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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
111

Injective objects

Dodson, Nancy Elizabeth January 1967 (has links)
Let R be a ring with an identity 1. Let A, B, and C be R-modules. The sequence A → [f above arrow] B→[g above arrow] C is exact providing f and g are R-homomorphisms and Im f =Ker g. Let 0 represent the R-module with precisely one element. An R-module J is injective if and only if for every exact sequence 0→A→ [f above arrow] B of R-modules and R-homomorphisms and every R-homomorphism g: A→J there exists an R-homomorphism h: B→J such that hf = g. This is a dual concept to that of a projective R-module. In the second chapter the idea of an injective R-module is studied quite intensively, and several different characterizations of injective · modules are proved. One of the principal results obtained is that every R-module is a submodule of an injective R-module. Further properties of injective R-modules are given in Chapter 3, including the concepts of injective dimension and an injective resolution of an R-module. Using these concepts the Shifting Theorem for injectives is proved. The basic definitions and results necessary for the development of the concept of injective for abstract categories are included in Chapter 4. An injective object is then defined in this general setting. Then the concept of an injective envelope is defined. The problems that arise, in the effort to restrict the category of topological groups to the appropriate subcategory so that the concept of an injective topological group is of interest, are investigated in Chapter 5. The development of the concept for one such restriction concludes this thesis. / Master of Science
112

On the Cohomology of the Complement of a Toral Arrangement

Sawyer, Cameron Cunningham 08 1900 (has links)
The dissertation uses a number of mathematical formula including de Rham cohomology with complex coefficients to state and prove extension of Brieskorn's Lemma theorem.
113

Conley-Morse Chain Maps

Moeller, Todd Keith 19 July 2005 (has links)
We introduce a new class of Conley-Morse chain maps for the purpose of comparing the qualitative structure of flows across multiple scales. Conley index theory generalizes classical Morse theory as a tool for studying the dynamics of flows. The qualitative structure of a flow, given a Morse decomposition, can be stored algebraically as a set of homology groups (Conley indices) and a boundary map between the indices (a connection matrix). We show that as long as the qualitative structures of two flows agree on some, perhaps coarse, level we can construct a chain map between the corresponding chain complexes that preserves the relations between the (coarsened) Morse sets. We present elementary examples to motivate applications to data analysis.
114

Regular realizations of p-groups

Hammond, John Lockwood 01 October 2012 (has links)
This thesis is concerned with the Regular Inverse Galois Problem for p-groups over fields of characteristic unequal to p. Building upon results of Saltman, Dentzer characterized a class of finite groups that are automatically realized over every field, and proceeded to show that every group of order dividing p⁴ belongs to this class. We extend this result to include groups of order p⁵, provided that the base field k contains the p³-th roots of unity. The proof involves reducing to certain Brauer embedding problems defined over the rational function field k(x). Through explicit computation, we describe the cohomological obstructions to these embedding problems. Then by applying results about the Brauer group of a Dedekind domain, we show that they all possess solutions. / text
115

The RO(G)-graded Serre spectral sequence /

Kronholm, William C., January 2008 (has links)
Thesis (Ph. D.)--University of Oregon, 2008. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 71-72). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.
116

Topology of singular spaces and constructible sheaves /

Schürmann, Jörg. January 2003 (has links)
Univ., FB Mathematik, Habil.-Schr., 2001--Hamburg, 2001.
117

Regular realizations of p-groups

Hammond, John Lockwood, January 1900 (has links)
Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.
118

Geometric Method for Solvable Lattice Spin Systems / 可解格子スピン系に対する幾何学的手法

Ogura, Masahiro 23 March 2023 (has links)
京都大学 / 新制・課程博士 / 博士(理学) / 甲第24398号 / 理博第4897号 / 新制||理||1700(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐藤 昌利, 教授 佐々 真一, 准教授 戸塚 圭介 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM
119

Graphs, Simplicial Complexes and Beyond: Topological Tools for Multi-agent Coordination

Muhammad, Abubakr 16 December 2005 (has links)
In this work, connectivity graphs have been studied as models of local interactions in multi-agent robotic systems. A systematic study of the space of connectivity graphs has been done from a geometric and topological point of view. Some results on the realization of connectivity graphs in their respective configuration spaces have been given. A complexity analysis of networks, from the point of view of intrinsic structural complexity, has been given. Various topological spaces in networks, as induced from their connectivity graphs, have been recognized and put into applications, such as those concerning coverage problems in sensor networks. A framework for studying dynamic connectivity graphs has been proposed. This framework has been used for several applications that include the generation of low-complexity formations as well as collaborative beamforming in sensor networks. The theory has been verified by generating extensive simulations, with the help of software tools of computational homology and semi-definite programming. Finally, several open problems and areas of further research have been identified.
120

Cohomology and K-theory of aperiodic tilings

Savinien, Jean P.X. January 2008 (has links)
Thesis (Ph.D.)--Mathematics, Georgia Institute of Technology, 2008. / Committee Chair: Prof. Jean Bellissard; Committee Member: Prof. Claude Schochet; Committee Member: Prof. Michael Loss; Committee Member: Prof. Stavros Garoufalidis; Committee Member: Prof. Thang Le.

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