Thesis (MAppSci (Manipulative Therapy)) --University of South Australia, 1992

The present study consists of the development of a MATLAB version of computer program (FORTRAN) developed by Papanicolaou (1992) to solve the governing small strain consolidation equation of second order non-linear transit partial differential equation of parabolic type. This program is modified to integrate the settling and consolidation processes together in order to provide continuous results from start to end of the process in a single run of MATLAB program. The study also proposes a method to calculate the batch curve by considering the variation of solids concentration in the suspension region. Instead of the graphical approach available in the literature, the program uses numerical approach (Newton-Raphson method) to calculate the solids concentration in suspension region at the interface of suspension and sedimentation regions. This method uses the empirical relationship between solids flux and solids concentration. The study also proposes a method to calculate the solids concentration, throughout the settling column, using the concept of characteristic. The present work also simulates the large strain consolidation model (Gutierrez, 2003). The results of present work closely match with the results of small strain model (Diplas & Papanicolaou, 1997) available in literature. / Master of Science

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Thesis advisor: Benjamin Howard / We study two moduli problems involving false elliptic curves with complex multiplication (CM), generalizing theorems about the arithmetic degree of certain moduli spaces of CM elliptic curves. The first moduli problem generalizes a space considered by Howard and Yang, and the formula for its arithmetic degree can be seen as a calculation of the intersection multiplicity of two CM divisors on a Shimura curve. This formula is an extension of the Gross-Zagier theorem on singular moduli to certain Shimura curves. The second moduli problem we consider deals with special endomorphisms of false elliptic curves. The formula for its arithmetic degree generalizes a theorem of Kudla, Rapoport, and Yang. / Thesis (PhD) — Boston College, 2015. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

University of Macau / Faculty of Science and Technology. / Department of Computer and Information Science

Choi, Yuet Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 68-72). / Abstracts in English and Chinese. / Acknowledgement --- p.i / Abstract --- p.ii / Contents --- p.vi / List of Figures --- p.viii / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Previous Works --- p.3 / Chapter 1.1.1 --- Template deformation --- p.3 / Chapter 1.1.2 --- Mesh partitioning --- p.3 / Chapter 1.1.3 --- Mesh Smoothing --- p.4 / Chapter 1.2 --- Overview of the approach --- p.5 / Chapter 1.3 --- Thesis outline --- p.7 / Chapter 2. --- Global Deformation --- p.8 / Chapter 2.1 --- The closet point method --- p.10 / Chapter 2.1.1 --- Computational complexity --- p.11 / Chapter 2.2 --- Deformation Techniques --- p.12 / Chapter 2.2.1 --- Existing deformation method --- p.12 / Chapter 2.2.2 --- Radial Basis Functions (RBFs) --- p.14 / Chapter 2.2.2.1 --- Computational complexity --- p.18 / Chapter 2.2.3 --- Result --- p.18 / Chapter 2.3 --- Face flip prevention --- p.20 / Chapter 2.3.1 --- Detection of the flipped face --- p.22 / Chapter 2.3.1.1 --- Common approach: --- p.22 / Chapter 2.3.1.2 --- Our Approach --- p.23 / Chapter 2.3.1.3 --- Comparisons of the face flip detection method: --- p.26 / Chapter 2.3.2 --- Local Subdivision --- p.27 / Chapter 3. --- Partitioning of the mesh --- p.29 / Chapter 3.1 --- Existing method --- p.29 / Chapter 3.2 --- Our approach --- p.31 / Chapter 3.3 --- Computational complexity --- p.34 / Chapter 4. --- Mesh smoothing algorithm --- p.35 / Chapter 4.1 --- The Laplacian flow method --- p.36 / Chapter 4.2 --- The mean-curvature method --- p.40 / Chapter 4.3 --- Our Approach --- p.43 / Chapter 4.3.1 --- The modified mean-curvature method --- p.43 / Chapter 4.3.2 --- The modified Laplacian flow method --- p.45 / Chapter 4.3.3 --- Feature constraints --- p.47 / Chapter 4.3.4 --- Computational complexity --- p.47 / Chapter 4.4 --- Comparison of the mesh smoothing approach --- p.48 / Chapter 5. --- Implementation and Results --- p.51 / Chapter 5.1 --- Construction of the template mesh and boundary curves --- p.51 / Chapter 5.2 --- Selection of the corresponding vertex pairs --- p.52 / Chapter 5.3 --- Results --- p.54 / Chapter 6. --- Conclusions --- p.63 / Chapter 6.1 --- Future development --- p.65 / Appendix A --- p.66 / Determination of the projected path on a mesh: --- p.66 / Reference --- p.68

Bezier curve is one of the most fundamental primitives for the modeling of fonts and two-dimensional (2D) computer graphics objects. How to efficiently render the Bezier curve becomes an important task for many embedded applications. This thesis first proposed a novel adaptive curve-rendering algorithm which can determine the coordinates of all the crossing points of the curve and scan-lines with the required accuracy for the graphics fill operation. Next, for the rendering of stroked Bezier curves, this thesis proposed several possible rendering circuit architectures. The performance and gate count of these architectures have been estimated, and compared in this thesis. It has been found that the design based on the table-lookup normal vector calculator can lead to the fastest circuit, while the design based on the Cordic operator represents the most economic design. A basic Bezier curve rendering circuit has been implemented in this thesis, and used to accelerate a prototype OpenVG embedded systems.