二维周期光子晶格中的非线性Landau-Zener隧穿

在二维周期光子晶格中研究了Kerr型非线性Landau-Zener隧穿. 首先在六方晶系光子晶格中推导出非线性三能级Landau-Zener隧穿模型, 在特殊初值条件下将其转化为非线性二能级模型. 对于三能级隧穿模型, 选择特殊初值, 研究了隧穿率随参数的变化规律. 关键词： 光子晶格 Kerr型非线性 Landau-Zener隧穿     

Joint value-distribution theorems on Lerch zeta-functions. II

We give corrected statements of some theorems from [5] and [6] on joint value-distribution of Lerch zeta-functions (limit theorems, universality, functional independence). We also present a new direct proof of a joint limit theorem in the space of analytic functions and an extension of a joint universality theorem. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 332–350, July–September, 2006.     

On Runge-Kutta-type methods for two-dimensional stochastic differential equations

In the multidimensional case, second-order weak Runge-Kutta methods for stochastic differential equation (SDE) need simulation of correlated random variables, unless the diffusion matrix of SDE satisfies the commutativity condition. In this paper, we show that this can be avoided for some types of diffusion matrices and test functions important for applications. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 403–412, July–September, 2006.     

Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

In this paper,the Dirichlet problem of Stokes approximate of non-homogeneous incompressibleNavier-Stokes equations is studied.It is shown that there exist global weak solutions as well as global andunique strong solution for this problem,under the assumption that initial density ρ_0(x)is bounded away from0 and other appropriate assumptions(see Theorem 1 and Theorem 2).The semi-Galerkin method is applied toconstruct the approximate solutions and a prior estimates are made to elaborate upon the compactness of theapproximate solutions.     

具有吸收-反射边界的Boltzmann-Poisson输运模型的整体弱解

本文研究具有吸收-反射边界的Boltzmann-Poisson输运模型的初这值问题,并利用速度平均的稳定性和L~1空间紧致性理论,在较弱的初边值条件下,证明了其整体弱解的存在性。     

On Cesari's property (Q)

In the present paper, we generalize, within the family of convex-valued multifunctions, a selection theorem of Cole (Ref. 1). This then leads us to prove some new results concerning Cesari's property (Q) and to the introduction of the Cesari limit of sets, which is then compared to the Kuratowski-Mosco limit.This work was done while the author was a visiting professor at the University of Pavia, Pavia, Italy. Financial support was provided by CNR and by NSF Grant No. 84-03135.     

The interaction between zonal flow and Rossby waves with scalar nonlinearity

The nonlinear interactions between zonal flow and Rossby waves are studied by numerical simulations with focus on the effects of scalar nonlinearity. The numerical results show that the scalar nonlinearity has an appreciable influence on the Rossby dipole evolution and can reduce the threshold of the disturbance energy increase.     

延时法测量条纹相机μs档扫描非线性

为实现μs档条纹相机扫描非线性标定,建立了基于延时可调信号源和外触发激光器的条纹相机μs档扫描非线性标定系统,弥补了标准具法的不足。系统通过延时值的递增,得到条纹相机扫描速度在全扫程的变化。系统中时间关系抖动来源主要是测试设备延时抖动和条纹相机触发延时抖动。时间抖动测试与分析显示,条纹相机延时抖动±0.6ns,测试设备延时抖动±0.3ns,系统总时间抖动±0.7ns。系统时间抖动会造成最终时间轴信息的起伏。大量数值模拟分析表明,时间轴起伏对系统时间抖动的影响±2ns,在可以接受的范围内。因此,该系统能够胜任条纹相机μs扫程时间信息的测量标定。     

Discrete semi-stable distributions

The purpose of this paper is to introduce and study the concepts of discrete semi-stability and geometric semi-stability for distributions with support inZ ₊. We offer several properties, including characterizations, of discrete semi-stable distributions. We establish that these distributions posses the property of infinite divisibility and that their probability generating functions admit canonical representations that are analogous to those of their continuous counterparts. Properties of discrete geometric semi-stable distributions are deduced from the results obtained for discrete semi-stability. Several limit theorems are established and some examples are constructed.