代数拓扑 meaning in English
algebraic topology
Examples
- Indeed, readers familiar with the fundamentals of algebraic topology can easily prove the correctness of this presentation .
事实上，熟悉代数拓扑基本原理的读者容易证明这个表示的正确性。 - The notion of fundamental group also came from topology . there are close relations with simple connectedness in representation theory of algebras for fundamental group , as was in algebraic topology
基本群的概念同样来自拓扑学，同它在代数拓扑中一样，它在表示论中与单连通性也有密切的联系。 - To completely avoid producing elements jointed at their corner nodes and checkerboard patterns , which frequently occur when the topology optimization of plane continuum is studied , the theory of topology analysis of plane continuum in topology optimization process and the simple algorithm for programming are studied . according to algebraic topology theory , the boundary of elements and plane continuum are operated as a one - dimensional complex . by use of the adjacency vector in graph theory , the structural topology is described and the topological operation is achieved on a computer . by above , the structural topological feature in the evolutionary process is gained . these methods are effcient and reliable . under topology constraints , according to the results of stress analysis , by deleting elements and moving nodes at the boundary , more satisfactory results can be gained by using a few numbers of elements and iterations . to demonstrate the efficiency of these methods , solutions including some well - known classical problems are presented
避免目前平面连续体结构拓扑优化过程中经常出现的单元铰接以及“棋盘格”等现象，研究了连续体结构拓扑优化过程的拓扑分析方法，以及在计算机上实现的简便算法.根据代数拓扑理论，单元及连续体的边界作为1 -复形进行运算.利用图论中的邻接向量概念，在计算机上实现了结构的拓扑描述及拓扑运算，得到了结构在拓扑演化过程中的拓扑特性，方法简单、可靠.在一定的拓扑约束下，根据应力分析结果，采用删除单元、单元退化、移动节点等方法，可以用较少单元得到更为满意的结果，提高计算效率.为演示方法的有效性，给出几个包括常见经典问题的解答