Physical Sciences and Mathematics Commons^™

Superconvergence In Iterated Solutions Of Integral Equations, Peter A. Padilla

Mathematics & Statistics Theses & Dissertations

In this thesis, we investigate the superconvergence phenomenon of the iterated numerical solutions for the Fredholm integral equations of the second kind as well as a class of nonliner Hammerstein equations. The term superconvergence was first described in the early 70s in connection with the solution of two-point boundary value problems and other related partial differential equations. Superconvergence in this context was understood to mean that the order of convergence of the numerical solutions arising from the Galerkin as well as the collocation method is higher at the knots than we might expect from the numerical solutions that are obtained …

The Solution Of Hypersingular Integral Equations With Applications In Acoustics And Fracture Mechanics, Richard S. St. John

Mathematics & Statistics Theses & Dissertations

The numerical solution of two classes of hypersingular integral equations is addressed. Both classes are integral equations of the first kind, and are hypersingular due to a kernel containing a Hadamard singularity. The convergence of a Galerkin method and a collocation method is discussed and computationally efficient algorithms are developed for each class of hypersingular integral equation.

Interest in these classes of hypersingular integral equations is due to their occurrence in many physical applications. In particular, investigations into the scattering of acoustic waves by moving objects and the study of dynamic Griffith crack problems has necessitated a computationally efficient technique …

Reaction-Diffusion Models Of Cancer Dispersion, Kim Yvette Ward

Mathematics & Statistics Theses & Dissertations

The phenomenological modeling of the spatial distribution and temporal evolution of one-dimensional models of cancer dispersion are studied. The models discussed pertain primarily to the transition of a tumor from an initial neoplasm to the dormant avascular state, i.e. just prior to the vascular state, whenever that may occur. Initiating the study is the mathematical analysis of a reaction-diffusion model describing the interaction between cancer cells, normal cells and growth inhibitor. The model leads to several predictions, some of which are supported by experimental data and clinical observations $\lbrack25\rbrack$. We will examine the effects of additional terms on these characteristics. …

Mathematical Models Of Tumors And Their Remote Metastases, Carryn Bellomo

Mathematics & Statistics Theses & Dissertations

Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.

It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model …

Error-Correcting Codes Associated With Generalized Hadamard Matrices Over Groups, Iem H. Heng

Mathematics & Statistics Theses & Dissertations

Classical Hadamard matrices are orthogonal matrices whose elements are ±1. It is well-known that error correcting codes having large minimum distance between codewords can be associated with these Hadamard matrices. Indeed, the success of early Mars deep-space probes was strongly dependent upon this communication technology.

The concept of Hadamard matrices with elements drawn from an Abelian group is a natural generalization of the concept. For the case in which the dimension of the matrix is q and the group consists of the p-th roots of unity, these generalized Hadamard matrices are called “Butson Hadamard Matrices BH(p, q)”, …