On the Topology and Isotopic Meshing of Plane Algebraic Curves

This paper presents a symbolic algorithm to compute the topology of a plane curve. This is a full version of the authors' CASC15 paper. The algorithm mainly involves resultant computations and real root isolation for univariate polynomials. Compared to other symbolic methods based on elimination techniques, the novelty of the proposed method is that the authors use a technique of interval polynomials to solve the system f(α, y),?f/?y(α, y)and simultaneously obtain numerous simple roots of f(α, y) = 0 on the α fiber. This significantly improves the efficiency of the lifting step because the authors are no longer required to compute the simple roots of f(α, y) = 0. After the topology is computed, a revised Newton's method is presented to compute an isotopic meshing of the plane algebraic curve. Though the approximation method is numerical, the authors can ensure that the proposed method is a certified one, and the meshing is topologically correct. Several nontrivial examples confirm that the proposed algorithm performs well.     

Isotopic Meshing of a Real Algebraic Space Curve

Journal of Systems Science and Complexity - This paper presents a new algorithm for computing the topology of an algebraic space curve. Based on an efficient weak generic position-checking method...     

On the Complexity of Computing the Topology of Real Algebraic Space Curves

Journal of Systems Science and Complexity - This paper presents an algorithm to compute the topology of an algebraic space curve. This is a modified version of the previous algorithm. Furthermore,...     

In-Plane Elastic Buckling of Arch

IntroductionAn arch resists its applied load by a combination ofbending and axial compression effects,and failselastically by excessive bending or by buckling inthe plane of loading.An arch with a symmetric in-plane load may suddenly deflect from symmetri…     

汕头市地方环境管理信息系统研究与实践

对汕头市环境部门主要职能进行调查，在此基础上进行系统需求分析，进而研究系统总体结构和主要模块建立，最后对系统主要模块和软件设计进行了探讨     

带锥台托盘KH2PO4晶体生长与位错分布

利用光学显微镜对采用锥台托盘及传统平托盘生长的晶体进行位错腐蚀观察，发现锥台托盘生长的晶体上半部分位错分布与平托盘生长的晶体相似，部分区域位错密度低于平托盘生长的晶体。对于锥台托盘生长的晶体下半部分，其柱面位错缺陷很少，位错集中在与锥台直接接触的下锥面。下锥面的存在阻止了柱面底部新位错的形成，为柱面生长提供了更好的生长条件。硬度分析表明使用锥台托盘一定程度上提高了晶体结晶完整性。