带双参数的非线性椭园型本征值问题

本文利用变分方法，将带双参数的非线性椭园本征值问题转化为约束极值问题，得出了非线性本征值问题的分歧解的存在性。     

卡氏积图的Laplacian谱半径的上界

对近年来图的Laplacian谱半径上界的研究成果进行了简单梳理.利用2个图的卡氏积图的特征值,讨论了2个循环图的卡氏积图的Laplacian谱半径的上界问题,得到了几个上界,推广了已有文献的结论.     

路或圈的笛卡尔乘积图的支撑树数

设G是路或圈的笛卡尔乘积图，t(G)表示G的支撑树数.该文借助于第二类Chebyshev多项式给出t(G)的公式，并考虑了t(G)的线性递归关系及渐近性态.     

A quasilinear Neumann problem with discontinuous nonlinearity

In this paper we study a quasilinear boundary value problem of Neumann type with discontinuous terms. In particular we consider a problem in which the p–Laplacian is involved. In order to prove the existence of solutions we replace this problem with a multivalued approximation of it and, using a variational approach for locally Lipschitz functionals, we prove two existence results for it.     

关于3维Minkowski空间中类空曲面的若干结果

在本文，我们证明２维黎曼流形能实现为Ｌ３中的类空极大曲面的充要条件是相应的Ｒｉｃｃｉ条件成立，此外还确定了Ｌ３中其平均曲率向量ｈ满足条件△ｈ＝λｈ（λ∈Ｒ）的类空曲面     

Applications of Markov spectra for the weighted partition network by the substitution rule

The weighted self-similar network is introduced in an iterative way. In order to understand the topological properties of the self-similar network, we have done a lot of research in this field.Firstly, according to the symmetry feature of the self-similar network, we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then, we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally, we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.     

Spectrum comparison on free boundary minimal submanifolds of Euclidean domains

In this paper, using ideas of Simons, Ros, and Savo, we prove a comparison between the spectrums of the stability operator and the Hodge–Laplacian acting on differential 1-forms on a compact minimal submanifold immersed into a Euclidean domain.     

干涉条纹边缘检测方法的比较与改进

研究了干涉条纹边缘检测中的Sobel算子和Laplacian算子,针对二者使干涉条纹变粗和模糊的现象,提出了改进的Laplacian算子。该改进算子先对干涉条纹利用Gauss函数进行平滑,然后再作Laplacian变换。实验结果表明,改进的Laplacian算子克服经典算子的不足,获得清晰的条纹边缘,满足了干涉条纹后续处理要求。     

A modification for the mask-filtering approach by superposing anisotropic derivatives in an image

We demonstrate a novel method to modify the mask-filtering approach by enlarging the gray-level difference of any two nearby pixels in an image. Derivatives are calculated in different directions respectively instead of isotropically. Some higher spatial frequencies are then selectively magnified. The final image has better sharpened fine characteristics than that enhanced by the conventional technique.     

结合NSDTCT和稀疏表示的遥感图像融合

为了提高全色图像与多光谱图像的融合质量,提出一种基于非下采样双树复轮廓波变换和稀疏表示的图像融合算法.对多光谱图像进行亮度-色度-饱和度变换,再对亮度分量和全色图像进行直方图匹配及亮度平滑滤波处理.利用非下采样双树复轮廓波变换处理亮度分量和全色图像,得到对应的高低频系数.对于低频系数,利用稀疏表示进行融合,采用空间频率和l1范数双指标取大的融合规则得到稀疏表示系数;对于高频系数,将改进的拉普拉斯能量和作为脉冲耦合神经网络的外部输入项,提出了改进的脉冲耦合神经网络的融合策略.最后进行非下采样双树复轮廓波逆变换和亮度-色度-饱和度逆变换得到融合结果.实验结果表明,该算法最大限度地保留光谱信息的同时可以提高空间分辨率,视觉效果及客观指标均优于经典的融合算法.