by Au Pat Nien. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 86-88). / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Valuations --- p.4 / Chapter 2.1 --- Preliminaries --- p.4 / Chapter 2.2 --- Complete Fields --- p.6 / Chapter 2.3 --- Unramified Extension of Complete Field --- p.10 / Chapter 2.4 --- Local Fields --- p.12 / Chapter 3 --- Ramification Groups and Hasse-Herbrand Function --- p.16 / Chapter 3.1 --- Ramification Groups --- p.16 / Chapter 3.2 --- "The Quotients Gi/Gi+1, i ≥ 0" --- p.17 / Chapter 3.3 --- The Hasse-Herbrand function --- p.19 / Chapter 4 --- The Norm Map --- p.21 / Chapter 4.1 --- Lemmas --- p.21 / Chapter 4.2 --- The Norm Map on the Residue Field of a Totally Ramified Extension of Prime Degree --- p.22 / Chapter 4.3 --- Extension of the Perfect Residue Field in a Totally Ramified Extension --- p.26 / Chapter 4.4 --- The Norm Map on Finite Separable Extension of Knr with K Perfect --- p.28 / Chapter 5 --- Cohomology of Finite Groups --- p.30 / Chapter 5.1 --- Preliminaries --- p.30 / Chapter 5.2 --- Mappings of Cohomology Groups --- p.32 / Chapter 5.2.1 --- Restriction and Inflation --- p.32 / Chapter 5.2.2 --- Corestriction --- p.34 / Chapter 5.3 --- Cup Product --- p.34 / Chapter 5.4 --- Cohomology Groups of Low Dimensions --- p.35 / Chapter 5.5 --- Some Results of Group Cohomology --- p.43 / Chapter 6 --- The Brauer Group of a Field --- p.57 / Chapter 7 --- The Norm Residue Map --- p.60 / Chapter 7.1 --- Determination of the Brauer Group of a Local Field --- p.60 / Chapter 7.2 --- Canonical Class --- p.62 / Chapter 7.3 --- The Reciprocity Law --- p.64 / Chapter 8 --- The Local Symbol --- p.74 / Chapter 8.1 --- Definition --- p.74 / Chapter 8.2 --- The Hilbert Symbol --- p.74 / Chapter 8.3 --- The Differential of the Formal Power Series --- p.76 / Chapter 8.4 --- The Artin-Schreier Symbol --- p.78 / Chapter 9 --- Characterization of a Norm Group --- p.81 / Bibliography

Lai, Chun Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 83-87). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Spectral sets in Rd --- p.11 / Chapter 2.1 --- Preliminaries --- p.11 / Chapter 2.2 --- Fundamental domains and convex sets in Rd --- p.15 / Chapter 2.3 --- Finite union of cubes --- p.20 / Chapter 3 --- Spectral theory on discrete groups --- p.27 / Chapter 3.1 --- Finite groups and Zd --- p.28 / Chapter 3.2 --- Rational spectrums and tiling sets --- p.32 / Chapter 3.3 --- Fuglede´ةs Problem in R1 --- p.37 / Chapter 3.4 --- "Failure of Fuglede´ةs Conjecture in Rd, d >3" --- p.42 / Chapter 4 --- Self-similar tiles in R1 --- p.49 / Chapter 4.1 --- Basics of self-similar tiles --- p.49 / Chapter 4.2 --- Self-similar tile digit sets and spectral problem --- p.52 / Chapter 4.3 --- Kenyon criterion --- p.55 / Chapter 5 --- Spectral self-similar measures --- p.66 / Chapter 5.1 --- Spectral self-similar measures --- p.66 / Chapter 5.2 --- One-dimensional self-similar measures --- p.72 / Chapter 5.3 --- General properties of spectral measures --- p.80 / Bibliography --- p.83

In voting theory, simple questions can lead to convoluted and sometimes paradoxical results. Recently, mathematician Donald Saari used geometric insights to study various voting methods. He argued that a particular positional voting method (namely that proposed by Borda) minimizes the frequency of paradoxes. We present an approach to similar ideas which draw from group theory and algebra. In particular, we employ tools from representation theory on the symmetric group to elicit some of the natural behaviors of voting profiles. We also make generalizations to similar results for partially ranked data.

The central problem addressed by this thesis is to attempt and reconcile our experience of time with our scientific understanding of time. Science tells us that time is static yet we experience it as dynamic. In the literature there tend to be two positions. Those who follow the science and claim that time is static and that our experience is mind-independent; those who favour our experience and question the science. I attempt to reconcile these positions. To do this I adopt terminology set out by McTaggart (1908) who termed the static view the B series and the dynamic view the A series. The literature that has developed out of this breaks down into the A Theory where time is the past, present and future; and the B Theory, where time is just involves events being earlier than or later than other events. I reject both positions as accounts of ontology. I adopt McTaggart’s C series, a series of betweenness only, on the grounds that it is this series that is mostly aligned to science. Given the C series, our experience requires explanation. A claim of mind-dependency is insufficient. I argue that the A series really refers to mind-dependent features that are brought out by our interaction with the C series; much like the way that colour is brought out by our interaction with a colourless world. The B series is the best description of the contents of time, not time itself. To examine the experience of time I adopt phenomenology to describe that experience. From within experience I show that certain features of that experience cannot be attributed to a mind-independent reality and use this as further evidence for the above claims. Finally I suggest that most theories of time are driven by the view that a theory of time has to be consistent. I examine recent developments in logic to see whether such a consistent requirement is needed. I conclude that the most we can get out of paraconsistent approaches is inconsistent experiences, not inconsistent reality. I conclude that the A series is the best description of our experience of time, the C series the best description of the ontology of time, and the B series as the best description of the contents of time. This reconciles our experience with our understanding of time. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1286776 / Thesis(PhD)-- School of Humanities, 2007

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Thesis (M.Sc.). / Written for the Dept. of Physics. Title from title page of PDF (viewed 2008/05/29). Includes bibliographical references.

Thesis (Ph. D.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains vi, 76 p. Includes abstract. Includes bibliographical references (p. 75-76).

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The following new results concerning 1-factorizations of the complete graph are proved: (1) There are exactly 6 equivalence classes of 1-factorizations of the complete graph with 8 vertices. (2). There are exactly 396 equivalence classes of 1-factorizations of the complete graph with 10 vertices. Representatives of each of the equivalence classes are presented. The size of the automorphism group of each equivalence class of 1-factorizations of the complete graph with 2n vertices for n ≤ 5 is also found. Several theorems and results related to 1-factorizations of the complete graph are presented, and the relationship to round robin schedules is shown. An application problem demonstrates the importance of the choice of the equivalence class of round robin schedules in the solvability of the problem. / Graduate