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1、广义组合KDV方程孤立波的轨道稳定性张卫国, 张 璐(上海理工大学 理学院, 上海 200093)摘要: 应用Grillakis提出的轨道稳定性理论,研究了广义组合KDV方程ut + aupux + bu2pux + duxx x = 0 (a, b, d, p=C, p0)的轨道稳定性. 利用轨道稳定性理论和谱分析得到了一类特殊形式孤波解的稳定性.关键词: 轨道稳定; 孤立波; 谱分析Orbital stability of solitary waves of generalized compound KDV equationsZHANG Wei-guo, ZHANG Lu(College
2、of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)Abstract: The abstract results of Grillakis are used directly and the orbital stability of solitary waves of compound KDV-type equation with nonlinear terms of any order is examined. ut + aupux + bu2pux + duxx x =
3、0 (a, b, d, p=C, p0). The orbital stability is obtained by using the abstract orbital stability theory and detailed spectral analysis.Key words: orbital stability; solitary waves; spectral analysis一类二阶常微分方程组边值问题三个正解的存在性李高尚, 刘锡平, 贾 梅, 李春岭, 李芳菲(上海理工大学 理学院, 上海 200093)摘要: 利用Leggett-Williams不动点定理,研究了在Stu
4、rm-Liouville边界条件下的一类二阶常微分方程组多个正解的存在性,得到了至少三个正解存在的充分条件.关键词: 边值问题; 正解; 不动点; 锥Existence of three positive solutions in boundary value problems of a class of second order ordinary differential systemsLI Gao-shang, LIU Xi-ping, JIA Mei, LI Chun-ling, LI Fang-fei(College of Science, University of Shanghai
5、 for Science and Technology, Shanghai 200093, China)Abstract: Boundary value problems of a class of second order ordinary differential systems are considered. Under Sturm-Liouville conditions, the existence of at least three positive solutions is proved by using Leggett-Williams fixed point theorem.
6、Key words: boundary value problem; positive solutions; fixed point; cone具有脉冲预防接种的SIQR流行病数学模型周艳丽1, 王贺桥2, 王美娟2, 徐长永2(1. 上海理工大学 医疗器械学院, 上海 200093; 2. 上海理工大学 理学院, 上海 200093)摘要: 讨论了一类具有脉冲预防接种且传染率为双线性的SIQR传染病模型. 在脉冲预防接种下,分析了无病周期解的存在性和全局渐近稳定性.关键词: 预防接种; 脉冲微分方程; 基本再生数; 周期解; 全局渐近稳定性SIQR epidemical model with
7、 impulsive vaccinationZHOU Yan-li1, WANG He-qiao2, WANG Mei-juan2, XU Chang-yong2(1. College of Medical Instrumentation, University of Shanghai for Science and Technology, Shanghai 200093, China; 2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)Abstrac
8、t: A SIQR model for spread of infectious disease in a population with impulsive vaccination is discussed. The reproduction number for the model is obtained, and the existence and global stability of the disease-free periodic solution are analysed.Key words: vaccination; impulsive differential equati
9、ons; basic reproduction number; periodic solution; global asymptotic stability含导数项的p-Laplacian算子多点边值问题三个正解的存在性李春岭, 刘锡平, 贾 梅, 李高尚, 李芳菲(上海理工大学 理学院, 上海 200093)摘要: 利用Leggett-Williams不动点定理的一个扩展定理,研究了非线性项含导数项的p-Laplacian算子多点边值问题,得到了三个正解存在的充分条件.关键词: 不动点定理; 正解; p-Laplacian算子; 边值问题Existence of three positive
10、 solutions in a multi-points boundary value problem of p-Laplacian operator with first-order derivativeLI Chun-ling, LIU Xi-ping, JIA Mei, LI Gao-shang, LI Fang-fei(College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)Abstract: The existence of three positive
11、 solutions in a multi-points boundary value problem of differential equation with a p-Laplacian operator is investigated. An extension of the Leggett-Williams fixed point theorem is utilized and a sufficient condition for the existence of three positive solutions is obtained.Key words: fixed-point t
12、heorem; positive solution; p-Laplacian operator; boundary value problem从网络质量控制角度观察无标度网络郭进利, 王翠萍(上海理工大学 管理学院, 上海 200093)摘要: 阐明了增长网络度分布概念. 从网络质量控制角度直观地给出增长网络无标度的严密定义,明确网络中枢点的概念,体现无标度网络稳健而又脆弱的特点. 指出Barabsi和Albert等人对择优增长网络模型的分析不能体现网络中枢点的原因. 考虑了节点吸引度的概率分布,提出Poisson增长择优连接网络(Poisson NPA模型),并且借助G-分布的性质证明了Po
13、isson NPA模型的无标度性.关键词: 复杂网络; 度分布; 中枢点; 无标度网络Observation on scale-free network from networks quality control perspectiveGUO Jin-li, WANG Cui-ping(Business School, University of Shanghai for Science and Technology, Shanghai 200093, China)Abstract: The paper expounds the concept of degree distribution o
14、f growing network. It provides the rigorous definition of scale-free growing network from the perspective of network quality controls, makes clear the concept of networks hubs, eliminates the concepts ambiguity of scale-free network in literatures, embodies the robustness and fragility characteristi
15、cs of the scale-free networks. It points out the reason, why the preferentially growing network model cannot reflect the hub in the analysis by Barabsi and Albert. In the light of G-distribution character, the scale-free nature of the preferential attachment network with Poisson growth is proved.Key
16、 words: complex networks; degree distribution; hub; scale-free networks消耗公共资源的谋利行为博弈的过度行为均衡点问题研究孙绍荣(上海理工大学 管理学院, 上海 200093)摘要: 在建立了弱再生资源的再生速度模型和谋利行为对资源的消耗模型的基础上,得出了在谋利行为下的弱再生公共资源的均衡曲线与均衡模型. 利用此模型分析了个人非理性、个人理性的不同均衡点,研究了这些均衡点之间的关系.关键词: 谋利行为; 成员数量; 行为控制; 弱再生资源; 数学模型Studying excessive behavior even point of benefit-seeking behavior gambling of c
