algebraic topology 中文意思是什麼
algebraic topology
解釋
代數的位相幾何-
Indeed, readers familiar with the fundamentals of algebraic topology can easily prove the correctness of this presentation.
事實上，熟悉代數拓撲基本原理的讀者容易證明這個表示的正確性。 -
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
避免目前平面連續體結構拓撲優化過程中經常出現的單元鉸接以及「棋盤格」等現象，研究了連續體結構拓撲優化過程的拓撲分析方法，以及在計算機上實現的簡便演算法.根據代數拓撲理論，單元及連續體的邊界作為1 -復形進行運算.利用圖論中的鄰接向量概念，在計算機上實現了結構的拓撲描述及拓撲運算，得到了結構在拓撲演化過程中的拓撲特性，方法簡單、可靠.在一定的拓撲約束下，根據應力分析結果，採用刪除單元、單元退化、移動節點等方法，可以用較少單元得到更為滿意的結果，提高計算效率.為演示方法的有效性，給出幾個包括常見經典問題的解答 -
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
基本群的概念同樣來自拓撲學，同它在代數拓撲中一樣，它在表示論中與單連通性也有密切的聯系。 -
Abstract : in this paper we servey some recent trands of applications of the method of algebraic topology to simple graphs. some fundamental concepts are introduced with theorems. several new problems are proposed
文摘:我們從組合拓撲方法在圖論的應用中，著重介紹與圖有關的幾種復形的近期研究動態，論述其中一些帶基礎性的問題，並提出一些可供研究的新問題 -
With these concepts, the following results are obtained : ( 1 ) the set of compact elements in an algebraic l - domain is an l - cusl ; ( 2 ) algebraic l - domains equipped with scott topology are the soberification of their sets of compact elements equipped with pseudoscott topology ; ( 3 ) the ideal completion of an l - cusl is an algebraic l - domain, obtaining a representation theorem for algebraic l - domains
證明了：任一代數l - domain的緊元集是l - cusl ；任一代數l - domain是其緊元集賦予alexandrov拓撲時的sober化；任一l - cusl的理想完備化是代數l - domain ，從而得到了代數l - domain的表示定理。 -
One kind of cellular automata has been researched. its algebraic properties such as characters of states, periodicity, and topology have been deeply discussed
深入地討論了一類加法細胞自動機的代數性質，如：狀態特徵、周期性、拓撲結構等。
分享友人