There are four division algebras namely, real numbers, complex numbers, quaternions and octonions. They can be used to represent a number of orthogonal groups. In particular, the groups SO(3) and SO(4) of rotations of 3- and 4-dimensional spaces, respectively, can be described in terms of quaternions. We start with reviewing these cases and next turn to the groups of rotations of 7- and 8- dimensional spaces and describe them in terms of octonions. Since octonions form a non-associative division algebra, we use Moufang Identities to overcome the difficulty of some calculations and provide transformations that generate groups SO(7) and SO(8), which is an alternative description for these orthogonal groups.

A global surgical rotation program has been developed at La Loma Luz Adventist Hospital in San Ignacio, Belize, by the Department of Surgery at East Tennessee State University in 2014. It encompasses a one-month rotation for surgery residents to travel to Belize, accompanied by a senior surgical attending, to participate in direct patient care. Residents are able to operate under supervision and practice both perioperative and medical management. Practitioners often collaborate with permanent facility surgeons and internists in order to assist with cases, discuss different practice strategies, and, ultimately, tailor patient care. In addition to providing residents with surgical experience, this rotation aims to advance the overall standard of medical care available to the community. Additional aims include healthcare promotion and education of patients. While this rotation was developed to provide residents surgical experience in an underserved country, we hope that it will further cultivate volunteerism and foster future participation.

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No / Rotation is a well-known operation on lists. We define its two-dimensional analogue and discuss its implementation in Prolog using difference lists. An application to the iterative solution of a system of linear equations by the Gauss¿Seidel method is given.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

To handle broken 3D models can be a very time consuming problem. Several methods aiming for automatic mesh repair have been presented in the recent years. This thesis gives an extensive evaluation of automatic mesh repair algorithms, presents a mesh repair pipeline and describes an implemented automatic mesh repair algorithm. The presented pipeline for automatic mesh repair includes three main steps: octree generation, surface reconstruction and ray casting. Ray casting is for removal of hidden objects. The pipeline also includes a pre processing step for removal of intersecting triangles and a post processing step for error detection. The implemented algorithm presented in this thesis is a volumetric method for mesh repair. It generates an octree in which data from the input model is saved. Before creation of the output, the octree data will be patched to remove inconsistencies. The surface reconstruction is done with a method called Manifold Dual Contouring. First new vertices are created from the information saved in the octree. Then there is a possibility to cluster vertices together for decimation of the output. Thanks to a special Manifold criterion, the output is guaranteedto be manifold. Furthermore the output will have sharp and clear edges and corners thanks to the use of Singular Value Decomposition during determination of the positions of the new vertices.

Four Rotations Pour Marimba (1996) by Eric Sammut has become one of the most important marimba compositions in serious concert solo marimba literature. Four Rotations Pour Marimba is a suite of four short pieces; each of them demonstrates a different musical character while incorporating similar compositional components and techniques. The goal of this thesis project is to create a stylistic analysis for providing the concert marimbist with insight into the interpretation of these four pieces and also giving composers a more in-depth understanding of Sammut's compositional method. This thesis includes a formal analysis and comparisons of compositional elements used in Four Rotations. A brief biography of Sammut and historical significance of Four Rotations Pour Marimba are also included.

No description available.

The vibrational entropy calculated by applying the harmonic oscillator approximation to all vibrational degrees of freedom is inherently inaccurate. One major reason is because low frequency modes such as internal rotations are not properly described by this approximation. Various techniques were developed in the past to overcome this problem. The hindered rotor potential can be approximated by a series of cosine functions, and the relevant coe cients can be determined by tting to a calculated potential energy surface. However, such a method is di cult and time consuming. Therefore, in this dissertation we propose and describe two less tedious approaches to determine entropy of internal rotational modes. The rst approximation is to express the barrier height in terms of the harmonic oscillator frequency, the local periodicity, and the reduced moment of inertia of the rotation and to approximate the torsional potential by a single cosine function. Thus, the 1D Schr odinger equation for internal rotations can be solved without nding the torsional potential, transition states, or barrier heights. We propose a further simpli cation to this approach, achieved through a simple mathematical formula, that interpolates the hindered rotor entropy between the free rotor and harmonic oscillator limits. We also propose a procedure to automatically determine the axis of rotation for any hindered rotor. The proposed methods were applied to determine the torsional entropy of n- alkanes from ethane to hexane. The entropies calculated from the proposed methods give good agreement with the experimental and accurately calculated values and have a signi cantly better accuracy than the harmonic oscillator approximation. Furthermore, we performed approximate and full hindered rotor treatments to nd the corrected vibrational entropy of bis(chromiumtricarbonyl) dibenzo[a,e]cyclooctatetraene (DBCOT). The eighth chapter of this dissertation is an independent molecular dynamics (MD) project to study how ethanol interacts with human and mouse Toll-Like- Receptor3 (TLR3) monomers and a TLR3-dsRNA complex. No major structural changes were observed during the ethanol docking and subsequent MD simulations, but the MD simulations revealed a reduction in the proportion of alpha helix present during a 1000 ns MD simulation on the h-TLR3 monomer in 0.5 percent ethanol.

Agricultural economists have long studied crop yields and risk to help farm-level risk management. Producers face difficult decisions every year regarding market prices, management practices, and the uncertainty of weather. In our research, we use crop yield records while incorporating the modern portfolio theory to find the optimal planting portfolios giving a specific risk level. Our assets are on corn, cotton, and soybeans yields from the Mississippi Delta region. This study is unique because there are not any previous studies using crop histories linked to the modern portfolio theory. The main idea is to realize how much of each asset or what percentage to invest in out of the specific portfolio. By having these portfolios readily available for farmers, we aim to diminish the risk to help producers with springtime decision-making. Armed with these findings, we can better understand the economic implications of how crop rotations factor into farm-level risk management.