中立型脉冲微分方程正解的存在性

本文利用Banach压缩映射原理，讨论了中立型时滞脉冲微分方程正解的存在性。     

双脉冲电子束源实验

2MeV直线感应加速器注入器系统由电子束产生器和脉冲功率系统组成。电子束产生器包括由感应腔组成的阴极电压叠加器、阳极电压叠加器和真空二极管及束输运系统。脉冲功率系统则包含初级功率源Marx、次级功率源Blumlein线和触发系统，其作用是为感应腔提供一个具有数十纳秒平顶宽度的高压脉冲，激发感应腔在感应腔间隙上获得一个加速电场。在2MeV注入器功率系统中，4个Blumlein线的充气开关是由发散装置的输出触发信号进行导通控制的。通过控制发散输出触发信号到达Blumlein线开关的时间，即可以实现Blumlein线开关在不同时间内触发导通，使Blumlein线依据所设定的时间顺序输出激励脉冲，从而在真空二极管上获得高压脉冲串。由于功率系统采用的是182C结构，即一根Blumlein线驱动两个感应腔，因此最多可以实现四脉冲串列。     

A Quasi-Symmetric Coupled Quantum Well and Its Electric-Optical Properties

We propose a novel coupled quantum well structure, i.e. a quasi-symmetric coupled quantum well (QSCQW). Based on the demands of optical switching devices for quantum well materials, the QSCQW configuration is further optimized. Consequently, in the case of low applied electric field 25kV/cm and low absorption loss 100cm^-1, a large field-induced refractive index change (for TE mode, n = 0.0106; for TM mode, n = 0.0115) is obtained in the QSCQW structure at the operation wavelength 1550hm. The value is in one or two order of magnitude larger than that in a rectangular quantum well and about 50% larger than that of five-step asymmetric coupled quantum well structure under the same working conditions. The refractive index change obtained with the optimized QSCQW under so low absorption loss and applied electric field is very attractive for semiconductor optical switching devices. This manifests that the QSCQW structure has a great potential for applications in ultra-fast and low-voltage optical switches and in travelling wave modulators.     

Existence, Multiplicity and Infinite Solvability of Positive Solutions for One-Dimensional p-Laplacian

The existence, multiplicity and infinite solvability of positive solutions are established for some two-point boundary value problems of one-dimensional p-Laplacian. In this paper, by multiplicity we mean the existence of m solutions, where m is an arbitrary natural number.     

On Best Approximations from RS-sets in Complex Banach Spaces

The concept of an RS-set in a complex Banach space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established,     

具P-Laplacian算子型周期边值问题解的存在性

本文利用拓扑度理论和一些分析技巧讨论了具p—Laplacian算子型周期边值问题(φp(χ’))’+d/dt gradF(χ)+gradG(χ)=e(t),χ(0)=χ(T),χ’(0)=χ’(T)解的存在性,在对阻尼项d/dtgradF(χ)没有任何限制的前提下,给出了解存在的充分条件.     

Sobolev-Hardy不等式与临界双重调和问题

该文讨论一类带有奇异系数的双重调和方程{△^2u-μu/|x|^s=f(x,u),x∈Ω,u=δu/δv=0,x∈δΩ，这里Ω包含R^N是包含0的有界光滑区域，u∈H0^2(Ω），μ∈R是参数，0≤s≤2,△^2=△△表示双重拉普拉斯算子，当f(x,u)=u^p,p=2N/N-4时，上述问题就是一个临界双重调和问题，该文运用Sobolev-Hardy不等式和变分方法，得到它的解的存在性的一些结果。     

矩阵损失下回归系数的线性估计的可容许性

针对广义的Gauss-Markoff模型Y=Xβ+θ,E(θ)=0,Cov(θ)=σ2V,其中X和V＞0是已知的n×p和n×n矩阵;β∈Rp和σ2＞0是未知参数,给出了矩阵损失条件下,Sβ的估计LY+a在非齐次线性估计类中可容许的充要条件.     

双无限随机环境中马氏链的瞬时性与不变函数

在随机环境中马氏链的研究领域,引入了一类π-不可约、常返和瞬时性的概念,给出了π-不可约链是瞬时链的一个充要条件,引入了双无限随机环境中马氏链不变函数的概念,讨论了它们的存在性及基本性质。最后,利用不变函数的性质,给出了π-不可约链是瞬时链的一个判别准则,此准则与不变函数有关。