利用驻波实验研究混沌现象

利用驻波实验演示了混沌现象,并对其进行了理论分析和计算机仿真研究.仿真结果与实验结果都表明:当连接点接近驻波波节处时,振动系统处于混沌运动状态;而当连接点接近驻波波腹处时,系统处于稳定驻波运动状态.     

一类非线性常微分方程振荡解的渐近表示

在本文中,我们讨论了非线性常微分方程y"=a0|x|αy3 a1|x|βy2 α2|x|γy α3|x|δ振荡解的渐近表示．在这个方程中将α0,α,α1,β,α2,γ,α3,δ分别换成0,0,6,0,0,0,sgn(x),1就是著名的第一类Painleve方程,而将α0,α,α1,β,α2,γ,α3,δ分别换成2,0,0,0,sgn(x),1,α0,就是著名的第二类Painleve方程．当α0,α,α1,β,α2,γ,α3,δ分别换成-β/3γ,0,0,0,1/γ,1,α,0时,可用于组合KdV方程孤立子解的化简．     

Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

多元线性回归应用于近代物理实验

本文介绍非线性方程转化直线性方程和多元线性回归法来分析近代物理实验中塞曼效应分裂干涉圆环多处选点测量的处理过程。     

OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

Numerical analysis for the periodic response of nonsmooth dynamic systems of high-dimension

This paper deals with the numerical solution of high dimensional dynamic systems with nonsmooth characteristics, such as structural elastoplasticity, mechanical clearance and dry friction. As a stable periodic response of the system attracts its transient response, it may be extracted from the transient response somehow. The paper suggests a novel iteration scheme to extrapolate the periodic response from a short time history of its transient response by curve fitting. Compared with the current schemes such as shooting and incremental harmonic balancing, the present scheme makes full use of the information within the transient response and the system characters, then its computation efficiency has increased by an order and the numerical convergence depending on the initial iteration has greatly improved.The subject supported by the Chinese Foundation of Aeronautical Science     

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wavccurrent field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does so by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best. Project supported by the Chinese Academy of Sciences.     

两个非线性方程的准确解

借助于计算机代数系统Ｍａｔｈｅｍａｔｉｃａ利用直接代数方法获得了两个有数学物理意义的非线性耗散－色散方程的准确解，这种方法也适用于高维非线性方程。     

金融时间序列分析与建模

介绍了金融时间序列分析与建模的主要理论、方法,着重论述了近20多年发展起来的非平稳时间序列的建模方法及工具,指出进一步的研究方向.最后,对上证综合指数这一金融时间序列进行了实证分析.     

NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD, the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1-and L2-norm space estimates and the 0((△t)2) estimate for time variable are obtained.