1511-1515 ISSN：1000-0593
通讯作者：
Guo Ping
作者机构：
[Xiong Ping; Zhang Jing] Univ S China, Sch Med, Dept Forens Med, Hengyang 421001, Peoples R China.;[Guo Ping] Univ S China, Sch Math & Phys, Hengyang 421001, Peoples R China.
通讯机构：
[Guo Ping] U;Univ S China, Sch Math & Phys, Hengyang 421001, Peoples R China.
关键词：
显微拉曼光谱;DNA降解;死亡时间间隔(PMI);相对峰强
摘要：
为了给死亡时间推断的研究提供新的途径与数据, 探讨了人死亡后组织细胞DNA含量变化与死后时间间隔关系. 将离体肾、肝组织置于特定环境中, 在不同时间点提取离体组织, 利用激光共焦显微拉曼光谱技术和统计学方法, 在拉曼位移测试范围内, 对死后不同时间肾、肝组织DNA含量变化进行拉曼光谱检测与统计学分析. 结果显示:人死亡后48~72 h, 随着死亡时间的推移, 肾、肝组织Raman光谱的主要散射峰峰位没有明显变化, 而其峰高有明显差异;所测组织的激光拉曼光谱特征峰的相对峰强值(I_(1094)/I_(2923))随死亡时间的推移而减小. 因此可以得出结论:人死亡后肾、肝组织细胞DNA含量随死亡时间延长呈下降趋势, 两者之间存在线性关系.
语种：
中文
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Stability and bifurcation analysis of a delayed predator-prey model of prey dispersal in two-patch environments
作者：
Xu, Changjin;Tang, Xianhua* ;Liao, Maoxin
期刊：
Applied Mathematics and Computation ,2010年216(10):2920-2936 ISSN：0096-3003
通讯作者：
Tang, Xianhua
作者机构：
[Xu, Changjin; Liao, Maoxin; Tang, Xianhua] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China.;[Xu, Changjin] Hunan Inst Engn, Fac Sci, Xiangtan 411004, Peoples R China.;[Liao, Maoxin] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Peoples R China.
通讯机构：
[Tang, Xianhua] C;Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China.
关键词：
Dispersion;Hopf bifurcation;Periodic solution;Predator-prey model;Stability
摘要：
In this paper, a class of delayed predator-prey model of prey dispersal in two-patch environments is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given. © 2010 Elsevier Inc.
语种：
英文
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Thermal and piezoelectric properties of Bi_(3.15)Nd_(0.85)Ti_30_(12) thin film prepared by metal organic decomposition
作者：
Hu He-ping;Dai Shun-hong;Zheng Xue-jun* ;Zhou Yi-chun;Feng Xue;...
期刊：
中国有色金属学报(英文版) ,2010年20(8):1424-1428 ISSN：1003-6326
通讯作者：
Zheng Xue-jun
作者机构：
[Zhang Da-zhi; Hu He-ping; He Lin; Dai Shun-hong; Zheng Xue-jun; Zhou Yi-chun] Xiangtan Univ, Fac Mat & Photoelect Phys, Xiangtan 411105, Peoples R China.;[Hu He-ping] Univ S China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Zheng Xue-jun; Zhou Yi-chun] Xiangtan Univ, Minist Educ, Key Lab Low Dimens Mat & Applicat Technol, Xiangtan 411105, Peoples R China.;[Feng Xue] Tsinghua Univ, Sch Aerosp, Beijing 100084, Peoples R China.
通讯机构：
[Zheng Xue-jun] X;Xiangtan Univ, Fac Mat & Photoelect Phys, Xiangtan 411105, Peoples R China.
关键词：
bismuth-layered perovskite;metal organic decomposition (MOD);thermal parameter;remnant polarization;effective piezoelectric coefficient
摘要：
Bi_(3.15)Nd_(0.85)Ti_3O_(12) (BNT) powder and thin film were prepared by metal organic decomposition (MOD) method. The heat flow curve of BNT powder was measured with a modulated temperature differential scanning calorimeter, and thermal physical parameters such as thermal conductivity coefficient and thermal diffusion coefficient were obtained from the heat flow curve. The phase identification, ferroelectric, and piezoelectric properties of BNT thin film annealed at 700 ℃ were investigated with X-ray diffractometer, ferroelectric analyzer, and scanning probe microscope. The results show that the thin films consisting of a single phase of bismuth-layered perovskite are polycrystalline, without a preferred orientation. Remnant polarization 2P_r is 63.2 μC/cm~2 under 530 kV/cm applied field, and the effective piezoelectric coefficient d33 is 30 pm/V
语种：
英文
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Traveling fronts of the volume-filling chemotaxis model with general kinetics
作者：
Ma, Manjun* ;Yang, Daoming;Tang, Hengsheng
期刊：
Applied Mathematics and Computation ,2010年216(11):3162-3171 ISSN：0096-3003
通讯作者：
Ma, Manjun
作者机构：
[Ma, Manjun] China Jiliang Univ, Coll Sci, Hangzhou 310018, Zhejiang, Peoples R China.;[Yang, Daoming; Ma, Manjun; Tang, Hengsheng] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Ma, Manjun] C;China Jiliang Univ, Coll Sci, Hangzhou 310018, Zhejiang, Peoples R China.
关键词：
Volume-filling chemotaxis models;General forms of kinetics;Existence of traveling fronts;Perturbation method;Fredholm theory;Banach fixed-point principle
摘要：
This paper is devoted to the study of traveling fronts for the volume-filling chemotaxis model with general kinetics by applying the perturbation method. The proof relies on the Fredholm theory and the Banach contractive mapping principle. The obtained results can easily detect the existence of traveling fronts for some models investigated in the known references. © 2010 Elsevier Inc. All rights reserved.
语种：
英文
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Periodic solutions for a system of the first order nonautonomous differential equations
作者：
Tang, Hengsheng;Zhang, Zhengqiu;Wang, Zhicheng;Ma, Manjun*
期刊：
Computers & Mathematics with Applications ,2010年60(7):1948-1958 ISSN：0898-1221
通讯作者：
Ma, Manjun
作者机构：
[Ma, Manjun; Tang, Hengsheng] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Ma, Manjun] China Jiliang Univ, Coll Sci, Hangzhou 310018, Zhejiang, Peoples R China.;[Wang, Zhicheng; Zhang, Zhengqiu] Hunan Univ, Coll Math, Changsha 410082, Hunan, Peoples R China.
通讯机构：
[Ma, Manjun] C;China Jiliang Univ, Coll Sci, Hangzhou 310018, Zhejiang, Peoples R China.
关键词：
Multiple periodic solutions;The first order nonautonomous differential system;Analytical techniques;Coincidence degree theory
摘要：
In this paper, we rigorously show the existence of multiple positive periodic solutions for a system of the first order nonautonomous differential equations in the form of ẋ=xF1(t,x,y),ẏ=yF 2(t,x,y). The proof relies on some analytical techniques and coincidence degree theory. As an application, we study two classes of biological population models, both of which have at least four positive periodic solutions. © 2010 Elsevier Ltd. All rights reserved.
语种：
英文
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Exact controllability to trajectories for a semilinear heat equation with a superlinear nonlinearity
作者：
Xu, Youjun* ;Liu, Zhenhai
期刊：
Acta Applicandae Mathematicae ,2010年110(1):57-71 ISSN：0167-8019
通讯作者：
Xu, Youjun
作者机构：
[Liu, Zhenhai; Xu, Youjun] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.;[Xu, Youjun] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Xu, Youjun] C;Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.
关键词：
Exact controllability;Kakutani Fixed-point Theorem;Superlinear nonlinearity
摘要：
In this paper, we consider exact controllability to trajectories for a semilinear heat equation with nonlinearity that has superlinear growth at infinity with Dirichlet boundary conditions in a bounded domain of ℝ N . The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem and generalize the previous results. © 2008 Springer Science+Business Media B.V.
语种：
英文
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General form of some rational recursive sequences
作者：
Liao, Maoxin* ;Tang, Xianhua;Xu, Changjin
期刊：
Computers & Mathematics with Applications ,2010年59(1):360-364 ISSN：0898-1221
通讯作者：
Liao, Maoxin
作者机构：
[Liao, Maoxin; Xu, Changjin; Tang, Xianhua] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China.;[Liao, Maoxin] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liao, Maoxin] C;Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China.
关键词：
Rational recursive sequence;Attractivity;Positive solution;Equilibrium;Converge
摘要：
In this note, we study the general form of some rational recursive sequences. By some modification of the methods and ideas, as well as the transformation from the paper [K. S. Berenhaut, J. D. Foley and S. Stević, The global attractivity of the rational difference equation yn = frac(yn - k + yn - m, 1 + yn - k yn - m), Appl. Math. Lett. 20 (2007), 54-58], we give a new proof for the conjectures posed therein. © 2009 Elsevier Ltd. All rights reserved.
语种：
英文
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Multiplicative convexity and its applications
作者：
Guan, Kaizhong*
期刊：
Journal of Mathematical Analysis and Applications ,2010年362(1):156-166 ISSN：0022-247X
通讯作者：
Guan, Kaizhong
作者机构：
[Guan, Kaizhong; Guan, KZ] Univ S China, Res Inst Math, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Guan, Kaizhong] U;Univ S China, Res Inst Math, Hengyang 421001, Hunan, Peoples R China.
关键词：
Alzer's inequality;Minc-Sathre's inequality;Monotonicity;Multiplicative convexity
摘要：
This paper is concerned with some sequences based on multiplicative convexity. Our results yield a class of new inequalities between ratios and differences of means, some of which extend the known ones.
语种：
英文
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Gorenstein syzygy modules
作者：
Huang, Chonghui;Huang, Zhaoyong*
期刊：
Journal of Algebra ,2010年324(12):3408-3419 ISSN：0021-8693
通讯作者：
Huang, Zhaoyong
作者机构：
[Huang, Chonghui; Huang, Zhaoyong] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China.;[Huang, Chonghui] Univ S China, Res Inst Math, Hengyang 421001, Peoples R China.
通讯机构：
[Huang, Zhaoyong] N;Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China.
关键词：
Gorenstein projective modules;Gorenstein n syzygy modules;n syzygy modules;Gorenstein projective dimension;Gorenstein transpose
摘要：
For any ring R and any positive integer n we prove that a left R-module is a Gorenstein n-syzygy if and only if it is an n-syzygy Over a left and right Noetherian ring we introduce the notion of the Gorenstein transpose of finitely generated modules We prove that a module M E mod R P is a Gorenstein transpose of a module A E mod R if and only if M can be embedded into a transpose of A with the cokernel Gorenstein projective Some applications of this result are given (C) 2010 Elsevier Inc All rights reserved
语种：
英文
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Research on adaptive temperature control in sound field induced by self-focused concave spherical transducer
作者：
Hu, Jiwen;Qian, Shengyou* ;Ding, Yajun
期刊：
Ultrasonics ,2010年50(6):628-633 ISSN：0041-624X
通讯作者：
Qian, Shengyou
作者机构：
[Qian, Shengyou; Ding, Yajun; Hu, Jiwen] Hunan Normal Univ, Coll Phys & Informat Sci, Changsha 410081, Hunan, Peoples R China.;[Hu, Jiwen] Univ S China, Coll Math & Phys, Hengyang 421001, Peoples R China.
通讯机构：
[Qian, Shengyou] H;Hunan Normal Univ, Coll Phys & Informat Sci, Changsha 410081, Hunan, Peoples R China.
关键词：
Self-focused concave source;Temperature control;Tumor therapy
摘要：
Temperature control of hyperthermia treatments is generally implemented with multipoint feedback system comprised of phased-array transducer, which is complicated and high cost. Our simulations to the acoustic field induced by a self-focused concave spherical transducer (0.5 MHz, 9 cm aperture width, 8.0 cm focal length) show that the distribution of temperature can keep the same "cigar shape" in the focal region during ultrasound insonation. Based on the characteristic of the temperature change, a two-dimensional model of a "cigar shape" tumor is designed and tested through numerical simulation. One single-point on the border of the "cigar shape" tumor is selected as the control target and is controlled at the temperature of 43 °C by using a self-tuning regulator (STR). Considering the nonlinear effects of biological medium, an accurate state-space model obtained via the finite Fourier integral transformation to the bioheat equation is presented and used for calculating temperature. Computer simulations were performed with the perfusion rates of 2.0 kg/(m<sup>3</sup> s) and 4.5 kg/(m<sup>3</sup> s) to the different targets, it was found that the temperatures on the border of the "cigar shape" tumor can achieve the desired temperature of 43 °C by control of one single-point. A larger perfusion rate requires a higher power output to obtain the same temperature elevation under the same insonation time and needs a higher cost for compensating the energy loss carried away by blood flow after steady state. The power output increases with the controlled region while achieving the same temperature at the same time. Especially, there is no overshoot during temperature elevation and no oscillation after steady state. The simulation results demonstrate that the proposed approach may offers a way for obtaining a single-point, low-cost hyperthermia system. ©2010 Elsevier B.V. All rights reserved.
语种：
英文
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Local Hopf bifurcation and global existence of periodic solutions in TCP system
作者：
Xu, Chang-jin;Tang, Xian-hua* ;Liao, Mao-xin
期刊：
应用数学和力学：英文版 ,2010年31(6):775-786 ISSN：0253-4827
通讯作者：
Tang, Xian-hua
作者机构：
[Xu, Chang-jin; Tang, Xian-hua; Liao, Mao-xin] Cent South Univ, Sch Math Sci & Comp Technol, Changsha 410083, Peoples R China.;[Xu, Chang-jin] Hunan Inst Engn, Fac Sci, Xiangtan 411004, Hunan, Peoples R China.;[Liao, Mao-xin] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Tang, Xian-hua] C;Cent South Univ, Sch Math Sci & Comp Technol, Changsha 410083, Peoples R China.
关键词：
TCP system;stability;local Hopf bifurcation;global Hopf bifurcation;periodic solution
摘要：
This paper investigates the dynamics of a TCP system described by a firstorder nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the positive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifurcating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu (Wu, J. H. Symmetric functional differential equations and neural networks with memory. © Shanghai University and Springer-Verlag Berlin Heidelberg 2010.
语种：
英文
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Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles
作者：
Guo, C. Q.* ;Zhang, C. H.;Paidoussis, M. P.
期刊：
Journal of Fluids and Structures ,2010年26(5):793-803 ISSN：0889-9746
通讯作者：
Guo, C. Q.
作者机构：
[Guo, C. Q.; Zhang, C. H.] Tsinghua Univ, Dept Hydraul Engn, Beijing 100084, Peoples R China.;[Guo, C. Q.] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Paidoussis, M. P.] McGill Univ, Dept Mech Engn, Montreal, PQ H3A 2K6, Canada.
通讯机构：
[Guo, C. Q.] T;Tsinghua Univ, Dept Hydraul Engn, Beijing 100084, Peoples R China.
关键词：
Critical flow velocity;Equation of motion;Fluid-conveying pipe;Laminar flow;Turbulent flow
摘要：
Considering the non-uniformity of the flow velocity distribution in fluid-conveying pipes caused by the viscosity of real fluids, the centrifugal force term in the equation of motion of the pipe is modified for laminar and turbulent flow profiles. The flow-profile-modification factors are found to be 1.333, 1.015-1.040 and 1.035-1.055 for laminar flow in circular pipes, turbulent flow in smooth-wall circular pipes and turbulent flow in rough-wall circular pipes, respectively. The critical flow velocities for divergence in the above-mentioned three cases are found to be 13.4%, 0.74-1.9% and 1.7-2.6%, respectively, lower than that with plug flow, while those for flutter are even lower, which could reach 36% for the laminar flow profile. By introducing two new concepts of equivalent flow velocity and equivalent mass, fluid-conveying pipe problems with different flow profiles can be solved with the equation of motion for plug flow. © 2010 Elsevier Ltd.
语种：
英文
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Identification of nonlinearity in k-approximate periodic parabolic equations
作者：
Xu, Youjun* ;Liu, Zhenhai;Li, Jing
期刊：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS ,2009年71(1-2):691-696 ISSN：0362-546X
通讯作者：
Xu, Youjun
作者机构：
[Liu, Zhenhai; Xu, Youjun; Li, Jing] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.;[Xu, Youjun] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Xu, Youjun] C;Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.
关键词：
k-approximate periodic solution;Identification;Parabolic equation
摘要：
This work is concerned with the identification of nonlinearities in k-approximate periodic parabolic equations with observations on a subdomain of the physical domain. Some approximation processes for the identification problems are given. ©2008 Elsevier Ltd. All rights reserved.
语种：
英文
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Oscillation of First-Order Neutral Differential Equations With Unbounded Delay and Euler Form
作者：
Guan, Kaizhong* ;Shen, Jianhua
期刊：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS ,2009年39(1):103-115 ISSN：0035-7596
通讯作者：
Guan, Kaizhong
作者机构：
[Guan, Kaizhong] Univ S China, Dept Math, Hengyang 421001, Hunan, Peoples R China.;[Guan, Kaizhong] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China.;[Shen, Jianhua] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China.;[Shen, Jianhua] Coll Huaihua, Dept Math, Huaihua 418008, Hunan, Peoples R China.
通讯机构：
[Guan, Kaizhong] U;Univ S China, Dept Math, Hengyang 421001, Hunan, Peoples R China.
关键词：
34K11;34K40;neutral differential equation;oscillation;unbounded delay
摘要：
In this paper, we investigate a first-order neutral differential equation with unbounded delay and Euler form. Some necessary and sufficient as well as explicit sufficient conditions for the oscillation of all solutions are established. © 2009 Rocky Mountain Mathematics Consortium.
语种：
英文
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Oscillation Criteria for a Class of Second-Order Nonlinear Differential Equations with Damping Term
作者：
Ouyang, Zigen;Zhong, Jichao;Zou, Shuliang
期刊：
Abstract and Applied Analysis ,2009年2009:1-12 ISSN：1085-3375
通讯作者：
Ouyang, ZG
作者机构：
[Ouyang, Zigen; Zhong, Jichao; Zou, Shuliang] Univ S China, Ctr Nucl Energy Econ & Management, Hengyang 421001, Peoples R China.;[Ouyang, Zigen; Zhong, Jichao] Univ S China, Sch Phys & Mat, Hengyang 421001, Peoples R China.
通讯机构：
[Ouyang, ZG ] ;Univ S China, Ctr Nucl Energy Econ & Management, Hengyang 421001, Peoples R China.
关键词：
A class of second-order nonlinear differential equations with damping term (r(t)|x′(t)|σ−1x′(t))′+p(t)|x′(t)|σ−1x′(t)+q(t)f(x(t))=0 are investigated in this paper. By using a new method;we obtain some new sufficient conditions forthe oscillation of the above equation;and some references are extended in this paper. Examples areinserted to illustrate this result. Published: 2009 First available in Project Euclid: 16 March 2010 zbMATH: 1181.34044 MathSciNet: MR2559281 Digital Object Identifier: 10.1155/2009/897058
摘要：
A class of second-order nonlinear differential equations with damping term (r(t) | x ′ (t) | -1 x ′ (t)) ′ +p(t) | x ′ (t) | -1 x ′ (t)+q(t)f(x(t))=0 are investigated in this paper. By using a new method, we obtain some new sufficient conditions for the oscillation of the above equation, and some references are extended in this paper. Examples are inserted to illustrate this result.
语种：
英文
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Dynamics of a HIV-1 Infection model with cell-mediated immuneresponse and intracellular delay
作者：
Zhu, Huiyan* ;Zou, Xingfu
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B ,2009年12(2):511-524 ISSN：1531-3492
通讯作者：
Zhu, Huiyan
作者机构：
[Zhu, Huiyan] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Zou, Xingfu] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada.
通讯机构：
[Zhu, Huiyan] N;Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
HIV-1 infection;Immune response;Intracellular delay;Stability
摘要：
In this paper, we consider a mathematical model for HIV-1 infection with intracellular delay and cell-mediated immune response. A novel feature is that both cytotoxic T lymphocytes (CTLs) and the intracellular delay are incorporated into the model. We obtain a necessary and sufficient condition for the global stability of the infection-free equilibrium and give sufficient conditions for the local stability of the two infection equilibria: one without CTLs being activated and the other with. We also perform some numerical simulations which support the obtained theoretical results. These results show that larger intracellular delay may help eradicate the virus, while the activation of CTLs can only help reduce the virus load and increase the healthy CD+ 4 cells population in the long term sense.
语种：
英文
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Persistence of periodic patterns for perturbed biological oscillators
作者：
Ma, Manjun;Ou, Chunhua* ;Zhao, Xiao-Qiang
期刊：
Journal of Differential Equations ,2009年247(9):2597-2619 ISSN：0022-0396
通讯作者：
Ou, Chunhua
作者机构：
[Ma, Manjun] Univ S China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Ou, Chunhua; Zhao, Xiao-Qiang] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada.;[Ma, Manjun] San Diego State Univ, Dept Math & Stat, Nonlinear Dynam Syst Grp, San Diego, CA 92182 USA.
通讯机构：
[Ou, Chunhua] M;Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada.
关键词：
Periodic solutions;Hyperbolicity;Rotating waves;Coupled oscillators
摘要：
We apply the perturbation method and the Implicit Function Theorem to study the persistence of periodic patterns for two perturbed general biological oscillators: one weakly coupled ordinary differential equation and one reaction-diffusion system. The proof relies also on the formal adjoint equation theory and the Lyapunov-Schmidt method. For the perturbed reaction-diffusion model, spatial-temporal patterns such as rotating waves are shown to exist. Numerical simulations are presented to illustrate our analytical results. (C) 2009 Elsevier Inc. All rights reserved.
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英文
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