一类具有星形结点的平面四次多项式系统的全局结构及其实例

主要讨论一类具有星形结点的平面四次多项式微分系统的全局结构,用系统的积分直线把相平面分成四类扇形区域,根据系统的有限远奇点的情况,给出了相应的实例及其全局结构。     

Analysis of three graph parameters for random trees

We consider three basic graph parameters, the node‐independence number, the path node‐covering number, and the size of the kernel, and study their distributional behavior for an important class of random tree models, namely the class of simply generated trees, which contains, e.g., binary trees, rooted labeled trees, and planted plane trees, as special instances. We can show for simply generated tree families that the mean and the variance of each of the three parameters under consideration behave for a randomly chosen tree of size n asymptotically ～μn and ～νn, where the constants μ and ν depend on the tree family and the parameter studied. Furthermore we show for all parameters, suitably normalized, convergence in distribution to a Gaussian distributed random variable. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

Node adaptive domain decomposition method by radial basis functions

During the last years, there has been increased interest in developing efficient radial basis function (RBF) algorithms to solve partial differential problems of great scale. In this article, we are interested in solving large PDEs problems, whose solution presents rapid variations. Our main objective is to introduce a RBF dynamical domain decomposition algorithm which simultaneously performs a node adaptive strategy. This algorithm is based on the RBFs unsymmetric collocation setting. Numerical experiments performed with the multiquadric kernel function, for two stationary problems in two dimensions are presented. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

对余弦型振荡函数Gauss积分的进一步探讨

克服了以往成果中对余弦型振荡函数进行Gauss积分的一些缺点,对余弦型振荡函数的Gauss积分的做了进一步的探讨.     

HANGING NODES IN THE UNIFYING THEORY OF A POSTERIORI FINITE ELEMENT ERROR CONTROL

A unified a posteriori error analysis has been developed in [18, 21-23] to analyze the finite element error a posteriori under a universal roof. This paper contributes to the finite element meshes with hanging nodes which are required for local mesh-refining. The twodimensional 1-irregular triangulations into triangles and parallelograms and their combinations are considered with conforming and nonconforming finite element methods named after or by Courant, Q1, Crouzeix-Raviart, Poisson, Stokes and Navier-Lamé equations Han, Rannacher-Turek, and others for the The paper provides a unified a priori and a posteriori error analysis for triangulations with hanging nodes of degree ≤ 1 which are fundamental for local mesh refinement in self-adaptive finite element discretisations.     

On structural properties of scale-free networks with finite size

Since many large real networks tend to present scale-free degree distribution, this paper investigates the structural properties of scale-free networks with finite size. Beginning with a comprehensive analysis of the degree distribution consisting of the concentration trend, dispersion and inequality, this paper then focuses on the discussion of heterogeneity and hub nodes of scale-free networks. The findings will help to improve our understanding of the structure and function of real networks.     

Identifying all-around nodes for spreading dynamics in complex networks

Identifying the most influential nodes in complex networks provides a strong basis for understanding spreading dynamics and ensuring more efficient spread of information. Due to the heterogeneous degree distribution, we observe that current centrality measures are correlated in their results of nodes ranking. This paper introduces the concept of all-around nodes, which act like all-around players with good performance in combined metrics. Then, an all-around distance is presented for quantifying the influence of nodes. The experimental results of susceptible-infectious-recovered (SIR) dynamics suggest that the proposed all-around distance can act as a more accurate, stable indicator of influential nodes.     

具有星形结点的平面五次系统的全局结构分析

该文对具有星形结点的平面五次系统的全局结构的拓扑分类应用Ⅰ Ⅳ型区域(见［2］),讨 论了平面五次系统（1）的全局结构的拓扑分类，并得到93种全局结构及其右边多项式系统的判定方法。      

Enhanced Charge Transfer Process and Photocatalytic Activity over a Phosphonate-based MOF via Amorphization Strategy

Recently, amorphous materials have gained great attention as an emerging kind of functional material, and their characteristics such as isotropy, absence of grain boundaries, and abundant defects are very likely to outrun the disadvantages of crystalline counterparts, such as low conductivity, and ultimately lead to improved charge transfer efficiency. Herein, we investigated the effect of amorphization on the charge transfer process and photocatalytic performance with a phosphonate-based metal–organic framework (FePPA) as the research object. Comprehensive experimental results suggest that compared to crystalline FePPA, amorphous FePPA has more distorted metal nodes, which affects the electron distribution and consequently improves the photogenerated charge separation efficiency. Meanwhile, the distorted metal nodes in amorphous FePPA also greatly promote the adsorption and activation of O₂. Hence, amorphous FePPA exhibits a better performance of photocatalytic C(sp³)−H bond activation for selective oxidation of toluene to benzaldehyde. This work illustrates the advantages of amorphous MOFs in the charge transfer process, which is conducive to the further development of high performance MOFs-based photocatalysts.     

一类基于点-面模式的低阶单元接触搜索方法

本文基于三个接触搜索准则提出接触预搜索概念。在接触预搜索阶段通过分级筛选方法逐步缩上可能接触点副的单元集;然后,给出动态有限元分析中适用分析中适用于大骨移的低阶单元接触点副的自动搜索算法。针对非线性动态接触问题有限元分析中常用低阶单元和点－面模式的搜索方式的情况,本文应用最近点投影搜索算法提出似以等参坐标为参数的另一种接触搜索算法。该搜索算法不须预先指定可能接触范围,从而极大地降低了数据的准备工作