In this dissertation, a new method for the numerical integration of two-dimensional partial differences is presented. The approach is based on obtaining an estimate of the 2-D Haar wavelet decomposition of the integrated differences by filtering and down-sampling the partial difference measurement data as an intermediate step. Then, this decomposition estimate is synthesized into an estimate of the integrated differences. The filterbanks required for estimating this decomposition are derived directly from the 2-D Haar Wavelet Analysis Filterbank. The order of operations of this process is manipulated in a novel way so that gradient or partial difference data can be used as input to the filterbank instead of the image data. The original data can then be obtained from this decomposition estimate using unmodified 2-D Haar Wavelet Synthesis Filterbanks. This use of the wavelet decomposition brings a reduction in computation complexity to less than 10 operations per pixel of the result. This dissertation shows that the data used for this algorithm may be calculated partial differences or discretely sampled gradient data measurements. This data set may have any-sized convex area of support as long as it is on a Cartesian grid. The method is stable as a component of a closed loop system as shown by simulations of a recently developed woofer-tweeter adaptive optics control system.

Supramolecular systems are held together by non-covalent forces, and include systems involving the interaction of small molecules with biomolecules such as DNA and proteins. The inherent reversibility of supramolecular systems means that dynamic processes are important for many of the functions achieved. The first objective of this work was to develop methodology to study the dynamics and binding mechanism of small molecules with DNA. Though there is a great deal known about the thermodynamics of molecules binding to DNA there is much less known about the binding dynamics. Aminoxanthones were chosen as appropriate guest molecules, and their photophysics were examined in a number of solvents, showing that both the singlet and triplet excited states are strongly affected by solvent polarity, with the excited state energies decreasing in polar solvents. Laser flash photolysis experiments for quenching of the triplet excited state by nitrite anions in the absence and presence of DNA allowed a residence time of microseconds to be estimated for these guests. These experiments also showed that this methodology is not widely applicable when studying the binding dynamics of small molecules with DNA, and that other fast kinetic techniques are necessary. Laser temperature jump experiments allow measurement of dynamics in supramolecular systems, while avoiding the problems encountered in laser flash photolysis experiments. A custom-built system was developed as an adaptation of systems described in the literature, with the main difference being a laser optimized for the excitation of water, and the ability to operate across a wide dynamic range. The laser and the detection systems for absorbance and fluorescence were successfully implemented and a number of artifacts were eliminated. The expected temperature jump was obtained and signals were detected by both fluorescence and absorption; the signal-to-noise ratio still needs improvement before systematic studies can be carried out. The second objective of this work was to study bimolecular reactions in proteins. Using biomolecules to effectively modulate reactivity in bimolecular reactions requires knowledge of the reaction mechanism. When the dimerization of 2-anthracenecarboxylate (AC) takes place in serum albumin proteins enantiomeric excess (ee) is obtained for the chiral products. There are a number of binding sites for AC in these proteins and it has been shown that a balance between strength of binding and mobility of the reactants is essential to achieve high ee's. In human serum albumin remarkable ee's of more than 80% are achieved. It is important to differentiate between reactant molecules bound to different binding sites so that the binding sites where reaction preferentially forms one enantiomer can be identified. Steady-state and time-resolved fluorescence studies identified two types of 2-anthracenecarboxylate bound to HSA: one that has a short lifetime and is very protected from the bulk aqueous solution, and one that has a longer lifetime, but is exposed to the bulk solution. Further work using binding site inhibitors allowed identification of a third type of molecule that has a longer lifetime, but is very protected from the bulk solution, which is likely the species responsible for the majority of the observed ee.

Supernovae of Type Ia, SNe Ia, are currently the most powerful tool of modern cosmology, but their progenitor scenario is not yet well constrained. Recent studies of SN Ia rates in radio-loud early-type galaxies, and members of rich clusters, suggest a possible influence on SN Ia explosions outside of the established correlation with the age of the parent galaxy's stellar population (via the current specific star formation rate, sSFR). These rates were used to show that the characteristics of SN Ia progenitor systems may be inconsistent with theoretical expectations of the most popular scenarios. The astrophysical question of this thesis is: do parent galaxy and environment influence the rates and properties of Type Ia supernovae, and, if so, how? Towards this end, we combine the database of Type Ia supernovae from the Canada-France-Hawaii Telescope's Supernova Legacy Survey with publicly available catalogs including: galaxy photometric and spectroscopic redshifts, radio and infrared sources, and members of galaxy groups and clusters. This is the most comprehensive set of multi-wavelength host properties and environment parameters for intermediate redshift Type Ia supernovae yet compiled. We present the SNLS SN Ia rate per unit mass in a variety of parent galaxy and environment samples. We also statistically assess the probability of discrepancies between our rates, those of previous works at low redshift, rates in the general population of galaxies, and predictions of established empirical SN Ia rate models. In general, we do not find statistically significant evidence for SN Ia rate enhancements over the general population in galaxies which are radio-loud, infrared-bright, or associated with galaxy groups and clusters. In cases where we do find a suggestive rate enhancement, it is always with less than 2-sigma confidence. These rates agree with established empirical rate models, which in turn are consistent with theoretical expectations of the most plausible progenitor scenarios. Furthermore, we find the properties of SNLS SNe Ia in these types of hosts and environments are consistent with the predictions of these scenarios. We conclude that, aside from the established correlation with host sSFR, no conclusive evidence is observed with SNLS data for strictly environmental effects on SN Ia rates. This supports their continued status as cosmological standard candles.

This work revolves around the development of microfluidic technology for use in biomedical diagnostics with a specific focus on analyte concentration. At the reduced scale inherent with microfluidic technologies the sensing of target species can be difficult since the sample volume is reduced to nanolitres leading to low amounts of target species. This necessitates the need to preconcentrate samples prior to the sensing step. The exclusion-enrichment phenomenon associated with concentration polarization has been used within microfluidic platforms for the purpose of analyte concentration though methods have all been inherently 1-D, axial configurations. Within this work a novel radial concentration strategy based on a single microfluidic layer on a uniform nanoporous film is presented. The active nanostructured region is defined by the microfluidics, providing flexibility and opening opportunities beyond the single-channel axial configurations to date. Radial geometries have not been previously shown operating as CP based concentration devices, though the unique geometry offers enhanced flux at the perimeter and the capability to focus samples down to small central regions. This focusing ability allows the concentration to take place on a separate layer and does not compete for space with other analysis fluidics. This radial configuration is numerically modeled and experimentally demonstrated.

This thesis examines Nuu-chah-nulth economic development and the changing nature of the relationships within our territories - the Ha’hoolthlii of our Ha’wiih - since Europeans first arrived and the occupation of our lands and waters by Settlers. I explore the implications of these changing relationships on Nuu-chah-nulth identity and our relational obligations within a worldview that understands that Heshookish tsawalk – “Everything is one.” I take a process-oriented perspective on identity beginning with the premise that living Nuu-chah-nulth-aht is more powerful and significant than simply being Nuu-chah-nulth. The recent proliferation of controversial economic development activities within Nuu-chah-nulth territories has spurred my interests in these issues. The form of economic development has some key characteristics that concern me. The first is that the economic development projects under way are of a particularly harmful and unsustainable nature. The second is the emerging trend of Nuu-chah-nulth partnerships in these ventures, epitomizing what I characterize as Aboriginal economic development. Instead of opposing development that threatens our traditional and adaptive practices, we are now involved as proponents and participants. To my surprise, these trends are not merely recent manifestations, but go back all the way to the arrival of Captain James Cook on our shores in the eighteenth century. At the heart of my research is our historically extensive participation in the various coastal commercial fisheries that have dramatically declined in recent decades. The purpose of this thesis is to create greater understanding of our present predicaments, re-evaluate our sense of agency, and encourage further critical debate on the potentially harmful economic development projects that will allow us to re-evaluate and heal our relationships within our territories.

This thesis introduces a new strategy of defending the vertices of a graph - secure paired domination, where guards are required to be paired and, when a vertex is attacked, one or two guards move to defend the attacked vertex, while keeping the graph dominated and the guards paired after the move. We propose nine possible definitions of secure paired domination, compare and contrast each with the others, and obtain properties and inequalities of the secure paired domination (SPD) numbers associated with the definitions. Based on each of the nine definitions, the SPD numbers of five types of special graphs, namely paths, cycles, spiders, ladders and grid graphs, are studied. We then compare the SPD number of an arbitrary isolate-free graph to various other parameters such as clique partition number, independence number, vertex- covering number, secure domination number and paired domination number. We establish that, for any graph without isolated vertices, its SPD number does not exceed twice the value of any of its other parameters mentioned above. Also, we give classes of trees for which some of the bounds are achieved. As conclusion, some open problems and directions for further studies regarding secure paired domination are listed.

Inspired by my own struggles with racism, this narrative and phenomenology study investigated how teachers of colour in the Canadian schooling system dealt with the pain of racism and how this process informed their teaching practice. I addressed this issue of racism and its relevance to the schooling process from an anti-racist theory of education theoretical framework. The study comprised of six women of colour who shared their experiences with racism through written narratives, face to face interviews, as well as electronic communications. While the study focused on the schooling experiences of the teachers, their narratives comprised of holistic experiences that included experiences in the schooling system as well as the general society. The data collected, revealed the following themes as central to the questions of the study: Knowledge of cultural, family, and political history gave the participants strength to stand against racism. However, most of the women carried the shame of being and knowing they were different. Trying to attain a form of standardized beauty was an ongoing struggle for the participants. All participants pointed to one teacher whose care was instrumental to their choice to become teachers. To the participants getting a good education was more important than worrying or paying attention to the pain of racism. However, all but one of the participants admitted to receiving treatment for racism related anxiety. Finally, the participants shared that by participating in the arts or having personal faith and beliefs was helpful tool that helped them negotiate the worlds of their cultural beliefs and traditions and that of mainstream (White society) society.

We present results evolving from established connections between zeta functions and different systems of polynomials, particularly the Riemann and Hurwitz zeta functions and the Bernoulli and Euler polynomials. In particular we develop certain results related to Apostol's deformation of the Bernoulli polynomials and obtain identities of Carlitz by a novel approach using generating functions instead of difference equations. In the last two chapters we work out new rapidly convergent series expansions of the Riemann zeta function, find coefficient symmetries of a polynomial sequence obtained from the cyclotomic polynomials by a linear fractional transformation of argument and obtain an expression for the constant term in an identity involving the gamma function.

The intersection of two Latin squares of the same order is the set of cells that contain the same entries in both Latin squares. Determining the order of this set can be asked for any type of Latin square and has been solved for most. Generalizing this to Latin squares of different orders leads to a conjecture of Dukes and Mendelsohn, which will be shown to be true. Results on the intersection of Latin squares, idempotent Latin squares, and idempotent symmetric Latin squares are explored. The relationship between the intersection problem for Latin squares and the intersection problem for Steiner triple systems will also be investigated. In addition to new results, past results are included presenting a common and clear notation. The proofs of some new results are able to replace proofs of past results as well as present a straightforward proof structure to new and past results. Two Latin squares of the same order are said to be r-orthogonal if the set of pairs occurring in corresponding cells has size r. Using this notation, two orthogonal Latin squares of order n are n2-orthogonal. The idea of r-orthogonality is generalized to Latin squares of different orders. The set of possible values is established for r and it is shown that this possible set can be obtained for pairs of Latin squares with certain orders.

Scholars writing on the rise of Hindutva, particularly in Gujarat state, have attributed its success to its ability to serve middle and upper caste and class interests. In recent state and Lok Sabha elections, though, Hindutva, through the Bharatiya Janata Party, has also made significant inroads outside of this elite, particularly in Adivasi (Aboriginal) communities. This electoral support has emerged alongside Adivasi participation in antiminority violence in the Dangs District in 1999 and the 2002 post-Godhra carnage. This thesis seeks to understand these developments and in doing so rejects predominant explanations which rely on a paternalistic false-consciousness approach that strips the Adivasi of independent political agency. It shows that the economic development of Adivasi communities has led to stratification and the emergence of an Adivasi elite. Bourdieu’s notion of symbolic capital is used to show that the psychological rewards that Hindutva is able to offer this elite have material consequences and thus this hegemony can serve the interests of these elements of Adivasi society.