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<p>Whether the growth series of a group is a rational function is investigated in this paper.Parry showed certain torus bundle groups of even trace exhibits rational growth, and thisresult has been extended by the author, Turbo Ho and Mark Pengitore. In this paper, bothresults are combined into a single proof used in [1], and the result is pushed further into thenegative case not covered in earlier works</p>

<p>Sheet specimens of alloy AZ31 were cross-rolled to equivalent strains of 0.05, 0.10, 0.30, 0.40, 0.56, and 0.77. The microstructure evolution was examined using a combination of optical metallography (OM), Electron Backscattered Diffraction (EBSD), Transmission Electron Microscopy (TEM) and X-ray diffraction (XRD). The results revealed significant activity of basal and non-basal slip as well as twinning. The twins were mainly of the contraction and double-twin (contraction-extension) types. In addition to the micron scale (1-5μm) twins observed on EBSD patterns, nano-scale twins were observed. The nano twins had a width of less than 0.20μm and existed either as individual/isolated twins or as twin-bundles that are several microns thick. The number of nano twin-bundles increased with increasing strain. Shear bands were also observed to form at high strains and eventually led to the failure of the sheet. As for the texture evolution, analysis of the pole figures shows an evident strengthening of the basal texture during the cross-rolling.</p> <p>Specimens of Mg alloy AZ31 cold-rolled to equivalent strains of 0.10 and 0.30 were selected and annealed at 250^oC. The progress of recrystallization was followed using OM, EBSD and TEM with special emphasis on the nucleation of recrystallization. The distribution of recrystallization nuclei was very heterogeneous due to the heterogeneity of the as-deformed microstructure. Twin/grain-boundary and twin/twin intersections as well as twin interiors were the dominant recrystallization nucleation sites. Significant recovery was observed in the non-recrystallized regions and this limited the growth of the recrystallized grains.</p> / Master of Applied Science (MASc)

This paper presents a new approach to the feature-matching problem for 3D reconstruction by taking advantage of GPS and IMU data, along with a prior calibrated stereo camera system. It is expected that pose estimates and calibration can be used to increase feature matching speed and accuracy. Given pose estimates of cameras and extracted features from images, the algorithm first enumerates feature matches based on stereo projection constraints in 2D and then backprojects them to 3D. Then, a grid search algorithm over potential camera poses is proposed to match the 3D features and find the largest group of 3D feature matches between pairs of stereo frames. This approach will provide pose accuracy to within the space that each grid region covers. Further refinement of relative camera poses is performed with an iteratively re-weighted least squares (IRLS) method in order to reject outliers in the 3D matches. The algorithm is shown to be capable of running in real-time correctly, where the majority of processing time is taken by feature extraction and description. The method is shown to outperform standard open source software for reconstruction from imagery. / Master of Science

A simulation model which incorporates the statistical- and numerical-based Lattice Green Function Local Load Sharing Model and a Fracture Mechanics-based Residual Strength Model has been developed. The model simulates creep rupture by imposing a fixed load of constant stress on the composite over the simulation duration. Simulation of the fatigue of glass fiber-reinforced composites is achieved by replacing the constant stress parameter in the model with a sinusoidal wave function. Results from the creep rupture model using fused silica fiber parameters, compare well with S-2 glass/epoxy systems. Results using Mandell's postulate that fatigue failure in glass fiber-reinforced polymeric composites is a fiber-dominated mechanism, with a characteristic slope of 10 %UTS/decade are consistent with available experimental data. The slopes of fatigue curves for simulated composites for three frequencies namely: 2, 5 and 10 Hz are within 12-14 %UTS/decade compared with that of 10.6-13.0%UTS/decade for unidirectionl glass reinforced composites (epoxy and vinyl ester) obtained from Demers' [40] data. / Master of Science