基于二元光学设计的高能激光窗口的初步探讨

对非均匀近场强度分布影响强激光远场聚焦效果的原因进行了分析。对高能激光窗口进行了二元光学设计。提高了光束强度分布的均匀性,改善了光束质量。介绍了二元光学设计的基本原理,采用随机并行扰动爬山法对窗口的位相分布、变换后的光束强度分布、衍射效率和光束均匀性进行了计算。计算结果表明,基于二元光学设计的激光窗口能有效地改善光束强度分布的均匀性,提高了发射光束的质量。     

烧蚀引起R－T不稳定性实验条件的初步研究

激光和辐射烧蚀引起的Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ（Ｒ－Ｔ）不稳定性是激光聚变的重要研究课题，本文讨论了Ｒ－Ｔ不稳定性实验的有关要求，在考虑烧蚀致稳的情况下，对特定的塑料薄膜靶用解析公式计算了Ｒ－Ｔ不稳定性线性发展阶段的积分增长指数随扰动波长、驱动源强度和持续时间的变化。给出某些感兴趣的物理图象，提供的信息可供有关实验和靶设计参考。     

Moist Potential Vorticity Anomaly with Heat and Mass Forcings in Torrential Rain Systems

The moist potential vorticity (MPV) equation is derived from complete atmospheric dynamic equations with both heat and mass forcings,with which the impermeability theorem of the “MPV substance” is proven.It is clarified that both heat and mass forcings induced by the intensive precipitation in torrential rain systems can lead to the MPV anomaly.The MPV substance anomaly is a dynamical tracer for tracking a torrential rain system.     

薄板声谐振子扰动的声学特征检测研究

为进行快速ＮＤＴ，研究了薄板声谐振子扰动和声学特征变化的关系，用有限元方法分析在睡无缺陷薄板的振动频率和振型。利用数字信号处理技术，实验研究了样品中缺陷对声学特征的影响。实现和理论分析结果一致性很好。研究结果有助于正确利用样品声学特征进行无损检测。     

三倍频激光束特性传输变换的近似模型

针对具有振幅和位相扰动的激光束的三次谐波转换，理论上研究了三倍频激光束特性的传输变换，给出了光束质量Ｍ２因子、振幅和位相扰动变换的近似解析模型，可为高功率激光驱动器的设计提供理论依据。     

退化的无穷维Hamilton系统的KAM定理

给出了一类较弱的非退化条件,证明了满足该弱非退化条件的退化可积的无穷维Hamilton系统在小扰动下的不变环面存在定理,同时还给出了存在不变环面的参数集合的测度估计.值得一提的是该非退化条件在解析情形下可能是最弱的(受有限维情况的启示).主要运用了KAM技巧证明不变环面的存在性,给出了与上述测度估计有关的小分母条件的测度估计.     

正则Cosine算子函数的乘积扰动定理

本文研究了正则cosine算子函数的乘积扰动性,在正则化算子C的值域不 一定稠密的一般情形下,获得了若干正则cosine算子函数的乘积扰动定理.     

An Exact Evolution Equation of the Curvature Perturbation for Closed Universe

As is well known, the exact evolution equation of the curvature perturbation plays a very important role in investigation of the inflaorresponding exacttion power spectrum of the flat universe. However, the c extension for the non-flat universes has not yet been given clearly. Interest in the non-flat, specially closed, universes has been aroused recently. The need for this extension is pressing. We start with the most elementary physical consideration and obtain finally this exact evolution equation of the curvature perturbation for the non-flat universes, as well as the evolutionary controlling parameter and the exact expression of the variable mass in this equation. We approximately perform a primitive and immature analysis on the power spectrum of non-flat universes. This analysis shows that the exact evolution equation of the curvature perturbation for the non-flat universes is very complicated, and we need to carry out many numerical and analytic works for this new equation in the future to judge whether the universe is fiat or closed by comparison of theories with observations.     

A Class of Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations with Boundary Perturbation

A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems is studied using the theory of differential inequalities.     

正则预解算子族的乘积扰动

设K∈C（R＋）和B是一个有界线性算子．作者证明如果犃生成一个指数有界的A正则预解算子族，那么BA，AB或A（I＋B），（I＋B）A也生成一个指数有界的k-正则预解算子族．此外，作者也给出了k正则预解算子族的加法扰动的相应结果．