직교 아틴 군을 생성하는 덴 뒤틀림들의 거듭제곱들

학위논문(박사)--서울대학교 대학원 :자연과학대학 수리과학부,2020. 2. 강정수.The author found right-angled Artin subgroups of mapping class groups, which are generated by powers of Dehn twists. For example, for fi nitely many simple closed curves of a surface, if the intersection numbers of all pairs do not exceed one, then the seventh powers of their Dehn twists generate a right-angled Artin subgroup of the mapping class group. Throughout the proof, we analyze the dual tree of a simple closed curve and tree actions of fundamental groups of surfaces and elliptic isometries of dual trees associated with lifts of Dehn twists. For every closed orientable surface of genus at least 2, we showed that there exists a faithful quasi-isometry action of the automorphism group of the surface group on a CAT(0) cube complex such that the restriction of the action to the inner automorphism group of the automorphism group of the surface group is an isometric action. We develop a method to compute lifts of Dehn twists using the pocsets inherited from CAT(0) cube complexes and bridges. (A pocset is a partially ordered set with a complementation, in addition, a bridge is a convex subcomplex, which is studied by Behrstock--Charney.)우리는 덴 뒤틀림으로 생성된 직교 아틴군을 구했습니다. 예를 들어, 어떤 곡면에서 유한 개의 단순 폐곡선의 모든 교차 수가 1 이하일 때, 그들의 덴 뒤틀림의 일곱 제곱은 직교 아틴군을 생성합니다. 이 증명에서 우리는 단순 폐곡선의 쌍대 나무와 그 위에서의 곡면 군의 작용을 분석했습니다. 그리고 덴 뒤틀림의 올림에 상응하는 타원형 등거리변환을 쌍대 나무에서 발견했습니다. 그리고 우리는 종수가 2 이상인 곡면에 대해 곡면군이 (동형사상으로) 충실히 작용하는 어떤 CAT(0) 입방 복합체에 그 곡면군의 자기동형군이 충실히 준동형사상으로 작용할 수 있음을 증명하였습니다. 자기동형군의 작용은 곡면군의 작용에 대한 모든 정보를 포함하고 있습니다. 이를 증명하기 위해 우리는 덴 뒤틀림의 올림을 계산하기 위한 몇 가지 방법을 개발했습니다. 이 방법은 CAT(0) 입방 복합체의 여원을 갖는 부분순서집합 구조와 다리를 이용합니다. 다리는 CAT(0) 입방 복합체의 볼록 부분복합체로써, Behrstock-Charney가 연구했습니다.Abstract 1 Introduction 1.1 Main theorems 1.2 Future research 1.3 Guide to the reader I Dehn twists and dual trees 2 Preliminaries for hyperbolic surfaces 2.1 Surfaces 2.2 Hyperbolic plane 2.3 Hyperbolic structure 2.4 Simple closed geodesics 2.4.1 Simple closed geodesics and minimal position 2.4.2 Simple closed geodesics and halfspaces 2.5 Collar lemma 2.6 Mapping class groups and Dehn twists 2.6.1 Outer automorphisms of fundamental groups of surfaces 3 Tree actions of fundamental groups of surfaces 3.1 Dual trees of simple closed geodesics 3.2 The fundamental groups of surfaces acting on dual trees 4 Lifts of Dehn twists 4.1 Automorphisms of Dehn twist classes and elliptic isometries on dual trees 4.2 Dehn twist automorphisms and multicurves 4.3 Right-angled Artin groups generated by powers of Dehn twists II Homomorphisms from Aut(Σ)) into the quasi-isometry groups of CAT(0) cube complexes 5 Preliminaries for CAT(0) cube complexes 5.1 Cube complexes and Gromov's characterization 5.2 Hyperplanes and halfspaces 5.3 Orientations 5.4 Combinatorial metrics 5.5 Dual cube complexes of nite-width discrete pocsets 5.6 Isomorphisms and isometries 6 Subpocsets, collapsings and bridges 6.1 Subpocsets 6.2 Convex subcomplexes 6.3 Bridges 6.3.1 Bridges between disjoint hyperplanes 6.3.2 Criterion for horizontal hyperplanes 7 Actions of fundamental groups of surfaces on dual cube complexes 7.1 Simple closed geodesics and wallspaces 7.2 Hyperbolic isometries on dual cube complexes 7.3 Right-handed pairs 8 Sliding quasi-isometries on dual cube complexes 8.1 The construction of sliding permutations 8.2 Sliding permutations on trees 8.3 Sliding permutations are quasi-isometries A Proofs of two propositions A.1 Proof of Proposition 3.1.3 A.2 Proof of Theorem 8.2.6 Bibliography Index Symbols Abstract (in Korean)Docto

가스 및 용매 분리를 위한 그래핀 멤브레인

학위논문 (박사)-- 서울대학교 대학원 공과대학 기계항공공학부, 2017. 8. 김용협.Membrane is the most representative technology to solve the environmental crisis facing the world such as global warming, air pollution, depletion of drinking water source by water pollution. Membrane technology means selectively separating only the desired substances from a mixed gas or solution. The principle of separation uses various principles such as physical, chemical, and mechanical. Primarily, selective separation techniques using size differences of mixed materials are used. For the recovery of wastewater produced in numerous factories or the recovery of oil spilled into the sea due to accidents, it is necessary to develop a membrane capable of selectively permeating water and oil. The situation in which water and oil are separated from each other frequently occurs and it is a necessary skill to maintain a clean environment. As the environmental pollution becomes serious, the amount of drinking water that people can drink is decreasing, and the development of new drinking water production technology is imminent due to environmental disasters such as global warming. The technology of converting seawater into freshwater, which accounts for 97% of the Earth, is an essential technology not only for the present but also for the future. Therefore, it is imperative to develop a high-performance membrane that can remove salts. In addition, the harmful gas generated from the power plant is mostly composed of CO2, and CO2 must be separated and collected in the atmosphere as a main cause of global warming. Therefore, it is urgent to develop a membrane fabrication technology capable of separating only desired gases such as CO2 from various gas molecules. It is necessary to develop high performance membrane technology with various applications. I have developed the CVHT process to improve the membrane performance. Using this process, a film can be produced due to the chemical bonding of graphene with excellent alignment. In this way, a high-performance membrane was prepared by separating the gas and the solution using a graphitic film having a very good structure.Chapter 1 Introduction 1 Chapter 2 Graphene oxide synthesis 4 2.1 Properties of graphene oxide 5 2.1.1 Graphene oxide 5 2.1.2 Mechanical property of graphene oxide 11 2.2 Hummers method 18 2.2.1 Conventional Hummers method 18 2.2.2 Modified Hummers method 21 2.3 Basic properties of GO 28 2.3.1 Morphology 28 2.3.2 Chemical structure 33 Chapter 3 Confined vapor-phase hydrothermal process 38 3.1 Conventional hydrothermal method 39 3.1.1 Graphene hydrogel 39 3.1.2 Graphene-reduction agent hydrogel 54 3.2 CVHT process 58 3.2.1 Need for graphitic film 58 3.2.2 New set-up for CVHT process 60 3.2.3 Thickness control of HGF 69 3.2.4 Mechanical property of graphitic film 75 3.2.5 Electrical property of graphitic film 82 Chapter 4 Gas separation property 86 4.1 Background of gas separation 87 4.1.1 Need for membrane 87 4.1.2 CO2/N2 and CO2/CH4 separation 91 4.2 Fabrication of graphitic membrane 94 4.2.1 Properties of graphitic film 94 4.2.2 XRD data of graphitic film 100 4.2.3 Experimental set-up 105 4.3 Gas separation performance 108 4.3.1 CO2/N2 separation 108 4.3.2 CO2/CH4 separation 116 Chapter 5 Liquid separation property 120 5.1 Background of liquid separation 121 5.1.1 Electrolyte in Li-ion battery 121 5.1.2 Water impurity in electrolyte 124 5.2 Liquid separation performance 128 5.2.1 Experimental set-up 128 5.2.2 Intrusion pressure 130 5.2.3 Separation performance of variable oils 134 5.2.4 Separation performance of electrolytes 136 Chapter 6 Conclusions 140 Bibliography 142 Abstract 151Docto