兰州大学机构库 >数学与统计学院
Hopf多面体链环的构筑及其拓扑性质研究
Alternative TitleConstruction of Hopf polyhedral links and their topological properties
杨曼曼
Thesis Advisor邱文元
2015-05-26
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
KeywordDNA多面体 多面体链环 纽结理论 新欧拉公式
AbstractDNA作为主要的遗传物质一直备受关注,纳米技术更是给人为控制和利用DNA提供了技术支持,DNA纳米技术应运而生。近几十年来,DNA纳米结构相继问世,大量的DNA三维立体结构在实验室合成。大量实验合成的新型DNA结构,打破了传统的化学结构和生物结构,给理论化学提出了严峻的挑战。建立与这些新型的三维结构相对应的理论模型,研究其构筑方法并进一步研究这些模型的本质特性是理论化学甚至拓扑学面临的重大问题和挑战,多面体链环应运而生。本文的主要内容包括:1、对实验室合成的DNA三维立体结构进行分类,并对合成机理加以概述;对自然界中存在以及实验室合成的蛋白质及RNA空间结构进行简单介绍。2、构建与星状DNA多面体结构相一致的多面体链环模型。从星状DNA结构以及纽结理论入手,寻找二者相似之处,确定模型-Hopf多面体链环。遵循从简单到复杂,从特殊到一般之规律研究Hopf多面体链环的构筑方法。3、打破传统的多面体链环构筑方法,提出了面构筑方法,并给出了用面构筑法构筑几种多面体链环的方法和过程。4、从纽结和多面体入手,对多面体链环的拓扑性质进行探讨和总结。归纳新欧拉公式对于Hopf多面体链环的适用范围,进一步给出Hopf多面体链环新欧拉示性数的取值范围及其形式。本文主要是以DNA多面体为实验基础,以纽结理论和多面体理论为理论基础,应用新方法探讨和拓展多面体链环理论。希望本文提供的方法和探讨结果能为合成更复杂的DNA甚至蛋白质结构提供新的思路和目标。
Other AbstractDNA has been considered to be the main genetic material, and nanotechnology provides technical support in controlling and using DNA. In the past decades, a lot of three-dimensional structures of DNA were synthesized in the laboratory. These structures has broken away from the traditional chemical and biological structures, and brought a challenge to the theory of chemistry. Establishment a theoretical model, the construct method and topological properties are very important. The contents of this thesis include: 1. Classify the DNA polyhedron and summarize the synthetic mechanism. In addition, a simple introduction of protein and RNA polyhedron will be made. 2. Build polyhedral link which is consistent with star DNA polyhedron structure, and study its constructing method. 3. Surface construction method is proposed by breaking the traditional building method of polyhedral link. The process to constructthe several polyhedral link by surface construction method will be illustrated. 4. Starting from the knot and polyhedra, the topological properties of polyhedral link were discussed and summarized. The applicative scope of new euler's formula in Hopf polyhedral links will be suggested. This thesis is based on DNA polyhedra synthesized by experiments, the kont theory and polyhedral theory. It explored and expanded polyhedral link theory by developing a new method. It hopes that the results of this paper can provide new ideas and goals for DNA or protein synthesis.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225696
Collection数学与统计学院
Recommended Citation
GB/T 7714
杨曼曼. Hopf多面体链环的构筑及其拓扑性质研究[D]. 兰州. 兰州大学,2015.
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