一般组合弹性结构的数学模型

研究由任意多个体、板、梁构成的一般组合弹性结构静态问题. 通过最小势能原理和虚功原理建立问题在向量表示下的数学模型. 在获得了一般组合弹性结构上的广义Korn不等式后, 利用Lax-Milgram引理证明了模型的唯一可解性. 在对解做合理的正则性假设的条件下, 由相应变分形式导出向量表示下的所有平衡方程, 并得到了一个对该问题进行有限元分析时有重要作用的恒等式.     

Spectral Anomalies in the Fraunhofer Diffraction Pattern

We study the spectral characteristics theoretically and experimentally in the Fraunhofer diffraction pattern formed by the diffraction of a spatially coherent, polychromatic light through a slit. It is found that the spectrum in some diffraction directions close to the singular direction is redshifted, compared to the spectrum of the incident polychromatic light, and blueshifted in other directions, and splits into two lines at the singular direction. We show that the experimental results are consistent with the theoretical expectations.     

Incoherently Coupled Grey Photovoltaic Spatial Soliton Families

A theory is developed for incoherently coupled grey photovoltaic soliton families in unbiased photovoltaic crystals. Both the properties and the forming conditions of these soliton families are discussed in detail. The theory can also be used to investigate the dark photovoltaic soliton families. Some relevant examples are presented, in which the photovoltaic-photorefractive crystal is of lithium niobate type.     

Temperature-Dependent Dynamic Properties of LixMn2O4 in Monte Carlo Simulations

Monte Carlo (MC) simulations are used to simulate the voltage profile and the ionic conductivity s of Li ions in LixMn2O4 and its dependence on the lithium concentration x. The open circuit potential shows clearly the two plateaus in the charge/discharge curve, which agrees well with the experimental results. The two plateaus become more and more steep when the temperature is increased. The simulated ionic conductivity shows an M-shaped curve in the plot of ionic conductivity cr versus x when the simulation temperature is low. Interestingly,the minimum valley, which lies at the middle single-phase area near x=0.5, disappears gradually when the temperature increases to 453K.     

Banach空间非线性混合型微分-积分方程整体解的存在性和唯一解

研究了Banach空间中非线性混合型微分-积分方程初值问题u′=f(t,u,Tu,Su),u(0)=x0的整体解,完全没有要求f的任何增性,利用Mnch不动点定理和比较结果得到了初值问题整体解的存在性和唯一解,并且给出了一致收敛于唯一解的迭代序列,改进推广和统一了已有的许多结果.     

德摩根一致代数的度量化

我们给出了德摩根一致代数可伪度量化的一个充分必要条件。     

关于Banach空间中凸泛函的广义次梯度不等式

本文在前人^[1,2]的基础之上，以凸泛函的次梯度不等式为工具，将Jensen不等式推广到Banach空间中的凸泛函，导出了Banach空间中的Bochner积分型的广义Jensen不等式，给出其在Banach空间概率论中某些应用，从而推广了文献[3—6]的工作．     

时间序列和渐近正态性的一个结果

Brockwell和Davis在[1]中给出了时间序列和渐近正态性方面的一个结果，本文用不同的方法且在较弱的条件下，得到了同样的结论。     

关于凸曲面的几个定义的关系

本文讨论了凸曲面的几种定义及其关系，发现有的定义是局部凸的定义，有的是整体凸的定义，有的则对于局部凸和整体凸都适合，最后给出了各种定义之间互推的证明，对于局部凸和整体凸定义之间不能推证的，则说明了原因．     

Radiative Lifetimes of Doubly Ionized Terbium

Radiative lifetimes of two short-lived levels （i.e. 4f^8 （TF6）6p^1/2 （6, 1/2）11/2,13/2） in Tb Ⅲ are measured by time-resolved laser-induced fluorescence （LIE） technique with a two-step excitation process. Free Tb Ⅲ ions are produced in a laser-induced plasma. Lifetime values are evaluated with a deconvolution procedure of the timeresolved fluorescence signal with the temporal shape of second-step excitation pulse （about 1 ns）. The lifetimes of the 4f^8 （^7F6）6p^1/2 （6, 1/2）11/2 and 4f^8（^7F6）6p^1/2 （6, 1/2）13/2 levels are determined to be 1.9 （2） and 2.0 （2）ns, respectively.