Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations

We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods can also be used to form a posteriori error estimators for accessing actual errors of the Petrov-Galerkin finite element solutions. Numerical examples are also provided to illustrate the theoretical results obtained in this paper.     

A total variation based approach to correcting surface coil magnetic resonance images

Magnetic resonance images which are corrupted by noise and by smooth modulations are corrected using a variational formulation incorporating a total variation like penalty for the image and a high order penalty for the modulation. The optimality system is derived and numerically discretized. The cost functional used is non-convex, but it possesses a bilinear structure which allows the ambiguity among solutions to be resolved technically by regularization and practically by normalizing the maximum value of the modulation. Since the cost is convex in each single argument, convex analysis is used to formulate the optimality condition for the image in terms of a primal-dual system. To solve the optimality system, a nonlinear Gauss-Seidel outer iteration is used in which the cost is minimized with respect to one variable after the other using an inner generalized Newton iteration. Favorable computational results are shown for artificial phantoms as well as for realistic magnetic resonance images. Reported computational times demonstrate the feasibility of the approach in practice.     

Comparison of theoretical methods for assessing the heat of formation of C1 and C2 chlorofluorocarbons and hydrochlorofluorocarbons

The heat of formation of a number of key C₁ and C₂ chlorofluorocarbons and hydrochlorofluorocarbons have been calculated by G3, G3MP2, G3MP2B3 and G3B3 methods. Based on the results of the atomization approach, it was found that the errors are approximately dependent upon the number of C-F or C-Cl bonds. Moreover, the bond additive correction (BAC) procedure and isodesmic reactions approach improved the accuracy and decreased these system errors significantly. The extended comparison between the BAC procedure and isodesmic reaction approaches had been made; the latter yielded the best results and showed broader applicability.     

Numerical simulation of the unsteady behaviour of cavitating flows

A 2D numerical model is proposed to simulate unsteady cavitating flows. The Reynolds‐averaged Navier–Stokes equations are solved for the mixture of liquid and vapour, which is considered as a single fluid with variable density. The vapourization and condensation processes are controlled by a barotropic state law that relates the fluid density to the pressure variations. The numerical resolution is a pressure‐correction method derived from the SIMPLE algorithm, with a finite volume discretization. The standard scheme is slightly modified to take into account the cavitation phenomenon. That numerical model is used to calculate unsteady cavitating flows in two Venturi type sections. The choice of the turbulence model is discussed, and the standard RNG k–εmodel is found to lead to non‐physical stable cavities. A modified k–εmodel is proposed to improve the simulation. The influence of numerical and physical parameters is presented, and the numerical results are compared to previous experimental observations and measurements. The proposed model seems to describe the unsteady cavitation behaviour in 2D geometries well. Copyright © 2003 John Wiley & Sons, Ltd.     

The prediction–correction approach to nonlinear complementarity problems

This paper presents a prediction–correction approach to solving the nonlinear complementarity problem (NCP). Each iteration of the new method consists of a prediction and a correction. The predictor is produced by an inexact Logarithmic-Quadratic Proximal method; and then it is corrected by the Proximal Point Algorithm. Convergence of the new method is proved under mild assumptions. Comparison to existing methods shows the superiority of the new method. Numerical experiments including the application to traffic equilibrium problems demonstrate that the new method is attractive in practice.     

原子吸收光谱分析背景校正技术的新进展

对在2004年推向市场的两种商品仪器所采用的两种新的背景校正方法,从方法的原理、演变与形成过程及分析性能等方面进行了较为详细的讨论和解析。     

Improving the energies of approximate wave functions using the concepts of density functional theory

A simple method, derived from DFT, for improving the energy of a trial density is modified for the case of atoms. It is assumed that errors in the interelectronic repulsion are the only significant ones. The errors in the energies of single‐ζ Slater orbitals for the atoms from He to Ne are reduced an average factor of 21. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

自旋相关相对论修正对重夸克偶素性质的研究

自旋相关的相对论修正对有限温度下重夸克偶素的结合和分解的影响进行了讨论,结果表明精细和超精细相互作用特影响对重夸克偶素性质的预言,特别是对ηc和J/ψ起着明显的作用.     

Kornai－Weibull排队模型的纰漏，修正与分析

本文首先指出Ｋｏｒｎａｉ－Ｗｅｉｂｕｌｌ排队模型（Ａ）中之接待率ｒ（ｙ_１）的定义是不正确的，并给出接待率ｒ（ｙ_１，ｙ₂）的正确定义．其次，证明了修正模型（１）有“正常状态”的充要条件是接待能力(?)于是，本文发现接待能力Ｓ的分歧值是Ｓ^＊；当Ｓ＜Ｓ^＊时，市场是短缺的；当Ｓ≥Ｓ^＊时，市场是不短缺的．     

基于反中值滤波的红外焦平面自适应非均匀性校正方法

分析了红外焦平面阵列非均匀性的噪声特性，提出了一种用反中值滤波为核心的红外焦平面自适应校正的方法。针对实际的图像进行了实验，实验证明该方法在校正效果、收敛速度、对静止目标保持能力及可硬件化等方面都有较好的表现。