Physical Sciences and Mathematics Commons^™

The Weil Pairing On Elliptic Curves And Its Cryptographic Applications, Alex Edward Aftuck

UNF Graduate Theses and Dissertations

This thesis presents the Weil pairing on elliptic curves as a tool to implement a tripartite Diffie-Helman key exchange. Elliptic curves are introduced, as well as the addition operation that creates a group structure on its points. In leading to the definition of the Weil pairing, divisors of rational functions are studied, as well as the Weierstrass }-function, which shows the complex lattice as isomorphic to elliptic curves. Several important qualities of the Weil pairing are proved, and Miller's algorithm for quick calculation is shown. Next, the bipartite Diffie-Helman key exchange is discussed over finite fields and elliptic curves. Finally …

Modeling And Synergy Testing Of Drug Combination Data: A Pharmacokinetic Analysis, Jacy Rebecca Crosby

UNF Graduate Theses and Dissertations

In this paper, we present and implement a method to assess the mathematical synergy of two-drug combinations based on a stochastic model. The drugs in question are two isomers that are applied to the human eye via a liquid eye drop. Techniques applied to the data in this paper can be applied to other two-drug combination studies.

We derive the mean and the variance terms of the drug combination "effects" in closed form using Ito's method of stochastic differential equations. The model fit of the data to the individual subject is examined by both statistical and graphical methods. Two estimation …

A General Theory Of Geodesics With Applications To Hyperbolic Geometry, Deborah F. Logan

UNF Graduate Theses and Dissertations

In this thesis, the geometry of curved surfaces is studied using the methods of differential geometry. The introduction of manifolds assists in the study of classical two-dimensional surfaces. To study the geometry of a surface a metric, or way to measure, is needed. By changing the metric on a surface, a new geometric surface can be obtained. On any surface, curves called geodesics play the role of "straight lines" in Euclidean space. These curves minimize distance locally but not necessarily globally. The curvature of a surface at each point p affects the behavior of geodesics and the construction of geometric …

Statistical Analysis Of Survival Data, Rexanne Marie Bruno

UNF Graduate Theses and Dissertations

The terminology and ideas involved in the statistical analysis of survival data are explained including the survival function, the probability density function, the hazard function, censored observations, parametric and nonparametric estimations of these functions, the product limit estimation of the survival function, and the proportional hazards estimation of the hazard function with explanatory variables.

In Appendix A these ideas are applied to the actual analysis of the survival data for 54 cervical cancer patients.