Riabouchinsky flow with partially penetrable obstacle

An explicitly solvable Riabouchinsky model with a partially penetrable obstacle is introduced. This model applied to the estimation of the efficiency of free flow turbines allows us to take into account the pressure drop past the lamina.     

Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Problems, Models and Complexity. Part II: Application to the DLSP

In Part I of this study, we suggest to identify an operations research (OR) problem with the equivalence class of models describing the problem and enhance the standard computer-science theory of computational complexity to be applicable to this situation of an often model-based OR context. The Discrete Lot-sizing and Scheduling Problem (DLSP) is analysed here in detail to demonstrate the difficulties which can arise if these aspects are neglected and to illustrate the new theoretical concept. In addition, a new minimal model is introduced for the DLSP which makes this problem eventually amenable to a rigorous analysis of its computational complexity.     

A nodal coupling of finite and boundary elements

This article presents and analyzes a simple method for the exterior Laplace equation through the coupling of finite and boundary element methods. The main novelty is the use of a smooth parametric artificial boundary where boundary elements fit without effort together with a straight approximate triangulation in the bounded area, with the coupling done only in nodes. A numerically integrated version of the algorithm is also analyzed. Finally, an isoparametric variant with higher order is proposed. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 555–570, 2003     

Molecular dynamics simulation of entropy and surface tension for grain boundary of α-Fe

The grain boundary is an interface and the surface tension is one of its important thermodynamic properties. In this paper, the surface tension of the ∑9 grain boundary for α-Fe at various temperatures and pressures is calculated by means of Computer Molecular Dynamics (CMD). The results agree satisfactorily with the experimental data. It is shown that the contribution of entropy to surface tension of grain boundary can be ignored. The project supported by the National Natural Science Foundation of China and the Science Foundation of Chinese Academy of Sciences.     

Regularization of singular systems of linear algebraic equations by shifts

Regularization of singular systems of linear algebraic equations by shifts is examined. New equivalent conditions for the shift regularizability of such systems are derived.     

求解P0函数互补问题的一种微分方程方法

本针对P0函数互补问题，给出了一种微方程方法，并且证明了P0函数互补问题的解是微分方程系统的渐进稳定平衡点。在适当的假设条件下，证明了所给出的算法具有二次收敛速度。几个数值例子表明了该算法的有效性。     

基于矩阵初等变换的n元函数极值的快速判别法

给出了 n元函数极值的一个充分条件 ,并结合矩阵的初等变换建立了 n元函数极值的一种快速判别法 ,最后给出了一个例子     

Manufacturing cell formation using similarity coefficients and a parallel genetic TSP algorithm: Formulation and comparison

Many algorithms have been proposed to form manufacturing cells from component routings. However, many of these do not have the capability of solving large problems. We propose a procedure using similarity coefficients and a parallel genetic implementation of a TSP algorithm that is capable of solving large problems of up to 1000 parts and 1000 machines. In addition, we also compare our procedure with many existing procedures using nine well-known problems from the literature.

The results show that the proposed procedure compares well with the existing procedures and should be useful to practitioners and researchers.     

A note on the complex semi‐definite matrix Procrustes problem

This note outlines an algorithm for solving the complex ‘matrix Procrustes problem’. This is a least‐squares approximation over the cone of positive semi‐definite Hermitian matrices, which has a number of applications in the areas of Optimization, Signal Processing and Control. The work generalizes the method of Allwright (SIAM J. Control Optim. 1988; 26 (3):537–556), who obtained a numerical solution to the real‐valued version of the problem. It is shown that, subject to an appropriate rank assumption, the complex problem can be formulated in a real setting using a matrix‐dilation technique, for which the method of Allwright is applicable. However, this transformation results in an over‐parametrization of the problem and, therefore, convergence to the optimal solution is slow. Here, an alternative algorithm is developed for solving the complex problem, which exploits fully the special structure of the dilated matrix. The advantages of the modified algorithm are demonstrated via a numerical example. Copyright © 2007 John Wiley & Sons, Ltd.