DNA多面体链环的拓扑性质 Alternative Title The topological properties of DNA polyhedra links 彭晓刚 Thesis Advisor 邱文元 2013-05-18 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 多面体链环 可视化 同胚变形 亏格 欧拉公式 Abstract 多种NDA多面体已经被实验合成，例如DNA四面体，DNA立方体，近几年又合成出结构更为复杂的DNA足球分子结构。为了更好的研究和描述这些NDA多面体的数学性质，多面体链环模型被广泛应用。多面体链环能够在一定程度上揭示DNA多面体的拓扑性质。我们通过构筑DNA多面体链环模型，利用数学拓扑等方法，得出DNA多面体链环中存在的一种数量关系。本论文的主要内容如下： 1将DNA多面体链环构造成模型，首先是将DNA多面体链环进行seifert构造，然后对于seifert链环图双层变化，即可视化的过程，之后根据数学拓扑同胚变换，将其变形为结构简单的多面体模型，最后将其压缩到任取一个的平面之内，完成模型构造。 2 将构造好的模型，分析前后亏格的变化，得出新构造模型中亏格数目，然后利用seifert环数，交缠点数，分支数和亏格数存在的关系，来研究双线覆盖的DNA多面体链环中这些量之间存在的内在规律。这种模型的构造，对研究DNA多面体链环提供了更为直观和简洁的思路， 3对n分支的DNA多面体链环，用这种构造模型，分析亏格的方法进行探索和研究，通过利用交叉点数，seifert环数，分支数和亏格之间的联系，结合构造模型后，这类DNA多面体链环的亏格规律，能够得出n分支DNA多面体的链环内在的数学关系。为DNA多面体链环提供了数学依据，同时为多面体链环的理论提供了参考。 Other Abstract The variety of NDA polyhedron have been experimental synthesized , such as DNA tetrahedron , DNA cube. in recent year, complex molecular structure of DNA soccer has been experimental .In order to study and description of these NDA polyhedron mathematical and the nature .The polyhedral links model was widely used。Polyhedron link to a certain extent reveals the topological properties of DNA polyhedron . We study the DNA polyhedron link model with the mathematical topology , draw the DNA the polyhedral links in a number of relationship . In this paper, the main contents are as follows： 1，DNA polyhedral links is configured model , first the DNA polyhedral links for the seifert constructed , and then double-layer changes for the seifert link diagram , you can visualize the process , after mathematical topology homeomorphic transform its deformation .Finally the simple structure of the polyhedral model , its compression to either take a plane within completion of the model structure 2,Analysis the genus of the DNA construct model before and after the change , draw the number of new tectonic model loss , and then use the number of the seifert links , the number of branches and the number of genus relationship to study the two-lane coverage polyhedron the internal laws of the link between these quantities . The structure of this model , the study of DNA polyhedral links provides a more intuitive and simple idea . 3 On the n branches DNA polyhedral links, we analysis the genus exploration with this structural model and research through the use of cross- points between the seifert ring number , the number of branches and genus , combined with the structural model , which of DNA polyhedral links the genus , draw n branched DNA polyhedron inner links mathematical relationship . Provide a mathematical basis for DNA polyhedral links and provides a reference for the polyhedral theory URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225719 Collection 数学与统计学院 Recommended CitationGB/T 7714 彭晓刚. DNA多面体链环的拓扑性质[D]. 兰州. 兰州大学,2013.
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