Humphreys (1990) defines a simple root system for a finite reflection group which is an important concept fundamental to the understanding of reflection groups as well as Coxeter complexes and Coxeter groups. The proof that Humphreys uses to establish the existence and uniqueness of these systems follows an indirect method that left portions of the proof as exercises to the reader. I present a more complete and direct proof using different organization and methods.

This project examines the intimate role slave claims played in the animosities which quickly developed from the acquisition of the Florida territory to the outbreak of the Second Seminole Indian War. By focusing on the Indian Agency and its first administrator, Gad Humphreys, this connection is made by suggesting that the territory's legislators were unwilling to allow the coexistence of Seminoles and blacks on the Florida frontier. The presence of these communities threatened developing Middle Florida plantations with significantly increased risks of both slave runaways and insurrection. In response, settlers and government officials pressed Humphreys to see not only that the Seminoles were pacified, but also that runaway slaves were apprehended and returned to their owners. The agent, however, held fundamentally different opinions on the subject of adjudicating these controversies than did the citizens under his direction, and his superiors in the War Department. When Humphreys regularly supported Seminole claimants in the often-bitter property contests, his actions were met with the disapproval of his superiors-particularly Governor William Pope DuVal-who felt that his first duty was to ensure the development of the territory's plantations. The claims of Margaret Cook and Mary Hannay, in particular, strained these once respectful relationships to the point where DuVal sought to have Humphreys removed on various charges of misconduct relating to his direction in the controversies. An investigation was initiated into a number of allegations, yet focused on his conduct in slave controversies, and found that far from acting inappropriately, Humphreys had performed his duty with exceptional integrity. Ultimately, however, DuVal's effort was successful. Humphreys was superceded in 1830 by John Phagan-an agent much more willing to take the harsh measures necessary to have the numerous slaves claimed by the territory's citizens surrenders. In examining the actions of Humphreys, the Indians under his charge, and the legislators he reported to, slave claim controversies of the 1822-1830 period clearly illustrate the centrality of the slavery issue on the Florida frontier, and inextricably connect slavery to the outbreak of the Second Seminole Indian War.

As many theorists have pointed out, queer history is often erased within traditional, heteronormative historiography. Consequently, historians cannot recount the gay and lesbian past by conventional techniques of evidence and documentation. Instead they recuperate and reinvent queer history using strategies normally associated with the writing of fiction. This thesis examines three works of late twentieth century lesbian historical fiction that rewrite the past in order to render visible queer intimacy, sexuality, and desire. Jeanette Winterson's The Passion (1987), Sarah Waters' Tipping the Velvet (1998), and Helen Humphreys' Leaving Earth (1997) employ spectacularly visible lesbian heroines who symbolically reverse lesbian invisibility in mainstream historical narratives by displaying themselves as public figures or stage performers. There are ongoing debates in contemporary queer theory and historiography about the extent to which it is politically useful to privilege highly visible individuals when recovering the marginalized gay and lesbian past. Winterson's, Waters', and Humphreys' novels enact this debate, and exemplify a trend in contemporary lesbian historical fiction in which lesbian heroines are empowered by their ability to control their own visibility and to ensure the perpetuation of their history.

No description available.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1965. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

In this essay I defend the notion of deductive explanation mainly against two types of putative counterexamples: those found in genuinely indeterministic systems and those found in complex dynamic systems. Using Railton's notions of explanatory information and ideal explanatory text, deductivism is defended in an indeterministic setting. Furthermore, an argument against non-deductivism that hinges on peculiarities of probabilistic causality is presented. The use of the notion of an ideal explanatory text gives rise to problems in accounting for explanations in complex dynamic systems, regardless of whether they are deterministic or not. These problems are considered in the essay and a solution is suggested. This solution forces the deductivist to abandon the requirement that an explanation consists of a deductive argument, but it is argued that the core of deductivism is saved in so far as we, for full explanations, can still adhere to the fundamental requirement: If A explains B, then A is inconsistent with anything inconsistent with B.

No description available.