Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 153-170). Also available in print.

Thesis (M.S.)--Ohio University, June, 1995. / Title from PDF t.p.

published_or_final_version / Obstetrics and Gynaecology / Master / Master of Philosophy

No description available.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 41-42). Also available via the Internet.

Thesis (Ph. D.)--University of Alberta, 2010. / Title from pdf file main screen (viewed on July 13, 2010). A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, Department of Mathematical and Statistical Sciences, University of Alberta. Includes bibliographical references.

No description available.

In this thesis we study Mahler's conjecture in convex geometry, give a short summary about its history, gather and explain different approaches that have been used to attack the conjecture, deduce formulas to calculate the Mahler volume and perform numerical analysis on it. The conjecture states that the Mahler volume of any symmetric convex body, i.e. the product of the volume of the symmetric convex body and the volume of its dual body, is minimized by the (hyper-)cube. The conjecture was stated and solved in 1938 for the 2-dimensional case by Kurt Mahler. While the maximizer for this problem is known (it is the ball), the conjecture about the minimizer is still open for all dimensions greater than 2. A lot of effort has benn made to solve this conjecture, and many different ways to attack the conjecture, from simple geometric attempts to ones using sophisticated results from functional analysis, have all been tried unsuccesfully. We will present and discuss the most important approaches. Given the support function of the body, we will then introduce several formulas for the volume of the dual and the original body and hence for the Mahler volume. These formulas are tested for their effectiveness and used to perform numerical work on the conjecture. We examine the conjectured minimizers of the Mahler volume by approximating them in different ways. First the spherical harmonic expansion of their support functions is calculated and then the bodies are analyzed with respect to the length of that expansion. Afterwards the cube is further examined by approximating its principal radii of curvature functions, which involve Dirac delta functions.

No description available.

Volume rendering, the direct display of data from 3D scalar fields, is an area of computer graphics still in its infancy. Only recently has graphics hardware advanced to a state where volume rendering became feasible. Volume rendering requires the analysis of large amounts of data, typically tens of megabytes. As hardware speeds increase, we can only expect the datasets to get larger. This thesis describes a reasonably fast, space efficient algorithm for volume rendering. The algorithm is device independent since it is written as an X Windows client. It makes no graphics calls to dedicated graphics hardware, but allows the X server to take advantage of such hardware when it exists. It can be run on any machine that supports X Windows, from an IBM-PC to a high-end graphics workstation. It produces a perspective projection of the volume, since perspective projections are generally easier to interpret than parallel projections. The algorithm uses progressive refinement to give the user a quick view of the dataset and how it is oriented. If a different orientation or dataset is desired, the user may interrupt the rendering process. Once the desired dataset and position have been determined, the progressive refinement process continues and the image improves in quality until the greatest level of detail is displayed. While this algorithm may not be as fast as algorithms written specifically for dedicated graphics hardware, its overall rendering time is acceptable. Hardware vendors who develop X servers that take advantage of their graphics capabilities will only enhance the performance of our algorithm. The device independence this algorithm provides is a major benefit for people who work in an environment of mixed hardware platforms. / Master of Science