Publications
Detailed Information
Analysis on simplical complex via kirchhoff's laws
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 국웅 | - |
| dc.contributor.author | 오중석 | - |
| dc.date.accessioned | 2019-05-07T07:00:21Z | - |
| dc.date.available | 2019-05-07T07:00:21Z | - |
| dc.date.issued | 2019-02 | - |
| dc.identifier.other | 000000155864 | - |
| dc.identifier.uri | https://hdl.handle.net/10371/152890 | - |
| dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2019. 2. 국웅. | - |
| dc.description.abstract | 이 논문에서는 단순 복합체 네트워크에서의 키르히호프 조건에 대해 소개하고, 단순 복합체 네트워크에서 키르히호프 조건과 고차원 신장 부분 그래프 간의 관계에 대해 증명한다. 이를 통해, 양의 저항에서만 정의할 수 있었던 네트워크의 실질 저항을 임의의 실수 저항이 주어진 단순 복합체 네트워크로 일반화한다. | - |
| dc.description.abstract | In this thesis, we introduce the notion of Kirchhoff's conditions for a simplicial network (X, R) where X is a simplicial complex and R is a set of resistances for the top simplices, and prove the relation between Kirchhoff's conditions and i-dimensional weighted spanning tree number. Then, we can generalize effective resistance for simplicial network (X, R) where resistances are real valued. | - |
| dc.description.tableofcontents | Contents
1 Kirchhoffs Conditions on Graphs 2 1.1 Graphs and Spanning Trees . . . . . . . . . . . . . . . . . . . . 2 1.2 Kirchhoffs Conditions and Spanning Trees . . . . . . . . . . . 14 2 Effective Resistance and Kirchhoffs Conditions 21 2.1 Effective Resistance . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Generalized Effective Resistance in Graphs . . . . . . . . . . . 30 3 On Higher Dimensional Spaces 33 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Kirchhoffs Conditions and Spanning Trees in Higher Dimensional Spaces. . . . . . . . . . . . . . . . . 36 Bibliography 38 | - |
| dc.language.iso | eng | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject.ddc | 510 | - |
| dc.title | Analysis on simplical complex via kirchhoff's laws | - |
| dc.type | Thesis | - |
| dc.type | Dissertation | - |
| dc.description.degree | Doctor | - |
| dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
| dc.date.awarded | 2019-02 | - |
| dc.contributor.major | Topological combinatorics | - |
| dc.identifier.uci | I804:11032-000000155864 | - |
| dc.identifier.holdings | 000000000026▲000000000039▲000000155864▲ | - |
- Appears in Collections:
- Files in This Item:
Item View & Download Count
Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.