THREE-SPHERE INEQUALITIES FOR SECOND ORDER SINGULAR PARTIAL DIFFERENTIAL EQUATIONS

In this article, we give the three-sphere inequalities and three-ball inequalities for the singular elliptic equation div(A▽u)-V u = 0, and the three-ball inequalities on the characteristic plane and the three-cylinder inequalities for the singular parabolic equation ■tu-div(A▽u)+ V u = 0, where the singular potential V belonging to the Kato-Fefferman- Phong’s class. Some applications are also discussed.     

具有正则型点的奇异微分算子的自共轭扩张

在П(L0)n R≠θ的条件下,本文讨论了具有中间亏指数的对称微分算式l(y)的自共轭域,其中П(L0)是由l(y)生成的最小算子L0的正则型域.使用方程l(y)=λ0y,(λ0∈П(L0)∩R)的实参数L2-解,我们对最大算子域DM进行新的分解,由此得到l(y)的自共轭域新的完全解析刻画,其中自共轭边界条件中矩阵M,N的确定与l(y)=λ0y在无穷远点的性质无关,仅与其在t=0点初始值的选择有关.由于自共轭箅子谱是实的,使用实参数λ0不仅有利于我们找到方程的显解,更重要的是可以得到谱的有关信息.     

Coupling three-field formulation and meshless mixed Galerkin methods using radial basis functions

In this work, we solve the elliptic partial differential equation by coupling the meshless mixed Galerkin approximation using radial basis function with the three-field domain decomposition method. The formulation has been adopted to increase the efficiency of the numerical technique by decreasing the error and dealing with the ill conditioning of the linear system caused by the radial basis function. Convergence analysis of the coupled technique is treated and numerical results of some solved examples are given at the end of this paper.     

A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems

This article reports a numerical discretization scheme, based on two‐dimensional integrated radial‐basis‐function networks (2D‐IRBFNs) and rectangular grids, for solving second‐order elliptic partial differential equations defined on 2D nonrectangular domains. Unlike finite‐difference and 1D‐IRBFN Cartesian‐grid techniques, the present discretization method is based on an approximation scheme that allows the field variable and its derivatives to be evaluated anywhere within the domain and on the boundaries, regardless of the shape of the problem domain. We discuss the following two particular strengths, which the proposed Cartesian‐grid‐based procedure possesses, namely (i) the implementation of Neumann boundary conditions on irregular boundaries and (ii) the use of high‐order integration schemes to evaluate flux integrals arising from a control‐volume discretization on irregular domains. A new preconditioning scheme is suggested to improve the 2D‐IRBFN matrix condition number. Good accuracy and high‐order convergence solutions are obtained. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

超越整函数半群的游荡域

设G是由一族超越整函数生成的半群,其中半群运算是函数的复合.在满足某些假设下,文中得到G在其游荡域内的极限函数要么是∞,要么属于G中某个函数φ的奇异值集合singφ~(-1)的导集.     

机器学习方法用于建立乙酰胆碱酯酶抑制剂的分类模型

我们构建了表征乙酰胆碱酯酶抑制剂分子组成、电荷、拓扑、几何结构及物理化学性质等特征的1559个描述符,通过Fischer Score排序过滤和Monte Carlo模拟退火法相结合进行变量筛选得到37个描述符,然后分别用支持向量学习机(SVM)、人工神经网络(ANN)和k-近邻(k-NN)等机器学习方法建立了乙酰胆碱酯酶抑制剂的分类预测模型.对于训练集的515个样本,通过五重交叉验证,各机器学习方法对正样本,负样本和总样本的平均预测精度分别为87.3%-92.7%,67.0%-81.0%和79.4%-88.2%;通过y-scrambling方法验证SVM模型是否偶然相关,结果正样本,负样本和总样本的平均预测精度分别为72.7%-82.5%,41.0%-53.0%和62.1%-69.1%,明显低于实际所建模型的预测精度,表明所建模型不存在偶然相关;对172个没有参与建模的外部独立测试样本,各机器学习方法对正样本,负样本和总样本的预测精度分别为93.3%-100.0%,74.6%-89.6%和86.1%-95.9%.所建模型中,SVM模型预测精度最好,且明显高于其它文献报道结果.     

Total Fractionation and Analysis of Polysaccharides from Leaves of Panax ginseng C. A. Meyer

The water-soluble polysaccharides isolated from the leaves of Panax ginseng C.A.Meyer were totally fractionated into one neutral fraction(GLPN-1),six acidic fractions(GLPN-2,GLPA-1a,GLPA-1b,GLPA-1c,GLPA-2 and GLPA-3) by a combination of ethanol precipitation,ion-exchange and gel permeation chromatography.All the fractions were analyzed by determining monosaccharide composition,molecular weight distribution.The results show that GLPN-1 was mainly composed of Gal(38.1%) and Ara(33.6%) and presumed to be an ar...     

A Cauchy integral method of the solution of the 2D Dirichlet problem for simply or doubly connected domains

In this paper we propose a new method for solving the 2D Laplace equation with Dirichlet boundary conditions in simply and doubly connected domains. Here, we apply the numerical algorithm based on truncated Fourier series and reduce the corresponding Fredholm integral equation to a finite system of linear equations.     

Composite finite element approximation for nonlinear parabolic problems in nonconvex polygonal domains

We study a new class of finite elements so‐called composite finite elements (CFEs), introduced earlier by Hackbusch and Sauter, Numer. Math., 1997; 75:447‐472, for the approximation of nonlinear parabolic equation in a nonconvex polygonal domain. A two‐scale CFE discretization is used for the space discretizations, where the coarse‐scale grid discretized the domain at an appropriate distance from the boundary and the fine‐scale grid is used to resolve the boundary. A continuous, piecewise linear CFE space is employed for the spatially semidiscrete finite element approximation and the temporal discretizations is based on modified linearized backward Euler scheme. We derive almost optimal‐order convergence in space and optimal order in time for the CFE method in the L^∞(L²) norm. Numerical experiment is carried out for an L‐shaped domain to illustrate our theoretical findings.     

Spectral Galerkin approximation and rigorous error analysis for the Steklov eigenvalue problem in circular domain

In this paper, we present spectral Galerkin approximation and rigorous error analysis for the Steklov eigenvalue problem in a circular domain. First of all, we use the polar coordinate transformation and technique of separation of variables to reduce the problem to a sequence of equivalent 1‐dimensional eigenvalue problems that can be solved individually in parallel. Then, we derive the pole conditions and introduce weighted Sobolev space according to pole conditions. Together with the approximate properties of orthogonal polynomials, we prove the error estimates of approximate eigenvalues for each 1‐dimensional eigenvalue problem. Finally, we provide some numerical experiments to validate the theoretical results and algorithms.