High Accuracy Analysis of the Adini's Nonconforming Element

Received September 14, 2000; revised September 25, 2001     

利用α-甲基苯乙烯合成佳乐麝香的研究

介绍一种新的佳乐麝香合成方法，并就反应的参数对反应过程的影响进行了探讨。     

我国装备制造业的现状与对策探讨

阐述了制造业的概念,然后引出了装备制造业的概念,并简要介绍了我国装备制造业的现状,在此基础上探讨了发展我国装备制造业可供选择的策略。     

一种高效的自适应彩色图像加密算法

将自适应的灰度图像加密算法引入彩色图像加密中,针对其安全性不理想和效率低等问题,采用耦合映像格子及AMS变换进行改进,设计一种新的自适应彩色图像加密算法。理论分析和仿真实验表明该加密算法操作简单、运算速度快、安全性高,能够在实际的并行计算平台上使用。     

Solving Third Order Differential Equations with Maximal Symmetry Group

The largest group of Lie symmetries that a third-order ordinary differential equation (ode) may allow has seven parameters. Equations sharing this property belong to a single equivalence class with a canonical representative v ^′′′(u)=0. Due to this simple canonical form, any equation belonging to this equivalence class may be identified in terms of certain constraints for its coefficients. Furthermore a set of equations for the transformation functions to canonical form may be set up for which large classes of solutions may be determined algorithmically. Based on these steps a solution algorithm is described for any equation with this symmetry type which resembles a similar scheme for second order equations with projective symmetry group. Received March 9, 2000; revised June 8, 2000     

On Constructing Unit Triangular Matrices with Prescribed Singular Values

We propose an efficient algorithm for computing a unit lower triangular n×n matrix with prescribed singular values of O(n ²) cost. This is a solution of the question raised by N. J. Higham in [4, Problem 26.3, p. 528]. Received July 21, 1999; revised November 4, 1999     

A Cascadic Multigrid Algorithm for Semilinear Indefinite Elliptic Problems

We propose a cascadic multigrid algorithm for a semilinear indefinite elliptic problem. We use a standard finite element discretization with piecewise linear finite elements. The arising nonlinear equations are solved by a cascadic organization of Newton's method with frozen derivative on a sequence of nested grids. This gives a simple version of a multigrid method without projections on coarser grids. The cascadic multigrid algorithm starts on a comparatively coarse grid where the number of unknowns is small enough to obtain an approximate solution within sufficiently high precision without substantial computational effort. On each finer grid we perform exactly one Newton step taking the approximate solution from the coarsest grid as initial guess. The linear Newton systems are solved iteratively by a Jacobi-type iteration with special parameters using the approximate solution from the previous grid as initial guess. We prove that for a sufficiently fine initial grid and for a sufficiently good start approximation the algorithm yields an approximate solution within the discretization error on the finest grid and that the method has multigrid complexity with logarithmic multiplier. Received February 1999, revised July 13, 1999     

A Class of Smoothers for Saddle Point Problems

In this paper smoothing properties are shown for a class of iterative methods for saddle point problems with smoothing rates of the order 1/m, where m is the number of smoothing steps. This generalizes recent results by Braess and Sarazin, who could prove this rates for methods where, in the context of the Stokes problem, the pressure correction equation is solved exactly, which is not needed here. Received December 4, 1998; revised April 14, 2000     

用VHDL-AMS进行概念设计

ＶＨＤＬ－ＡＭＳ是ＶＨＤＬ向模拟和混合信号领域的诉展,ＶＨＬＤ－ＡＭＳ为设计者提供了在概念级处理复杂系统的能力,随着ＶＨＤＬ－ＡＭＳ的标准化,将诞生处理复杂的模拟和混合信号模型的有效的模拟器,文中介绍了ＶＨＬＤ－ＡＭＳ模拟扩展的主要内容,展示了一个混合模式模拟环境,并给出了模拟解算器的构成,讨论了连续和离散模拟的同步问题;用４个例子说明ＶＨＤＬ－ＡＭＳ在概念设计中的应用。     

Comparison of the Hansen-Sengupta and the Frommer-Lang-Schnurr existence tests

The Krawczyk and the Hansen-Sengupta interval operators are closely related to the interval Newton operator. These interval operators can be used as existence tests to prove existence of solutions for systems of equations. It is well known that the Krawczyk operator existence test is less powerful that the Hansen-Sengupta operator existence test, the latter being less powerful than the interval Newton operator existence test. In 2004, Frommer et al. proposed an existence test based on the Poincaré-Miranda theorem and proved that it is more powerful than the Krawczyk existence test. In this paper, we complete the classification of these four existence tests showing that, in practice, the Hansen-Sengupta existence test is actually more powerful than the existence test proposed by Frommer et al.