An acceleration method for integral equations by using interpolation post-processing

Two post-processing techniques are widely used in the literature in the context of convergence acceleration. One of them is an interpolation technique, used for partial differential equations and integral differential equations, and the other is an iteration technique used for integral equations. These two techniques, interpolation and iteration, are quite different, and the former is simpler. Can we use the interpolation technique for integral equations instead of using the second iteration technique? This report gives a positive answer.

     

Preparation and third-order nonlinear optical properties of self-organized complex oxide Ce: BaTiO3 quantum dots

Pulsed laser ablation epitaxial Strancky-Krastanow growth of self-organized complex oxide Ce:BaTiO₃ quantum dots on MgO(lOO) substrates is demonstrated. Atomic force microscopy and X-ray diffraction are used to observe the structure and the growth process of the self-organized complex oxide quantum dots. The average dimension, height, and the density of self-organized complex oxide Ce:BaTiO₃ quantum dots are given. The nonlinear refractive indexes of the wetting layer and the selforganized ordered quantum dots are determined by the single beam Z-scan method. The mechanisms of the nonlinear effect enhancement for these low-dimensional structure are discussed.     

Numerical Simulation for Convection-Diffusion Problem with Periodic Micro-Structure

In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problems is provided. The error estimates between the exact solution and the approximation solution, of the homogenized equation or the two-scale finite element scheme are analyzed. It is shown that the scheme provided in this article is convergent for any fixed diffusion coefficient 5, and it may be convergent independent of δ under some conditions. The numerical results demonstrating the theoretical results are presented in this article.     

Superconvergence analysis and a posteriori error estimation of a finite element method for an optimal control problem governed by integral equations

In this paper, we discuss the numerical simulation for a class of constrained optimal control problems governed by integral equations. The Galerkin method is used for the approximation of the problem. A priori error estimates and a superconvergence analysis for the approximation scheme are presented. Based on the results of the superconvergence analysis, a recovery type a posteriori error estimator is provided, which can be used for adaptive mesh refinement. The research project is supported by the National Basic Research Program under the Grant 2005CB321701 and the National Natural Science Foundation of China under the Grant 10771211.     

Superconvergence analysis of the nonconforming quadrilateral linear-constant scheme for Stokes equations

In this paper, the superconvergence analysis of the nonconforming quadrilateral linear-constant scheme for Stokes Equations is discussed. The superclose property is proven for rectangular meshes; then global superconvergence is derived by applying a postprocessing technique. In addition, some numerical examples are presented to demonstrate our theoretical results. The research was supported by National Natural Science Foundation of China (No. 60474027).     

A sparse finite element method with high accuracy Part I

Summary. In this paper, we develop and analyze a new finite element method called the sparse finite element method for second order elliptic problems. This method involves much fewer degrees of freedom than the standard finite element method. We show nevertheless that such a sparse finite element method still possesses the superconvergence and other high accuracy properties same as those of the standard finite element method. The main technique in our analysis is the use of some integral identities. Received October 1, 1995 / Revised version received August 23, 1999 / Published online February 5, 2001     

插值与逼近混合的三重细分法

提出了一种新的四点三重插值曲线细分法和一种含参数的三次B-样条曲线细分法,利用提出的这两种曲线细分方法得到了一种插值与逼近混合的三重曲线细分法。 这种混合细分法将插值细分和逼近细分统一为同一格式。 给出了这种混合细分法的几何解释,分析了其连续性, 并将其推广到曲面情形,提出了四边形网格上的1-9插值曲面细分法和张量积三次B-样条曲面细分法。利用这两种曲面细分法,得到了插值与逼近相混合的三重曲面细分法,并分析了其连续性。 数值实例表明,方法是合理有效的。     

疏水性多糖的合成及荧光法研究其在水中的自聚集行为

由胆固醇与１,６－已二异氰酸酯反应合成了１,６－已二异氰酸酯胆固醇单脂（Ｉ）,然后通过葡聚糖与（Ｉ）反应合成了具有自聚集性质的葡聚糖,测得葡聚糖主链上每１００个糖环含有３－５个胆固醇。我们采用探针式超声波来制得胆固醇修饰葡聚糖「ＣＨＤ」的水溶液,同时用Ｎ－苯基－α－萘胺「ＰＮＡ」作为荧光探针来研究ＣＨＤ自聚集过程。在实验中我们发现,每一种葡聚糖溶液,都存在着一个临界浓度。在此浓度之上,ＰＮＡ的荧光     

吲哚七甲川类荧光探针在生物体应用的研究现状

菁染料是一种商品化的近红外荧光染料, 其光谱范围位于近红外区域, 此光谱区域内生物基体光吸收或荧光强度较小, 因此利用菁染料对生物体进行成像, 可以降低背景干扰. 吲哚七甲川菁染料是一类具有代表性的菁染料, 其由吲哚杂环、七甲川链和N-取代基侧链组成, 由于具有溶解性好, 最大吸收波长可调, 摩尔消光系数大等优良的光学性质, 被广泛用于肿瘤靶向治疗、蛋白标记、痕量金属离子检测等生物方面. 以吲哚七甲川为母体, 通过向母体中引入活性基团或改变它们的结构, 使探针具有不同的功能, 这已成为生物领域荧光成像的研究热点. 分别从检测金属阳离子、pH变化、小分子和靶向标记肿瘤细胞、蛋白质等方面综述了近年来用于生物体荧光成像的吲哚七甲川类荧光探针的研究进展, 其中也对荧光探针在生物体内(模型)分布、光学成像及代谢方面进行了介绍, 最后讨论了这类荧光探针存在的问题及发展趋势.