Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

NON-FULL-TIME COLLEGE PROFESSORS: A NARRATIVE INQUIRY INTO THE NON-FULL-TIME FACULTY ROLE

The rate of non-full-time faculty members has increased rapidly over the last decade (Louis, 2009; MacKay, 2014; Meranze & Newfield, 2013), as the post-secondary landscape of fluctuating enrolment, fiscal and operational challenges, and the requirement to hire specialized skill sets have required institutions to rely heavily on this demographic. In the Ontario Colleges of Applied Arts and Technology (CAATs) system, institutions have tried to preserve and enhance educational quality with fewer resources through greater reliance on non-full-time faculty. The purpose of this study was to explore the perceptions and experiences of teaching and support of non-full-time faculty at one Eastern Ontario college. Employing a narrative inquiry methodology, data were collected from four participants through their writing three individual letters at the end of each month and participating in one interview at the end of the contract period. The data were analyzed and coded. This analysis revealed five themes: motivation, connection and engagement, compensation, teaching and development, and performance evaluation. Differences in the participants’ perceptions tended to reflect divergences across career stage: retired versus early career. The compensation package provided to non-full-time faculty was considered inadequate for those in the early career stage, especially comparing it to that of full-time faculty. In addition, the amount of previous teaching experience was an important indicator for the appropriate level of teaching resources and support provided by the institution. The newer faculty members required a higher level of support to combat feelings of role isolation. The temporary nature of the role made it difficult to establish a feeling of a strong connection to the institution and subsequently opportunities to engage further to deepen the relationship. Despite these differences across participants, autonomous motivators were consistent across all narratives, as participants expressed their desire to teach and share their knowledge to help students achieve their goals. Participants concluded their narratives by sharing future advice for faculty interested in pursuing the role. The narratives provided areas for improvement that would help increase the level of job satisfaction for non-full-time college faculty members: (a) establishing a more thorough performance evaluation process to align with institutional supports, (b) offering more diverse teaching resources to better prepare faculty and enhance teaching practices, (c) overhauling the compensation package to better recognize the amount of time and effort spent in the role and aligning with the compensation provided to full-time faculty, and (d) including rewards and incentives as part of the compensation package to enhance the level of commitment and availability for the role. These changes might well increase the job satisfaction and improve the retention of non-full-time faculty members.

An impulsive differential equation model for Marek's disease

Many dynamical processes are subject to abrupt changes in state. Often these perturbations can be periodic and of short duration relative to the evolving process. These types of phenomena are described well by what are referred to as impulsive differential equations, systems of differential equations coupled with discrete mappings in state space. In this thesis we employ impulsive differential equations to model disease transmission within an industrial livestock barn. In particular we focus on the poultry industry and a viral disease of poultry called Marek's disease. This system lends itself well to impulsive differential equations. Entire cohorts of poultry are introduced and removed from a barn concurrently. Additionally, Marek's disease is transmitted indirectly and the viral particles can survive outside the host for weeks. Therefore, depopulating, cleaning, and restocking of the barn are integral factors in modelling disease transmission and can be completely captured by the impulsive component of the model. Our model allows us to investigate how modern broiler farm practices can make disease elimination difficult or impossible to achieve. It also enables us to investigate factors that may contribute to virulence evolution. Our model suggests that by decrease the cohort duration or by decreasing the flock density, Marek's disease can be eliminated from a barn with no increase in cleaning effort. Unfortunately our model also suggests that these practices will lead to disease evolution towards greater virulence. Additionally, our model suggests that if intensive cleaning between cohorts does not rid the barn of disease, it may drive evolution and cause the disease to become more virulent.