Boundary knot method for 2D and 3D Helmholtz and convection–diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration‐free, boundary‐type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non‐singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection–diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

Real-time accurate hand path tracking and joint trajectory planning for industrial robots (I)

Previously, researchers raised the accuracy for a robot’s hand to track a specified path in Cartesian space mainly through increasing the number of knots on the path and the number of the path’s segments, which results in the heavier online computational burden for the robot controller. Aiming at overcoming this drawback, the authors propose a new kind of real-time accurate hand path tracking and joint trajectory planning method. Through selecting some extra knots on the specified hand path by a certain rule and introducing a sinusoidal function to the joint displacement equation of each segment, this method can greatly raise the path tracking accuracy of robot’s hand and does not change the number of the path’s segments. It also does not increase markedly the computational burden of robot controller. The result of simulation indicates that this method is very effective, and has important value in increasing the application of industrial robots. Foundation item: Foundation of the Robotics Laboratory, Chinese Academy of Sciences (No. RL200002) Biography of the first author: TAN Guan-zheng, Dr., professor, born in Oct. 1962, majoring in artificial intelligence, robotics and automation.     

纽结理论与三叶结分子合成研究进展

拓扑学中的纽结理论在化学和生物学中有非常重要的应用,首先介绍了纽结理论在化学中的应用发展,然后对三叶结分子合成方法的发展及其可能的反应机理进行了阐述。     

Almost strictly total positivity of NUAT B-spline basis

Total positivity of spline basis has been well known in the theory of computer aided geometry design, which is highly related with good shape preserving property. Almost strictly total positivity is stronger, which could determine the positive minors while the other is zero. In this paper, a geometrical approach is proposed to prove the collection matrices of NUAT B-spline basis are almost strictly totally positive. In this paper, knot insertion algorithm combined with coefficient variation of NUAT B-spline function, we put forward an intuitive and geometrical method.     

基于ADO.NET的记录插入设计改进方案

在传统记录插入设计方案的基础上提出一种基于ADO.NET记录插入设计的改进方案。该改进方案不仅保留传统设计方案的优势,而且克服原有设计方案的弱点,是一种应用价值更高的设计方案。     

对含内孔面模型的切割仿真研究

为了快速封堵含内孔的面模型被切割后形成的中空截面轮廓,以便完整的表达模型.采用先剖分外轮廓,以封堵整个截面的轮廓,然后依次去除内轮廓区域的思想,最终实现中空面的封堵.先使用逐点插入算法剖分整个中空截面轮廓,然后删除已检测到的内孔洞的区域,在确保剖切面内所有轮廓顶点不发生任何变化的要求下.实现了含内孔面模型的快速切割仿真,并使用实例加以验证.该算法可以广泛地应用于各种含内孔面模型的切割仿真,尤其在医学手术仿真中.     

应用NURBS曲面磨光多面体

本文应用ＮＵＲＢＳ曲面磨光多面体,产生了处处Ｃ′连续的过渡曲面．多面体的磨光分为边的磨光和顶点的磨光两种情形,边的磨光相对较容易,而顶点的磨光则很困难．本文所采用的应用ＮＵＲＢＳ曲面磨光多面体的顶点和边的方法,不仅可以统一实现二者的磨光操作,而且方法简单且统一,产生了Ｃ′连续的过渡面．较之以前的方法,首先,利用ＮＵＲＢＳ曲面可以精确地描述对边磨光所用的柱面（等半径或非等半径）,其次,在对顶点的磨光中,同以往的方法不同,将与该顶点相邻的边的过渡曲面相互分离,并首次引入了“补面”的概念,使得对该点所产生的过渡曲面处处Ｃ′连续．本算法首先构造用以磨光多面体顶点和边的ＮＵＲＢＳ曲面的边界曲线网络图产生边界曲线的控制点及其权值（ＮＵＲＢＳ表示）,然后依据连续性准则,产生ＮＵＲＢＳ曲面的控制信息．     

Symbolic computation with finite biquandles

A method of computing a basis for the second Yang–Baxter cohomology of a finite biquandle with coefficients in Q$\mathbb{Q}$ and _Zp${\mathbb{Z}}_p$ from a matrix presentation of the finite biquandle is described. We also describe a method for computing the Yang–Baxter cocycle invariants of an oriented knot or link represented as a signed Gauss code. We provide a URL for our Maple implementations of these algorithms.     

纽结带形建筑表皮的拓扑学分析

引进拓扑学的纽结理论来指导分析纽结带形表皮的设计,首先从分析纽结带形表皮的拓扑学特征入手,提出了纽结类带形表皮和链环类带形表皮设计的造型规律,同时利用琼斯多项式来阐述纽结带形表皮的拓扑同痕不变量,并分别对纽结带形表皮的复杂度,以及纽结带形表皮间的环绕、串联和拼合进行阐述,力求利用拓扑学中纽结理论解决一些建筑纽结带形表皮的设计中所遇到的问题。     

氧化铝生产过程液位测量的方法研究

在铝冶炼生产过程中,槽罐液位测量是否准确,直接关系到生产是否正常进行。本文结合氧化铝液位测量情况,重点介绍斜插安装取压法的隔离原理、防堵原理,及取压管长度的测量方法,取压管材料尺寸选取及安装。将研究结果应用到氧化铝液位的测量上,经验证,斜插安装取压法在工业测量中对提高仪表运行周期、准确度及降低成本方面有效。