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。     

Spectrum of a homogeneous graph

We describe the spectrum of the Laplacian for a homogeneous graph acted on by a discrete group. This follows from a more general result which describes the spectrum of a convolution operator on a homogeneous space of a locally compact group. We also prove a version of Harnack inequality for a Schrödinger operator on an invariant homogeneous graph.     

A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula

In this article, a novel numerical method is proposed for nonlinear partial differential equations with space- and time-fractional derivatives. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor's formula. The fractional derivatives are considered in the Caputo sense. Several illustrative examples are given to demonstrate the effectiveness of the present method. Results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. Results also show that the numerical scheme is very effective and convenient for solving nonlinear partial differential equations of fractional order.     

基于微分算子的边缘检测法在基因芯片图像识别中的应用

一种基于梯度算子和拉普拉斯算子检测医学基因芯片荧光数字图像边缘的方法．数字图像经过图像增强等预处理以后，突出了我们感兴趣的数字图像特征，根据数字图像灰度变化的趋势，用灰度变化的一阶导数(梯度算子)检测图象中的边缘区域；用灰度变化的二阶导数确定图像边缘的中心位置．最后根据某些预定的准则把满足这些准则的象素组成一条边缘．     

Non-linear ground state representations and sharp Hardy inequalities

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.     

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.     

Weighted scattering matrices of regular coverings of graphs

We give a decomposition formula for the determinant det(I ? U(λ)) of the weighted bond scattering matrix U(λ) of a regular covering of G. Furthermore, we define an L-function of G, and give a determinant expression of it. As a corollary, we express some determinant of the weighted bond scattering matrix of a regular covering of G by means of its L-functions.     

Flow of a viscoelastic fluid with the fractional Maxwell model between two side walls perpendicular to a plate

The unsteady flow of a viscoelastic fluid with the fractional Maxwell model between two side walls perpendicular to a plate is investigated. Exact solutions for the velocity field are established by means of the Fourier and Laplace transforms. The similar solutions for Maxwell and Newtonian fluids can be obtained as limiting cases of our results. In the absence of side walls, all solutions that have been determined reduce to those corresponding to the motion over an infinite plate.     

A Cautionary note on modeling with fractional Lévy flights

Temporal scaling and infinite variance are two stylized features often seen together in times series of complex systems. We find that because of their infinite moments samples from fractional Lévy flights produce bi-linear scaling functions which may be incorrectly attributed as evidence of multifractality. We argue that it is unnecessary to consider truncated fractional Lévy flights which are inherently problematic.     

Majorization for certain classes of analytic functions defined by fractional derivatives

Here we investigate a majorization problem involving starlike function of complex order belonging to a certain class defined by means of fractional derivatives. Relevant connections of the main results obtained in this paper with those given by earlier workers on the subject are also pointed out.