Electronic Thesis or Dissertation

In this thesis, we study modelling with non-linear ordinary differential equations, and the existence of positive solutions for Boundary Value Problems (BVPs). These problems have wide applications in many areas. The focus is on the extensions of previous work done on non-linear second-order differential equations with boundary conditions involving first-order derivative. The contribution of this thesis has four folds. First, using a fixed point theorem on order intervals, the existence of a positive solution on an interval for a non-local boundary value problem is obtained. Second, considering a different boundary value problem that consists of the first-order derivative in the non-linear term, an increasing solution is obtained by applying the Krasnoselskii-Guo fixed point theorem. Third, the existence of two solutions, one solution and no solution for a BVP is proved by using fixed point index and iteration methods. Last, the results of Green's function unify some methods in studying the existence of positive solutions for BVPs of nonlinear differential equations. Examples are presented to illustrate the applications of our results.

Author Keywords: Banach Space, Boundary Value Problems, Differential Equations, Fixed Point, Norm, Positive Solutions

The objective of this thesis is to create a foundation for a digital comparative collection of chert types found on archaeological sites in Ontario, both local and non-local varieties, and to evaluate the impact of a digital reference collection on the confidence and accuracy of the user in comparison to hard copy guides or hand samples that are more often traditionally used. Spatial and temporal variation in the use of different lithic raw materials has shown to provide insight into cultural interaction, resource exchange and control across multiple periods in the study of Indigenous archaeology; however comparative collections needed to conduct analyses remain accessible only in a physical form. This study will build a foundation, develop a prototype using a represented sample of hand specimens from the William Fox Northeastern North American Lithic Reference Collection (referred to hereafter as The Fox Collection) at Trent University, and create a prototype digital system to assist the user in identifying the chert type through the use of a simple expert system using a decision tree. The digital identification system was tested by a group of volunteers with to compare accuracy and confidence in analysis against traditional methods of hand samples and hard copy guides. When supplied with the digital reference collection, a statistically significant improvement in the accuracy and confidence of chert identification was identified.

Author Keywords: database design, digital comparative collection, digital identification system, expert system, Ontario archaeology, raw material analysis

Research to date on social problem solving typically focuses on elementary school aged children. However, adolescents and young adults may experience more novel and emotionally complex social conflicts that require different skills to navigate them successfully. Previous research has highlighted executive function (EF) and emotion regulation as possible skills that help with social problem solving. The current study examined the potential relation between EF, emotion regulation, and social problem solving. The sample consisted of 174 participants with a mean age of 19.60 years. Results showed that the shifting component of EF was associated with being able to take different perspectives when coming up with a solution for a social conflict involving a romantic partner. Additionally, emotion regulation was associate with perspective taking in the overall social problem solving process with a romantic partner. These results suggest that both EF and emotion regulation are involved in the ability to take different perspectives during a social conflict in this age range.

Author Keywords: Emotion Regulation, Executive Function, Social Problem Solving

Parody has been a strategy within cultural production since the ancient Greeks: "paraodia" referred to a song sung alongside the main narrative thread of a dramatic work; the prefix "para-" also signifies "against." In A Theory of Parody: The Teachings of Twentieth-century Art Forms, Linda Hutcheon offers this core definition: parody is "a form of repetition with ironic critical distance, marking difference rather than similarity … [with] tension between the potentially conservative effect of repetition and the potentially revolutionary impact of difference" (xii). This and other aspects of Hutcheon's theory guide my interpretations of works by three contemporary artists working in Canada: Sybil Lamb's novel I've Got a Time Bomb; Ursula Johnson's (Mi'kmaq) three-part exhibition Mi'kwite'tmn (Do You Remember); and Kent Monkman's (Cree and Irish) exhibition Shame and Prejudice: A Story of Resilience.

I argue that the presence of parodic elements in these artists' works enables them to do two things: to claim spaces that enable recognition of their subject positions, and to critique an aspect of hegemonic norms in contemporary society. I read Lamb's novel as a critique of the heteronormative gender binary via parody of the picaresque genre and of heteronormative discourse/language. Certain pieces in Monkman's exhibition parody the epistemological and display strategies of traditional Eurocentric anthropological museums and archives, as can Johnson's work; her sculptural-installations may also be read as parodying the traditions of Mi'kmaw basket-making. The work of both artists critiques colonial narratives that sought (and may still seek) to denigrate and/or erase Indigenous peoples; such narratives of cultural genocide were both tacitly and directly propagated by museums. I analyze these three artists' works, considering key features of parody (ambiguity; irony and "double-voicedness"; trans-contextualization; and humour), and their effects (defamiliarization; ontological instability; complicity; and laughter). Parody challenges the post-structuralist emphasis on the "decoder," (viewer/reader) reinstating the "encoder" (artist/author) as agent. Decoders recognize their complicity within the context of the hegemonic narrative, whether the heteronormative gender binary or colonialism, and may come to shift perception – as per Hutcheon's "potentially revolutionary impact."

Author Keywords: contemporary art, Indigenous art, museum history, parody, picaresque, transgender literature

Forestalling biodiversity loss through the establishment of protected areas is a universally accepted conservation strategy, yet despite established guidelines for protected area coverage and placement, much of the world is currently failing to meet its commitments to conservation planning and landscape protection. Calls for the United States to protect more land usually focus on the need for strategic selection of land parcels to bolster protected area coverage and network functionality, but to date there lacks focused research on either the role of private protected areas in conservation planning or the factors affecting individual protected area selection and importance. We determined gaps in conservation planning in the contiguous United States by analyzing the connectivity of protected area networks by state, and assessing the importance of private protected areas in improving linkages in protected area connectivity. We found that all states had low coverage from protected areas (average <8.4% of total land mass), and especially private protected areas (average <1.1% of total land mass), and that the overall contribution of such areas to protected area network connectivity also was low. Terrain ruggedness was identified as the main factor affecting the current location of protected areas, and that protected area spatial layout is a primary influence on landscape connectivity. We conclude that establishment of private protected areas could offer a viable conservation tool for increasing protected area coverage and connectivity, but that current efforts are inadequate to either adequately link existing protected areas or to meet established land protection guidelines.

Author Keywords: Aichi Target 11, conservation planning, graph theory, network theory, private conservation, protected areas

The Spanish Civil War was a theatre of political tension where democracy, communism, and fascism clashed during the interwar period, starting in July 1936 and ending in April 1939. The war defied the traditional concept of a civil war as Germany, Italy, and the Soviet Union became involved. All three saw Spain as a testing ground for new military technologies. Meanwhile the United States government stayed steadfast in its isolationist approach to foreign conflict and sent no aid to either side. American military attachés, who are military observers to foreign nations, in Spain witnessed the ongoing conflict, creating detailed reports of their observations before, during, and after the war. This thesis argues that the reports, which contained valuable information regarding military technology and doctrine, had little impact on American military innovation during the interwar period. This was due to both politically dictated neglect and doctrine prejudice regarding European conflicts. Based on the attaché reports, this thesis will explain what Germany, Italy, and the Soviet Union learned about aviation, tanks, and artillery from their participation in Spain. This will be contrasted with the state of the United States' military at the same time to demonstrate not only the little impact the attaché reports had on the trajectory of the American military, but how the military lagged behind those in Spain upon the beginning of the Second World War.

Author Keywords: American military attachés, Germany, Italy, Military Intelligence Division, Soviet Union, Spanish Civil War

This thesis centres on a series of intergenerational life history interviews with and about Jean Koning, a 95-year-old white Settler woman who has engaged in different forms of Indigenous-Settler solidarity work for over fifty years—work that is highly regarded by many Indigenous and non-Indigenous peoples in southwestern and central Ontario. I bring Jean's stories and perspectives, many of which stand in stark contrast to dominant discourses of "reconciliation," into conversation with scholars who examine Indigenous refusal and Settler (un)certainty. Through this, I attempt to better understand how colonial knowledge structures and ways of thinking operate in practise, how these might be resisted, and how this resistance relates to land repatriation. I argue that a commitment to unsettling uncertainty and to meaningful listening may be required by Settlers in a stand against various colonial ways of thinking, such as cognitive imperialism.

Author Keywords: Cognitive imperialism, Decolonization, Indigenous-Settler relations, Life history, Reconciliation, Settler uncertainty

With wide applications in many fields such as engineering, physics, chemistry, biology and social sciences, semi-linear equations have attracted great interests of researchers from various areas. In the study of existence of solutions for such class of equations, a general and commonly applied method is the compression cone method for fixed-point index. The main idea is to construct a cone in an ordered Banach space based on the linear part so that the nonlinear part can be examined in a relatively smaller region.

In this thesis, a new class of cone is proposed as a generalization to previous work. The construction of the cone is based on properties of both the linear and nonlinear part of the equation. As a result, the method is shown to be more adaptable in applications. We prove new results for both semi-linear integral equations and algebraic systems.

Applications are illustrated by examples. Limitations of such new method are also discussed.

Keywords: Algebraic systems; compression cone method; differential equations; existence of solutions; fixed point index; integral equations; semi-linear equations.

Author Keywords: algebraic systems, differential equations, existence of solutions, fixed point index, integral equations, semi-linear equations

This thesis addresses the inclusion of women within Classic Maya works of art, consisting of, for this purpose, private-consumption ceramic vessels and large scale public monuments. Through the use of Feminist and Gender Theory, Performance Theory, and Iconographic Theory, the roles of women in iconographically depicted ceremonial performance is assessed. A Microsoft Access database was constructed in order to look at various aspects of female depiction, including but not limited to, bodily action, costume, and paraphernalia. The context, individual action, and associated paraphernalia of women performing numerous roles were analyzed, in which women were found to participate in many of the same roles as men, although there are some roles from which either men or women are excluded, and certain paraphernalia items with which women are not associated.

Author Keywords: Archaeology, Feminism, Gender Theory, Iconography, Maya Art, Performance Theory

This thesis reports the outcomes of a mixed methods exploratory study on young children's spatial reasoning and mathematics involving unplugged (offline) coding with young children (JK-Grade 2). Intrigued by the increased push for coding in schools, teachers and researchers worked together in a collaborative research process to design a sequence of unplugged coding activities and document student thinking. Qualitative results include the mapping of a hypothetical learning trajectory for unplugged coding focused on location and movement, as well as an analysis of the computational, spatial and mathematical thinking in unplugged coding. The grid was found to be a fundamental spatial structure that supported student thinking across all domains. Quantitative data included a range of spatial and mathematics measures that were administered pre-post with a subsample of 55 students. Findings showed strongest gains in mental rotations/visualization and magnitude comparison, suggesting this as a promising area for further study.

Author Keywords: Early Years, Learning Trajectories, Spatial Reasoning, Unplugged Coding, Young Children