变分迭代法解时滞微分方程(英文)

变分迭代法被用于解时滞微分方程,通过这种方法我们得到了他们的准确解和数值解。一些例子说明了这种方法的有效性,结果显示这种方法对于解时滞微分方程是一种有力的直接的数学方法。     

Global analysis for a delayed SIV model with direct and environmental transmissions

In this paper, we propose a new SIV epidemic model with time delay, which also involves both direct and environmental transmissions. For such model, we first introduce the basic reproduction number $\mathscr{R}$ by using the next generation matrix. And then global stability of the equilibria is discussed by means of Lyapunov functionals and LaSalle''s invariance principle for delay differential equations, which shows that the infection-free equilibrium of the system is globally asymptotically stable if $\mathscr{R}<1$ and the epidemic equilibrium of the system is globally asymptotically stable for $\m     

Pressure–volume–temperature equations of state of Au and Pt up to 300 GPa and 3000 K: internally consistent pressure scales

By using a Mie–Grüneisen-type analysis method, the pressure–volume–temperature equations of state (P–V–T EOSs) of Au and Pt have been determined up to 300?GPa and 3000?K based on the experimental shock Hugoniot and thermodynamic data. The calculated results of Au and Pt show an excellent agreement with available experimental volume compression data over a wide range of pressures and temperatures. A comparison of our results with previous theoretical investigations has also been done. In addition, we have further examined the consistency of our results and the P–V–T EOS of MgO [K. Jin, X.Z. Li, Q. Wu, H.Y. Geng, L.C. Cai, X.M. Zhou, and F.Q. Jing, The pressure–volume–temperature equation of state of MgO derived from shock Hugoniot data and its application as a pressure scale, J. Appl. Phys. 107 (2010), pp. 113518] using simultaneous volume measurements of Au, Pt, and MgO at various temperatures. The good agreement among the P–V–T EOSs of Au, Pt, and MgO implies that these EOSs can be used as the reliable pressure scales in high pressure–temperature diamond anvil cell experiments.     

Dynamic analysis of Michaelis–Menten chemostat-type competition models with time delay and pulse in a polluted environment

In this paper, a new Michaelis–Menten type chemostat model with time delay and pulsed input nutrient concentration in a polluted environment is considered. We obtain a ‘microorganism-extinction’ semi-trivial periodic solution and establish the sufficient conditions for the global attractivity of the semi-trivial periodic solution. By use of new computational techniques for impulsive differential equations with delay, we prove and support with numerical calculations that the system is permanent. Our results show that time delays and the polluted environment can lead the microorganism species to be extinct.     

Analysis of a stochastic recovery-relapse epidemic model with periodic parameters and media coverage

This paper addresses, motivated by mathematical work on infectious disease models, the impacts of environmental noise and media coverage on the dynamics of recovery-relapse infectious diseases. A susceptible-infectious-recovered-infectious model is formulated with both vertical transmission and horizontal transmission. The existence and uniqueness of the positive global solution is studied by constructing suitable Lyapunov-type function. Then, the existence of positive periodic solutions is verified by applying Khasminskii"s theory. The existence of positive periodic solutions indicates the continued survival of the diseases. Besides, sufficient conditions for the extinction of the diseases are obtained. Numerical simulations then demonstrate the dynamics of the solutions. The paper extends the results of the corresponding deterministic system.     

Configuration of virtual cameras for ground based 360° three-dimensional display

Most technologies provide three-dimensional (3D) display in the front of screens which are in parallel with the walls, and the sense of immersion is decreased. To get the right ground based 3D imaging, cameras’ imaging planes should be parallel to the public focus plane, and the cameras’ optical axes should be shifted to the center of the public focus plane in both vertical and horizontal directions. Virtual cameras are used to display 3D model in computer system. Two virtually capturing methods for ground based 3D display are presented. The position of virtual camera is determined by the observer's eye positions in the real world. When the observer stands in the displayed circumcircle on the ground, off-axis perspective projection virtual cameras are used. If the observer stands out the circumcircle, offset perspective projection virtual cameras and the orthogonal projection virtual cameras are adopted. An experimental system for ground based 360° 3D display is demonstrated for viewing horizontally, which provides high-immersion 3D visualization. The displayed heights are compared with the measured results.     

带有环境反馈的不对称劳动分工博弈模型

带有环境反馈的两策略博弈被广泛研究,本文研究带有环境反馈的三策略博弈模型.环境被分为富裕斑块和贫穷斑块,富裕的斑块可以为玩家提供额外的环境收益,而贫穷斑块不为玩家提供任何收益.首先,建立模仿者动力学模型,推导模型平衡点稳定性的充分条件.该模型平衡点的稳定性取决于各策略的成本、富裕环境的收益、策略C对策略A和策略B的干扰以及策略A和策略B的合作效益.此外,通过对模型进行数值模拟,可以发现与初始期望结果一致,并且得到了在异质环境下各策略的频率.     

Applications of Nonlinear Effects in Highly Nonlinear Photonic Crystal Fiber to Optical Communications

Unique dispersion characteristics and enhanced nonlinearity make the small-core photonic crystal fiber (PCF) an ideal candidate for nonlinear optical devices to telecommunication applications. Some technical reasons behind great research interest of highly nonlinear PCFs in optical communication components are reviewed. Nonlinear effects in highly nonlinear PCFs and their research progress are presented. Several typical applications including WDM sources, optical amplification, optical switching, wavelength conversion, optical regeneration and all-optical demultiplexing etc are introduced, together with state-of-the art performances. Some new possible applications and future prospects are discussed.     

解线性方程组的松弛方法及其应用

线性方程组在科学和工程领域中有着重要的应用,松弛方法是求解线性方程组的有效算法之一.本文在著名的Gauss-Seidel迭代法的基础上,研究了一种有效的松弛方法.理论分析表明,该方法能收敛到线性方程组的唯一解.此外,我们还将该方法应用在鞍点问题和PageRank问题的求解上,并得出了相应的数值结果.结果表明该方法比现有的松弛方法更有效.     

Dynamics of a novel nonlinear SIR model with double epidemic hypothesis and impulsive effects

In this paper, the propagation of a nonlinear delay SIR epidemic using the double epidemic hypothesis is modeled. In the model, a system of impulsive functional differential equations is studied and the sufficient conditions for the global attractivity of the semi-trivial periodic solution are drawn. By use of new computational techniques for impulsive differential equations with delay, we prove that the system is permanent under appropriate conditions. The results show that time delay, pulse vaccination, and nonlinear incidence have significant effects on the dynamics behaviors of the model. The conditions for the control of the infection caused by viruses A and B are given.