词语大全 algebraic topology中文翻譯

Posted 2022-08-12 中文

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词语大全 algebraic topology中文翻譯

Indeed, readers famipar 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。

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 apppcations 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,并提出一些可供研究的新問題

To pletely 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 plex . by use of the adjacency vector in graph theory , the structural topology is described and the topological operation is achieved on a puter . by above , the structural topological feature in the evolutionary process is gained . these methods are effcient and repable . 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，采用刪除單元、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