强迫布鲁塞尔振子双稳周期吸引子的初值流域

本文利用数值方法,在几组典型参数值下,详细地考察了弱耦合强迫布鲁塞尔振子在超临界情况下双稳周期运动的周期与初值的关系。首次在初值平面x_0—y_0上的一定范围内,给出了导致不同周期运动的初值分布(流域)。计算结果还表明:在此范围内不存在多重稳定态,因而从一个方面进一步加强了弱耦合条件下的强迫布鲁塞尔振子与圆映象的可比性。     

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.     

关于混合型多项式Hammerstein积分方程正解迭代求法

本文给出了混合型多项式Ｈａｍｍｅｒｓｔｅｉｎ积分方程正解的迭代求法，并将所得结果应用到二阶非线性常微分方程的边值问题     

教学机器人实验系统的开发

本文首先介绍了教学机器人实验系统的设计思想和系统构成，然后对其工作方式及与上位机的联机操作方法作了简要的说明，最后对该系统中模拟通用机器人语言所开发的模拟机器人语言的语句及应用这种机器人语言进行编程的特色作了专门的阐述．     

建立社会主义市场经济必须首先解放思想

从传统的计划经济向社会主义市场经济的转变，必须从计划经济体制下所形成的旧的思想观念中解放出来，树立适应社会主义市场经济的新观念，这是建立社会主义市场经济的需要。我国十几年的改革开放的实践已证明，在马克思主义的指导下，打破习惯势力和主观偏见的束缚，从实际出发，解放思想，是改革开放和进行社会主义建设的首要条件。     

题串与串题

本文从几个具体的例题出发，通过逐步分析并挖掘深入，类比串通，阐述了“题串”与“串题”教学的益处与作用。     

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases:ε/μ2→0(μ→0),μ2/ε→0 (ε→0) andε=μ2, the uniformly valid asymptotic solution is obtained by using the expansion method of two small parameters and the theory of differential inequality.     

Banach空间二阶非线性微分方程的弱Carathéodory解

本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果     

Challenging Students to View the Concept of Area in Triangles in a Broad Context: Exploiting the Features of Cabri-II

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12–15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). Cabri-Geometry (software), Université de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct: (a) pairs of equivalent triangles “in as many ways as possible” and to study their area and their perimeter using any of the tools provided and (b) “any possible sequence of modifications of an original triangle into other equivalent ones”. As regards the concept of area and in contrast to a paper and pencil environment, Cabri provided students with different and potential opportunities in terms of: (a) means of construction, (b) control, (c) variety of representations and (d) linking representations, by exploiting its capability for continuous modifications. By exploiting these opportunities in the context of the given open tasks, students were helped by the tools provided to develop a broader view of the concept of area than the typical view they would construct in a typical paper and pencil environment.     

Aggregate error locator and error value computation in AG codes

The aggregate error locator is defined and a computation method is given. The aggregate error locator is then used in a type of Forney algorithm to compute the error values in the received words of a Ca,b algebraic geometry code.