| DNA 多面体和蛋白质链环的不变量研究 |
| Alternative Title | Studies on the Invariants of the Links Based on DNA Polyhedron and Protein
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| 刘淑雅 |
| Thesis Advisor | 张和平
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| 2013-11-29
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| Degree Grantor | 兰州大学
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| Place of Conferral | 兰州
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| Degree Name | 博士
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| Keyword | 平图
链环图
刚性点图
DNA 多面体
多面体链环
链环不变量
HOMFLY 多项式
kauffman 多项式
色多项式
亏格
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| Abstract | 本论文的内容可以概括为以下四个部分:一、背景知识. 第一部分主要介绍了本文的研究背景与基础知识. 二、多面体链环的HOMFLY 多项式与相关不变量. 我们的研究工作主要集中在如何获得不同类型的多面体链环的链环不变量. 首先, 将多面体链环按照DNA 多面体的结构类型对应的分为两大类, 即：I-多面体链环和II-多面体链环. 三、二连通平图上的链环的亏格.首先, 一大类有向链环基于二连通平图的中间图的操作被生成了. 然后证明了这些链环在它们的所有定向链环中具有最小的Seifert 环数. 最终, 这些链环的亏格可根据图的度和与链环的分支数来给出.四、刚性点图的多项式不变量.偶度的刚性点图, 可看作是一些边打结或相互缠绕的图. 在这里,运用组合的方法, 将任意给定的偶度的刚性点图与一个链环集联系起来, 从而建立了定向刚性点图的HOMFLY 多项式和未定向刚性点图的Kauffman 多项式. |
| Other Abstract | The main content of this thesis is divided into four parts.
I. Background Knowledge. In the first part, we introduce our research background and some basic knowledge used in this thesis.II. The HOMFLY polynomial of polyhedral links and their invariants Our research work has mainly focused on how to obtain their link invariants for a variety of the polyhedral links. III. Genera of the links derived from 2-connected plane graphs First, a large family of links has been generated base on the medial graph of 2-connected plane graphs. Then, we shown that these oriented links have the smallest number of seifert circles over all orientations of these links. At last, the genera of these links are given as a formula in terms of the link component number and the degree sum of graph.IV. The polynomial invariants of rigid-vertex graphs An even-degree and rigid-vertex graph, can be viewed as some edged-knotted or edged-linked graphs. We here associate an even-degree and rigid-vertex graph with a simplified set of links via combination method. Hence we establish HOMFLY polynomial and Kauffman polynomial of these links. |
| URL | 查看原文
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| Language | 中文
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| Document Type | 学位论文
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| Identifier | https://ir.lzu.edu.cn/handle/262010/225720
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| Collection | 数学与统计学院
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Recommended Citation
GB/T 7714 |
刘淑雅. DNA 多面体和蛋白质链环的不变量研究[D]. 兰州. 兰州大学,2013.
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