Geometric inequalities for initial data with symmetries

We consider a class of initial data sets (Σ,h,K) for the Einstein constraint equations which we define to be generalized Brill (GB) data. This class of data is simply connected, U(1)²-invariant, maximal, and four-dimensional with two asymptotic ends. We study the properties of GB data and in particular the topology of Σ. The GB initial data sets have applications in geometric inequalities in general relativity. We construct a mass functional M for GB initial data sets and we show:(i) the mass of any GB data is greater than or equals M, (ii) it is a non-negative functional for a broad subclass of GB data, (iii) it evaluates to the ADM mass of reduced t − φi symmetric data set, (iv) its critical points are stationary U(1)²-invariant vacuum solutions to the Einstein equations. Then we use this mass functional and prove two geometric inequalities: (1) a positive mass theorem for subclass of GB initial data which includes Myers-Perry black holes, (2) a class of local mass-angular momenta inequalities for U(1)²-invariant black holes. Finally, we construct a one-parameter family of initial data sets which we show can be seen as small deformations of the extreme Myers- Perry black hole which preserve the horizon geometry and angular momenta but have strictly greater energy.

The effect of economic inequality on voter turnout in Canadian federal elections, 1979-2011

Since the 1990s, voter turnout in Canadian federal elections has decreased considerably. During the same period, economic inequality significantly increased. Although there is much theoretical work, there have been few empirical studies examining the effect of economic inequality on voter turnout. Using data collected from both national and international sources, I conducted an aggregate level, time series analysis of national turnout and economic inequality for Canadian federal elections between 1979 and 2011. Moreover, this thesis tests Schattschneider's (1960) hypothesis, which argues that increasing rates of voter abstention are a result of economic inequality magnifying differences in relative power between affluent and non-affluent citizens. The findings indicate that economic inequality has a strong negative effect on voter turnout.

Role of metalliferous mudstones and graphitic shales in the location, genesis, and paleoenvironment

The Cambrian Tally Pond volcanic belt in central Newfoundland contains numerous volcanogenic massive sulphide (VMS) deposits, prospects, and showings that are locally associated with metalliferous mudstones and/or graphitic shales. Deposits in the belt are bimodal felsic-type VMS that are both base metal- (e.g., Duck Pond, Boundary) and precious metal-enriched (e.g., Lemarchant). At the Lemarchant deposit metalliferous mudstones are genetically and spatially associated with mineralization, whereas the relationship of other mudstones and shales to massive sulphide mineralization is more intricate and remains not fully understood. Metalliferous mudstones represent a hiatus in the volcanic activity where the deposition of hydrothermal products dominated over the abiogenic background sedimentation and/or dilution by volcaniclastic-epiclastic material. Lithogeochemical signatures allow one to distinguish between predominantly hydrothermally or detritally (i.e., non-hydrothermal) derived material. Metalliferous mudstones with a significant hydrothermal component, like those at Lemarchant, have elevated Fe/Al and base-metal contents, compared to detrital shales, and shale-normalized negative Ce and positive Eu anomalies, indicative of deposition from high temperature (>250°C) hydrothermal fluids within an oxygenated water column. Mudstones and shales sampled from other locations in the Tally Pond volcanic belt have more variable signatures ranging from hydrothermal (signatures as above) to non-hydrothermal (no positive Eu-anomalies, flat REE patterns), with some that have mixed (hydrothermal and detrital) signatures. Both S and Pb isotopic compositions indicate that proximal sulphides hosted in mudstones immediately associated with massive sulphide mineralization within the Lemarchant deposit contain a higher proportion of sulphur derived from hydrothermal sources and processes, and have more juvenile lead contributions, when compared to sulphides distal (not associated with massive sulphides) from mineralization. Lead and Nd isotopic compositions of both whole rock and minerals in the Lemarchant mudstones indicate involvement of underlying crustal basement during massive sulphide formation and throughout the evolution of the Tally Pond belt. Metalliferous mudstones precipitated early in the massive sulphide depositional history, but also have undergone syn- and post-ore-forming processes and have a larger lateral extent than the mineralization. Using lithogeochemistry, whole rock and in situ stable and radiogenic isotopes it is possible to distinguish prospective vent proximal (immediately associated with massive sulphide mineralization) from less prospective distal (not associated with massive sulphides) depositional environments and to reconstruct the paleotectonic setting on a deposit- to regional-scale for the Lemarchant deposit and other mudstone-associated prospects in the Tally Pond volcanic belt.

Organic carbon sources and their transfer in a gulf of Mexico coral reef ecosystem

Coral reefs face unprecedented threats throughout most of their range. Poorly planned coastal development has contributed increased nutrients and sewage contamination to coastal waters, smothering some corals and contributing to overgrowth by macroalgae. My approach to assessing the degree to which coral reef ecosystems have been influenced by terrestrial and anthropogenic organic carbon inputs is through the use of carbon (C) and nitrogen (N) stable isotopes and lipid biomarkers in a marine protected area, the Coral Reef System of Veracruz: Parque Nacional Sistema Arrecifal Veracruzano (PNSAV) in the southwest Gulf of Mexico. Firstly, I used a C and N stable isotope mixing model and a calculated fatty acid (FA) retention factor to reveal the primary producer sources that fuel the coral reef food web. Secondly, I used lipid classes, FA and sterol biomarkers to determine production of terrestrial and marine biogenic material of nutritional quality to pelagic and benthic organisms. Finally, I used coprostanol to determine pollutant loading from sewage in the suspended particulate matter. Results indicate that phytoplankton is the major source of essential metabolite FA for marine fish and that dietary energy from terrestrial sources such as mangroves are transferred to juvenile fish, while seagrass non-essential FA are transferred to the entire food web mainly in the rainy season. Sea urchins may be the main consumers of brown macroalgae, especially in the dry season, while surgeon fish prefer red algae in both dry and rainy seasons. C and N isotopic values and the ratio C:N suggest that fertilizer is the principal source of nitrogen to macroalgae. Thus nitrogen supply also favored phytoplankton and seagrass growth leading to a better nutritional condition and high retention of organic carbon in the food web members during the rainy season when river influence increases. However, the great star coral Montastrea cavernosa nutritional condition decreased significantly in the rainy season. The nearest river to the PNSAV was polluted in the dry season; however, a dilution effect was detected in the rainy season, when some coral reefs were contaminated. In 2013, a new treatment plant started working in the area. I would suggest monitoring δ¹⁵N and the C: N ratio in macroalgae as indicators of the nitrogen input and coprostanol as an indicator of human feces pollution in order to verify the efficiency of the new treatment plant as part of the management program of the PNSAV.