奇摄动Volterra型积分微分方程Robin问题

本文利用上、下解证明了Volterra型积分微分方程解的存在性。然后，应用所获得的微分不等式理论，在适当的假设下，通过构造特殊的上、下解函数，证明Volterra型 奇摄动积分微分方程解的存在性，并给出一致有效的解的渐近估计。     

Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model

In many applications materials are modeled by a large number of particles (or atoms) where any one of particles interacts with all others. Near or nearest neighbor interaction is expected to be a good simplification of the full interaction in the engineering community. In this paper we shall analyze the approximate error between the solution of the simplified problem and that of the full-interaction problem so as to answer the question mathematically for a one-dimensional model. A few numerical methods have been designed in the engineering literature for the simplified model. Recently much attention has been paid to a finite-element-like quasicontinuum (QC) method which utilizes a mixed atomistic/continuum approximation model. No numerical analysis has been done yet. In the paper we shall estimate the error of the QC method for this one-dimensional model. Possible ill-posedness of the method and its modification are discussed as well.

     

Principal frequency and existence of solutions for quasilinear elliptic obstacle problems

In this paper, we are interested in the first eigenvalue of p-Laplacian and the relation between the first eigenvalue and the existence (or nonexistence) of nontrivial (positive) solution for quasilinear elliptic obstacle problems. Utilizing the fact that obstacle problem have consanguineous relations with corresponding equation, we get a simple approach to study the properties of solutions of obstacle problems, such as existence and nonexistence, regularity and stability, etc. In this paper we are mainly concerned with the existence and nonexistence.     

Rb原子饱和吸收稳频半导体激光器系统

用饱和吸收光谱法对半导体激光器进行稳频，通过对反馈回路的优化设计，得到具有高信噪比的饱和吸收光谱微分误差信号，从而大大提高了半导体激光器的频率锁定灵敏度及长期稳定性，该中用于Rb原子的激光冷却与囚禁。     

各向异性磁化等离子体JEC-FDTD算法

将色散介质的电流密度卷积-时域有限差分(JEC-FDTD)算法推广到各向异性磁化等离子体色散介质.该算法同时解决了电磁波在各向异性和频率色散介质中传播的难题，给出了各向异性磁化等离子体JEC-FDTD算法的公式.计算磁化等离子体平板对平行于磁场传播的电磁波的反射和透射系数，通过与解析结果的比较，验证了该算法的高效性和高精度. 关键词： 色散介质 FDTD算法 各向异性 磁化等离子体     

抽样调查的设计与分析(Ⅱ)

本文讨论抽样调查实践中有关设计和数据分析中的若干问题．第二部分主要涉及数据处理与统计分析问题．     

光子加速器的理论研究

研究了光子加速器(即利用等离子体中的朗谬尔波实现光脉冲频率上转换)所涉及的基本物理问题.文中导出了在存在朗谬尔波的条件下,光脉冲频率对于等离子体本底密度及电子密度扰动的依赖关系,并就最大频率转换、光脉冲俘获、波的加速位相(accelerating phase)以及位相滑动(phase slippage)效应进行讨论.     

Parameter Estimation for Multiscale Diffusions

We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized single-scale model to such multiscale data. We demonstrate, numerically and analytically, that if the data is sampled too finely then the parameter fit will fail, in that the correct parameters in the homogenized model are not identified. We also show, numerically and analytically, that if the data is subsampled at an appropriate rate then it is possible to estimate the coefficients of the homogenized model correctly. The ideas are studied in the context of thermally activated motion in a two-scale potential. However the ideas may be expected to transfer to other situations where it is desirable to fit an averaged or homogenized equation to multiscale data.     

一种低频大功率调频声波束扫描发射系统

本文介绍一种中心工作频率在４．５ｋＨｚ发射电功率８ｋＷ的１６基元线列阵发射系统，并介绍了使用ＤＳＰ５６００１数字信号处理产生线性调频扫描波束发射信号及接收信号的频域处理和和一些测试结果。     

Estimation of parameters in the discrete distributions of order k

This paper considers estimating parameters in the discrete distributions of order k such as the binomial, the geometric, the Poisson and the logarithmic series distributions of order k. It is discussed how to calculate maximum likelihood estimates of parameters of the distributions based on independent observations. Further, asymptotic properties of estimators by the method of moments are investigated. In some cases, it is found that the values of asymptotic efficiency of the moment estimators are surprisingly close to one.