On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

The Social Enterprise as an Alternative Work Option for Persons with Developmental Disabilities: A Case Study of Staff Perspectives at Common Ground Co-operative

Traditional employment options for persons with developmental disabilities are lacking. Employment options available for persons with developmental disabilities are reflective of the medical and social model perspectives of disability; with segregated and supported employment reinforcing the idea that persons with developmental disabilities are incapable and competitive employment missing the necessary accommodations for persons to be successful. This study examined social enterprises as an alternative employment option that can balance both medical and social model perspectives by accommodating for weaknesses or limitations and recognizing the strengths and capabilities of persons with developmental disabilities in the workplace. Moreover, this study is part of a broader case study which is examining the nature and impacts of a social enterprise, known as Common Ground Co-operative (CGC), which supports five social purpose businesses that are owned and operated by persons with developmental disabilities. This study is part of the Social Business and Marginalized Social Groups Community-University Research Alliance. To date, a case study has been written describing the nature and impacts of CGC and its related businesses from the perspectives of the Partners, board members, funders and staff (Owen, Readhead, Bishop, Hope & Campbell, in press & Readhead, 2012). The current study used a descriptive case study approach to provide a detailed account of the perceptions and opinions of CGC staff members who support each of the Partners in the five related businesses. Staff members were chosen for the focus of this study because of the integral role that they play in the successful outcomes of the persons they support. This study was conducted in two phases. In the first phase five staff members were interviewed. During this stage of interviews, several themes were presented which needed to be examined in further detail, specifically staff stress and burnout and duty of care for business Partners versus the promotion of their autonomy. A second phase of interviews was then conducted with one individual participant and a focus group of seven. During both interview phases, Staff participants described an employment model that creates a non-judgemental environment for the business Partners that promotes their strengths, accommodates for their limitations, provides educational opportunities and places the responsibility for the businesses on the persons with developmental disabilities cultivating equality and promoting independence. Staff described the nature of their role including risk factors for stress, the protective factors that buffer stress, and the challenges associated with balancing many role demands. Issues related to the replication of this social enterprise model are described.

Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].