一类非线性Schr(o)dinger方程的非协调有限元分析

在半离散格式下研究一类带幂次非线性项的Schr(o)dinger方程的非协调矩形EQrot1元方法.直接利用插值技巧和该单元的两个特殊性质(相容误差比插值误差高一阶及其插值算子与传统的Ritz投影是一致的),给出相应的收敛性分析及误差估计.     

一类带扩散的聚合物模型的定性分析

本文研究一类带扩散的聚合物模型,并在参数γ＞0和γ＜0两种不同情形给出定性分析.主要运用抛物型方程比较原理和相应常微分方程的结论得到反应扩散方程的先验估计和渐近性分析.     

面板数据空间误差分量模型的GMM估计及其应用

本文研究面板数据空间误差分量模型(Spatial Error Components Model,SEC)的估计方法。为克服极大似然法在SEC模型估计中运算的困难,本文提出基于广义矩估计的可行广义最小二乘法(GMM-GLS),证明了估计量的一致性及有限样本下的有效性;并应用此模型,研究2000-2007年中国30个省(西藏除外)的物质资本存量、人力资本存量及能源消耗对实际GDP的影响,结果表明,采用SEC模型所得估计结果更为符合经济现实。     

美式障碍期权定价的总体最小二乘拟蒙特卡罗模拟方法

障碍期权的价格依赖于其标的资产的价格路径,实际市场中标的资产的价格变化存在跳跃现象。本文在跳跃扩散模型下使用总体最小二乘拟蒙特卡罗方法(TLSFM)对美式障碍期权定价问题进行了研究。TLSFM使用随机化的Faure序列并结合总体最小二乘回归方法,改进了Longstaff等提出的最小二乘蒙特卡罗模拟方法(LSM)。通过基于TLSFM与LSM和改进的三叉树方法的美式障碍期权定价结果的比较分析,说明了基于TLSFM的美式障碍期权定价具有结果稳定,时效性更强的优势。     

基于M估计的纵向数据线性混合模型中方差的齐性检验

本文对纵向数据的线性混合模型,用Fisher得分法得到了参数的M估计(稳健估计),给出了其渐近性质,研究了M估计下异方差的Score检验问题,并对检验统计量的功效进行了模拟,最后通过葡萄糖数据的实例说明了本文方法的有效性。     

一类非线性趋化方程的能控性及时间最优控制

本文研究一类非线性趋化方程的局部能控性和时间最优控制的存在性问题.该方程不仅具有非线性的drift-diffuion项?·(χu?v),而且具有非线性的细菌消耗项uf(v).研究该方程主要运用了相应线性方程的零能控性和Kakutani不动点定理的方法.     

一类半线性椭圆方程柯西问题的正则化方法

构造并利用一种广义分数Tikhonov正则化方法研究一类半线性椭圆方程柯西问题.基于所构造的正则化解满足一个非线性积分方程,首先证明正则化解的存在唯一性和稳定性;继而在对精确解的先验假设下给出并证明正则化方法的收敛性;最后设计一种迭代算法计算正则化解,并通过相应的计算结果验证了所提方法的稳定可行性.     

Resonant energy transfer from nanocrystal Si to β-FeSi2 in hybrid Si/β-FeSi2 film

The photoluminescence （PL） characteristics of hybrid β-FeSi2/Si and pure β-FeSi2 films fabricated by pulsed laser deposition at 20 K are investigated. The intensity of the 1.54-μm PL from the former is enhanced, but the enhancement vanishes when the excitation wavelength is larger than the widened band gap of Si nanocrystal. Time-resolved PL decay measurements reveal that the lifetime of the photo-excited carriers in the hybrid β-FeSi2/Si film is longer than that in the pure β-FeSi2 film, providing evidence that the PL enhancement results from the resonant charge transfer from nanocrystalline Si to β-FeSi2.     

Effect of vacancy charge state on positron annihilation in silicon

The charge-state-dependent lattice relaxation of mono-vacancy in silicon is studied using the first-principles pseu- dopotential plane-wave method. We observe that the structural relaxation for the first-neighbor atoms of the mono-vacancy is strongly dependent on its charge state. The difference in total electron density between with and without charge states in mono-vacancy and its relevant change due to the localized positron are also examined by means of first-principles simu- lation, demonstrating the strong interplay between positron and electron. Our calculations reveal that the positron lifetime decreases with absolute charge value increasing.     

Auditory filter based broadband MUSIC algorithm for sound source localization

Based on the analysis of the shortcomings of broadband MUSIC algorithm with short-time Fourier transform （SF-MUSIC） for sound source localization, a broadband MUSIC algorithm with auditory filter （AF-MUSIC） was proposed. The proposed algorithm first em- ploys auditory filter bank to decompose the signals received on the microphone array, and then locates the sound source with MUSIC algorithm over every frequency channel. At last, by combining with the subinterval frequency estimation, the final localization result is gained. Evaluations on the proposed algorithm prove that comparing with the SF-MUSIC algorithm, the AF-MUSIC algorithm decreases the average error of the estimation results with 2.5479 de- gree in different source conditions. The accuracy of sound source DOA estimation is enhanced effectively.