MULTISCALE HOMOGENIZATION OF NONLINEAR HYPERBOLIC EQUATIONS WITH SEVERAL TIME SCALES

We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting.We obtain an accurate homogenization result.We also show that as the nonlinear term depends on the microscopic time variable,the global homogenized problem thus obtained is a system consisting of two hyperbolic equations.It is also shown that in spite of the presence of several time scales,the global homogenized problem is not a reiterated one.     

Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales

In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△=A（t）x on time scales. Moreover, for the nonlinear perturbed equation x△= A（t）x ＋ f（t, x） we give the instability of the zero solution when f is sufficiently small.     

含噪音高频数据动态整合估计波动率的方法

时间域和状态域方法是两种常见的非参数估计方法.前者主要使用的是最近的历史数据,而后者则主要依赖于过去的历史信息.本文在时间域上,通过对含噪音高频数据采用双时间尺度方法获得其波动率,进而获得经动态整合后的波动率.     

BOUNDEDNESS AND DISSIPATION FOR DYNAMIC EQUATIONS ON TIME SCALES

In this paper we investigate the boundedness and dissipation for dynamic equations on time scales. By using Lyapunov type function and its Dini-derivative, the boundedness and dissipation criteria for first-order IVP's are obtained. Some examples are given. Finally, we tentatively investigate convergence of the system.     

水分子的化学式仍然应该是H2O

本刊曾在《物理新闻与动态》栏（2003，32（12）：841）上报道过德国柏林技术大学关于在短时间尺度（几阿秒）下探测到水分子的化学式不是H2O，而是H1．5O，当时这个研究成果曾使物理学界很为震动，因而有更多的科学家投身于此项研究中，最近美国Ben Gurion大学的科学家们利用高能中子对纯净的D2O水进行轰击，并在短时间尺度内（10^-17—10^-18s）测量它的反常光散射，     

当代气候的层次和时间序列建模

本文不沿用能量平衡等基本定律，而是在气候层次理论和时间序列的基础上，构造了一个三次非线性气候模式。模拟结果表明，该模式可以近似地描述当代气候的一些特性。     

铁磁合金的快速磁化

由于磁性材料在存储以及其他方面的应用正在向更快速和更小型化方向推进,因此了解固体的物理特性,其中包括电子、光子和声子间的相互作用是极为重要的一个方面．由同步辐射光源产生的x射线是获得超快时间尺度下各种元素具体信息的唯一手段。     

正则长波方程的格子Boltzmann模型

提出了用于正则长波方程的5-Bit格子Boltzmann模型。应用Chapman-Enskog展开和多重尺度技术,通过选择平衡态分布函数的高阶矩,得到了时间尺度t₀上的守恒律,从而给出三阶精度的算法。模型中的参数通过稳定性分析给出。     

OSCILLATION CRITERIA FOR STRONGLY SUPERLINEAR AND STRONGLY SUBLINEAR HIGHER ORDER DYNAMIC EQUATIONS ON TIME SCALES

We establish some new criteria for the oscillation of even order nonlinear dynamic equation. We study the case of strongly super-linear and the case of strongly sub-linear subject to various conditions.     

Artificial boundary conditions for Euler–Bernoulli beam equation

In a semi-discretized Euler-Bernoulli beam equa- tion, the non-nearest neighboring interaction and large span of temporal scales for wave propagations pose challenges to the effectiveness and stability for artificial boundary treat- ments. With the discrete equation regarded as an atomic lattice with a three-atom potential, two accurate artificial boundary conditions are first derived here. Reflection co- efficient and numerical tests illustrate the capability of the proposed methods. In particular, the time history treatment gives an exact boundary condition, yet with sensitivity to nu- merical implementations. The ALEX （almost EXact） bound- ary condition is numerically more effective.