兰州大学机构库 >化学化工学院
扩展的阿基米德多面体链环及其性质研究
Alternative TitleInvestigations of extended Archimedean links and their properties
郑翔
Subtype硕士
Thesis Advisor邱文元
2014-05-24
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword纽结理论 DNA多面体 多面体链环 病毒多面体 阿基米德多面体 多面体生长规律
Abstract本论文从几何学和拓扑学的角度出发,将几何学中的多面体理论和拓扑学中的纽结理论应用到病毒衣壳结构和DNA多面体分子的理论研究中,通过建立新的DNA多面体纽结和链环的理论模型对病毒衣壳结构和DNA多面体分子进行描述,同时对这些模型的拓扑特征和性质进行了分析和讨论。1、研究背景包含实验背景和理论基础。20世纪下半叶至今,化学家和生物学家们利用DNA分子合成了大量复杂而精细三维结构,病毒分子蛋白衣壳的蛋白质链相互缠绕会形成多面体链环结构,关于病毒多面体和DNA多面体的介绍。理论基础囊括了多面体理论和纽结理论。2、交叉构造的环状富勒烯链环和碳纳米管链环与DNA多面体链环有着极其相似的结构。对交叉构造的环状富勒烯链环和碳纳米管链环的Seifert环数以及新欧拉示性数等拓扑性质进行研究,证明了DNA多面体新欧拉公式的适用性。3、提出并阐述了扩展的阿基米德多面体的构筑过程。以阿基米德多面体为基础模型,得到了8种可扩展的阿基米德多面体类及其生长规律,其中扩展的截半二十面体,扩展的截角立方体,扩展的截角二十面体这3类多面体为首次发现。这一类病毒多面体的构筑可以解释病毒衣壳结构以及富勒烯结构。
Other Abstract1.The part of the research background includes experimental background and theoretical basis. The introduction of viral polyhedron and DNA polyhedron providesthe thesis with experimental background and research goals. Theoretical basis contains polyhedral theory and knot theory, which provides theoretical tool for the study of this thesis. 2. Crossed toroidal fullerenes and carbon nanotube links have fairly similar structureswith DNA polyhedra links. 3. The building process ofthe extended Archimedean solid is expounded. Archimedean solid being as the basic model, the Goldberg method is applied to 13 kinds of Archimedean solids and 8 extensible Archimedean solids and growth law are gained.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/237066
Collection化学化工学院
Recommended Citation
GB/T 7714
郑翔. 扩展的阿基米德多面体链环及其性质研究[D]. 兰州. 兰州大学,2014.
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