一类非线性椭圆方程的刘维尔型定理

设（Mⁿ,g）是一个n维非紧的完备黎曼流行.本文考虑有正解的非线性椭圆方程△_fu+au log u=0的刘维尔型定理,其中a是一个非零常数.利用Bochner公式和极大值原理,获得了以上方程在Bakry-Emery里奇曲率有下界时正解的Li-Yau型梯度估计和某些有关的刘维尔理论,推广了文献[7]的结果.     

量子模型分析激光驻波原子透镜的像差

采用量子模型对近共振激光驻波原子透镜会聚Cr原子束、形成纳米量级光栅结构的物理过程进行数值模拟。为提高原子透镜的成像质量,对各种像差,如衍射像差、球差、色差、及原子束发散角、原子磁支能级、原子同位素等因素引起的像差进行了理论分析。模拟结果表明,相比粒子光学模型,量子模型能更加精确地描述原子会聚结果,且能解释原子在驻波光场中的衍射现象。在各种像差中,原子束发散角是最主要的因素,其影响大于衍射像差、球差、色差。原子的磁支能级、同位素等因素对像差影响很小,可以忽略不计。激光冷却准直原子束的方法可以减小束发散角引起的像差,压缩原子速度Vz分布范围的方法可以减小色差。     

不可分辨跃迁阵模型下类镍金离子M带谱的理论计算

 用不可分辨跃迁阵模型(UTA model)计算类镍金(Au ⁵¹⁺)谱中8个跃迁阵的特征参数: 平均波数(kav)、半宽度(FWHM)、总强度(W)和谱线数(L)。利用高斯分布线型,根据各个阵的总强度进行叠加,得到了在总体上与实验相一致的结果,使得在实验中对金M带谱进行时间或空间的高分辨率测量成为可能。     

一类非线性反应扩散方程解的Blow—up问题

本文得用极大值原理研究一类非线性反应扩散方程在各种边界条件下解的Ｂｌｏｗ－ｕｐ问题，给出了整体解不存在的一系列定理，并得到了Ｂｌｏｗ－ｕｐ时间Ｔ的上界。     

Matching Extension Missing Vertices and Edges in Triangulations of Surfaces

Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M₀ in containing M such that .     

一类零膨胀广义线性模型极大似然估计的相合性与渐近正态性

讨论了响应变量为单参数指数族且在零点处膨胀的广义线性模型的大样本性质,对其参数进行了极大似然估计,给出了一些正则条件.基于所提出的正则条件,证明了模型参数极大似然估计的相合性与渐近正态性.     

基于Poisson-Markov分布最大后验概率的多通道超分辨率盲复原算法

在Poisson和Markov随机场分布假设基础上,改进了存在噪声时多通道互限制原则,提出了一种基于最大后验概率判据的多通道图像盲复原算法,可在无需已知通道内离散点扩散函数性质、类型和具体分布等先验知识的情况下,在图像幅度限制约束空间和离散点扩散函数能量恒定约束空间内,通过对图像和离散点扩散函数的交替迭代,使两者收敛到全局最优解,最终复原出超分辨率图像.对计算机模拟和实际存在微平移、微离焦情况的图像处理表明：算法在不同信噪比水平和非命中PSF尺寸下具有良好的图像复原效果和稳定性. 关键词： 泊松-马尔科夫分布 最大后验概率 多通道 盲复原     

Maximum principles for generalized solutions of quasi-linear elliptic equations

1　IntroductionandMainRrsultsSincethe 1 950s,therehasbeenarapidprogressinthestudyoftheregularitytheoryforgeneralizedsolutionsofsecond_orderlinearellipticequationsindivergenceformwithseveralvariables,whichhasplayedanimportantroleinthestudyofquasi_linearequations (seeRefs.[1 ,2 ] ) .But,inspiteofthefactthatMorry[3 ]provedtheFredholmAlternativetheoremwithrespecttotheexistenceofgeneralizedsolutionsofsecond_orderlinearellipticequationsindivergenceform (whichisageneralizationoftheclassicaltheory)a…     

Size ramsey numbers of stars versus 4‐chromatic graphs

We investigate the asymptotics of the size Ramsey number î(K_1,nF), where K_1,n is the n‐star and F is a fixed graph. The author 11 has recently proved that r?(K_1,n,F)=(1+o(1))n² for any F with chromatic number χ(F)=3. Here we show that r?(K_1,n,F)≤ n²+o(n²), if χ (F) ≥ 4 and conjecture that this is sharp. We prove the case χ(F)=4 of the conjecture, that is, that r?(K_1,n,F)=(4+o(1))n² for any 4‐chromatic graph F. Also, some general lower bounds are obtained. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 220–233, 2003     

An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.