A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

极小相关组的Matlab实现及其在编码中的应用

纠错码技术是通信技术中不可或缺的一项技术,并在当今的通信技术发展中占有很高的地位,线性分组码是常用的一种纠错码,其纠错能力的计算需要以线性分组码最小码距的计算为基础。向量组极小相关组的提出,引入了向量组的距的定义,为线性分组码纠错能力的计算提供了新思路,极小相关组的有效而且快速求解方法研究将是一个新课题,针对计算机通信科学发展的需求,基于遍历法的思想,运用Matlab软件编写程序求解向量组的极小相关组,并将程序简单应用于具体向量组极小相关组的计算以及线性分组码纠错能力的计算。     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

Multicriteria decision making under uncertainty

Formalization for problems of multicriteria decision making under uncertainty is constructed in terms of guaranteed and weak estimates. A relevant definition of the vector maximinimax value is given. Parameterization and approximation of maximum, minimax, and maximinimax values based on the inverse logical convolution are suggested. An application for multicommodity networks is considered. Received: December 13, 2000 / Accepted: August 21, 2001?Published online May 8, 2002     

一类按学生素质优劣排序的数学方法

用模糊学方法定量评定了学生的综合素质，并按素质的优劣给学生进行了排序，这里是将数学方法引入教学管理的初步尝试。     

Specific anti-tumor effect induced by attenuated Salmonella typhimurium vaccine expressing extracellular region of vascular endothelial growth factor receptor 2

The purposes of this research were to study the stable expression of exogenous gene encoding therapeutic protein in attenuated Salmonella typhimurium, observe the metabolism of oral gene vaccine carried by attenuated Salmonella typhimurium in BALB/c mouse, and investigate the feasibility of prevention and treatment of tumors by the recombinant bacteria. Recombinant plasmid pcDNA3.1 VEGFR2(n1-7) was transformed into competent attenuated Salmonella typhimurium SL3261 to develop oral DNA vaccine SL3261-pcDNA3.1 VEGFR2(n1-7). To observe whether the exogenous gene can be expressed in the recombinant bacteria, PCR was performed to amplify the CMV promoter of the eukaryotic expression vector as the proof of stable expression of exogenous protein; transmission elec- tron microscopy (TEM) was applied to observe the morphology of the recombinant bacteria to confirm that the exogenous gene has no impact on the growth of the bacteria, and then BALB/c mice were immunized with the gene vaccine. After inoculation of the gene vaccine, the recombinant bacteria SL3261 could be detected in the tissues such as small intestine, colon, liver and spleen. And then, mice in each group were challenged with tumor cells. The results of animal experiment showed that tumor growth of the mice in experimental group was inhibited and survival time of immunized mice was prolonged compared with control groups. A higher lymphocyte infiltration in tumors from animals treated with DNA vaccine was observed. Immunohistochemical analysis of tumor samples revealed an en- hanced accumulation of CD8 cytotoxic T lymphocytes, as well as an increase in CD4 cells in the tumors of animals treated with the oral gene vaccine compared to tumors from control group mice. Ultrastructure of the tumor tissue showed that tumor cells in the samples of the immunized mice were well-differentiated. Our research confirmed that the exogenous gene can be stably expressed in the attenuated Salmonella typhimurium and has no impact on the growth of the recombinant bacteria; the exogenous gene can de delivered to the host by attenuated Salmonella typhimurium to produce anti-tumor effect with no obvious cytotoxity to the host. In this study, it is established that attenuated Salmonella typhimurium could be used as a vector for oral gene vaccine, and our study provided a theoretical basis for the body distribution and the metabolism of the recombinant bacteria. This strategy may provide a simple, safe and effective way for the prevention and treatment of tumors.     

电动势的测定及其应注意的问题

本课题通过用不同的方法测定的电动势分析,经过电动势测定的误差分析,找到各种方法的利弊,并且对电极制备以及测定电动势的装置进行改进,近而对问题进行探讨。改进后找到实验和研究的捷径,从而在高等学校化学实验以及生产中节省很多的人力和财力。     

A model study for the steady state error of numerical approximations of inviscid flow equations on Cartesian grid

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. In this paper we consider the influence of the refined interfaces on the steady state errors for second‐order three‐point difference approximations of flow equations. Since the various characteristic components of the Euler equations should behave similarly on such grids with regard to refinement‐induced errors, it is sufficient enough to conduct the analysis on a scalar model problem. The error we consider is a global error, different to local truncation error, and reflects the interaction between multiple interfaces. The steady state error will be compared to the errors on smooth refinement grids and on uniform grids. The conclusion seems to support the numerical findings of Yamaleev and Carpenter (J. Comput. Phys. 2002; 181: 280–316) that refinement does not necessarily reduce the numerical error. Copyright © 2005 John Wiley & Sons, Ltd.     

A posteriori error estimates for a time discrete scheme for a phase-field system of Penrose-Fife type

A time discrete scheme is used to approximate the solution toa phase field system of Penrose–Fife type with a non-conservedorder parameter. An a posteriori error estimate is presentedthat allows the estimation of the difference between continuousand semidiscrete solutions by quantities that can be calculatedfrom the approximation and given data.