Quadratic reciprocity for the rational integers and the Gaussian integers

This thesis begins by giving a brief time line of the origins of Number Theory. It highlights the big theorems that have been constructed in this subject, along with the mathematicians who constructed them. The thesis, then, goes on to prove the Law of Quadratic Reciprocity for the Jacobi symbol. This includes proving Eisenstein's Lemma for the Jacobi symbol. Then, it is shown that Gauss's Lemma has an even greater generalization than Eisenstein's Lemma. Finally, this thesis shows the similarities between the rational integers and the Gaussian integers, including proving the Law of Quadratic Reciprocity for the Gaussian integers and constructing a similar version of Gauss's Lemma for the Gaussian integers

“Something In This Slippery World That Can Hold”: A Trans Feminist Analysis Of Moby-Dick

This paper argues that Moby-Dick dramatizes several long-standing issues that pertain to gender. The focus on trying to determine the objective truth of perceived reality and the motif of body modification combine to form a prescient exploration of modern debates and conflicts surrounding gender, not only as it is embodied but how it is conceptualized

Painful Belonging: Violence In J.M. Coetzee's Fiction

J.M. Coetzee’s fiction invites its readers to engage with the representation of political violence during and after the Apartheid period in South Africa. His work wrestles with a consideration of the processes that inform the hierarchization of individuals — whether they be human or non-human — and how consequential iterations of physical and psychological violence affect victims, perpetrators, and bystanders. In short, his fiction represents the consequences of encountering and attempting to represent the Other. By comparing Waiting for the Barbarians and Disgrace, I have isolated three distinct ethical considerations that inform Coetzee’s representative engagement with violence in both texts: first, the infliction of direct physical pain on bodies that are marked as vulnerable due to specific ontological categories they possess; second, the violence perpetrated through the functioning of sovereign power in both ambiguous and specific spaces; and finally, the violence embedded within the criteria of citizenship and statelessness. The core of my analysis lies in arguing the fundamental interconnectedness of these three categories. Though they are distinct and can be examined in isolation, they also simultaneously and necessarily inform each other and tend to unfold in a myriad of combinations and settings — for example, the infliction of physical violence in a political setting can be understood as an articulation of the tenuous relationship between perpetual sovereign power and the precariousness of national belonging. This quality of fundamental association between these categories moves across the spaces and contexts of these two novels, and as I hope to show, may extend to non-fictional political violence. In order to effectively delineate the connection between these three considerations, I rely primarily on the theoretical scaffolding provided by the political philosophers Hannah Arendt and Giorgio Agamben, as well as the works of Elaine Scarry, Susan Sontag, and Idelber Avelar on violence. This project unfolds over four chapters; the introduction, which contextualizes Coetzee within debates surrounding global literature, and the subsequent three chapters, which conduct examinations of the three modes of political violence represented in both novels

Comparison of two methods of improving speed in the 100 yard dash

The purpose of this study was to determine if a weight training program, used as a supplementary program to a conventional sprint training program, would improve the speed of the sprinters. Seventy-one ninth grade boys participated in the study. There were two groups, the experimental group (A) and the control group (B). Group A had thirty-eight boys while group B had only thirty-three boys. The study was carried out Monday through Friday of each week for a period of six weeks. The control group (B) performed only a designed program of sprint training, while the experimental group (A) used a supplementary program of weight training with the sprint training program. The raw data of the means were treated statistically through a "t" test to determine if there were a significant difference at the .05 level of confidence. From the results of this study it is concluded that weight training, when used as a supplement to sprint training does increase the running speed of the sprinter

Cultural Theory and Management of Common Property Resources

Cultural theory utilizes concepts drawn from social anthropology, sociology, and organization theory to explain the social and cultural biases of policy actors and interest groups. Certain ideas of nature are associated with each cultural bias; these ideas of nature are in turn associated with types of resource management institutions. By identifying an actor or group's culture bias, analysts can explain the success or failure of different management activities. This paper explains the evolution of cultural theory from its anthropological roots to its applications in ecological management. It then applies cultural theory to a typology of common property resources and illustrates its usefulness by examining grazing subsidies in the American southwest

A model for the development of an African literature curriculum in the secondary schools of Sierra Leone

The purpose of this study was to provide a decision-making model that would be used in the development of an African Literature curriculum to be adopted in the secondary schools of Sierra Leone. Emphasis was put on the decision-making process in Sierra Leone, especially in terms of allowing lay members of the community to participate in curriculum decisions. A critical look at the current decision-making process in Sierra Leone as it relates to curriculum development and implementation was undertaken and the Vroom model for decision-making was analysed and adapted to suit the Sierra Leone situation. After examining the way decisions affecting curriculum development in Sierra Leone were made and the role of the various officials connected with their implementation, existing curriculum and instructional practices were attacked at their most vulnerable points, especially in terms of their lack of relevance to the cultural aspirations of the students currently enrolled in the secondary schools of Sierra Leone

Nutritional modulation of growth and maturation and the development of specific age-related diseases : secondary analysis of NHANES II

Four age-related subsamples were selected from the Second National Health and Examination Survey (NHANES II) in order to test hypotheses involving relationships between dietary intake, method of infant feeding, rate of growth and maturation, and incidence of later life disease. Relationships between variables of interest were first placed within a comprehensive conceptual framework linking overnutrition during infancy and childhood to accelerated growth, accelerated sexual maturation, and increased incidence of later life disease. Six hypotheses were tested in order to explore key implications of this conceptual framework. Hypotheses were grouped within three areas of analysis: (a) nutrition and growth, (b) nutrition, growth, and sexual maturation, and (c) growth, maturation, and age-related disease

Contextual Factors in the Development of State Wildlife Management Regimes in the United States of America

Edwards & Steins (The Role of Contextual Factors in Common Pool Resource Analysis. Paper presented to 7th Conference of the International Association for the Study of Common Property, Vancouver, British Columbia, June 1998) developed an analytic framework for multiple-use common pool resource (CPR) regimes that emphasizes the importance of contextual factors. As a preliminary application of the framework, this paper ‘backsolves’ from outcomes to underlying contextual factors, and identifies primary cultural factors that occur in the development of American state wildlife management agencies. The factors are then placed into five categories: physical, political, economic, legal and scientific. The resulting examination of the management regime clarifies changes in agencies’ action strategies, and potential patterns of interaction, as they respond to new institutional pressures from recreation and conservation interests. The paper concludes with four important research directions that have emerged from the discussion. (1) Are contextual factors better expressed as a matrix (network/decision tree/hierarchy) rather than a list? (2) To what extent do spatial factors influence contextual factors? (3) How do contextual factors affect decisions at the three levels of institutional choice: constitutional, collective and operational? (4) How can we develop a structured research agenda that examines increasingly complex CPRs as we refine the analytic framework

Multiple-Use commons, collective action, and platforms for resource use negotiation

This is a guest editorial for the September 1999 issue of Agriculture and Human Values

Decolonization in the Former Soviet Borderlands: Politics in Search of Principles

As the public and private institutions of the post-Soviet world are reconfigured, the prominence of local politics in determining who decides what, when, and how may not necessarily be bad. Recent empirical analysis of Third World public and private interaction has offered strong arguments that local politics may determine the outlines of local government more efficiently than centrally driven campaigns (de Soto 1989). The failure of the collectivist experiment in Russia and its borderlands is a lesson of importance for theoreticians and practitioners alike. Any analyst who truly seeks to understand institutions, hierarchy, and collective forms of management cannot afford to ignore it