Physical Sciences and Mathematics Commons^™

Apparent Contours For Piecewise Smooth Surfaces, Sarah Marie Jackman

UNF Graduate Theses and Dissertations

The set of points on an embedded surface $M$ that are tangent to a set viewing direction $\mathbf{v}$ is called the contour generator of $M$. The projection of those points to an image plane is called a surface's apparent contour. Apparent contours hold certain properties that allow for reconstruction of the original surface using only the information of the apparent contour. In this paper, we explore the structure of the apparent contour through contact classes and singularity types. Additionally we examine the properties of apparent contours that allow for 3 dimensional reconstruction. Our goal is to extend the properties of …

Elliptic Functions And Iterative Algorithms For Π, Eduardo Jose Evans

UNF Graduate Theses and Dissertations

Preliminary identities in the theory of basic hypergeometric series, or `q-series', are proven. These include q-analogues of the exponential function, which lead to a fairly simple proof of Jacobi's celebrated triple product identity due to Andrews. The Dedekind eta function is introduced and a few identities of it derived. Euler's pentagonal number theorem is shown as a special case of Ramanujan's theta function and Watson's quintuple product identity is proved in a manner given by Carlitz and Subbarao. The Jacobian theta functions are introduced as special kinds of basic hypergeometric series and various relations between them derived using the triple …

The Lie Algebra Sl2(C) And Krawtchouk Polynomials, Nkosi Alexander

UNF Graduate Theses and Dissertations

The Lie algebra L = sl2(C) consists of the 2 × 2 complex matrices that have trace zero, together with the Lie bracket [y, z] = yz − zy. In this thesis we study a relationship between L and Krawtchouk polynomials. We consider a type of element in L said to be normalized semisimple. Let a, a^∗ be normalized semisimple elements that generate L. We show that a, a^∗ satisfy a pair of relations, called the Askey-Wilson relations. For a positive integer N, we consider an (N + 1)-dimensional irreducible L-module V consisting of the homogeneous polynomials in two variables …

Dynamics Of Mutualism In A Two Prey, One Predator System With Variable Carrying Capacity, Randy Huy Lee

UNF Graduate Theses and Dissertations

We considered the livelihood of two prey species in the presence of a predator species. To understand this phenomenon, we developed and analyzed two mathematical models considering indirect and direct mutualism of two prey species and the influence of one predator species. Both types of mutualism are represented by an increase in the preys' carrying capacities based on direct and indirect interactions between the prey. Because of mutualism, as the death rate parameter of the predator species goes through some critical value, the model shows transcritical bifurcation. Additionally, in the direct mutualism model, as the death rate parameter decreases to …

Minimizing Reaction Systems, Matthew R. Thomas

UNF Graduate Theses and Dissertations

The theoretical model for reaction systems is a relatively new framework originally proposed as a mathematical model for biochemical processes which take place in living cells. Growing interest in this research area has lead to the abstraction of the model for non-biological purpose as well. Reaction systems, with a well understood behavior, have become important for studying transition systems. As with any mathematical model, we want to simplify a given implementation of the model as much as possible while maintaining functional equivalence. This paper discusses the formal model for reaction systems, how we can simplify them with minimization techniques, some …

The Subconstituent Algebra Of A Hypercube, Jared B. Billet

UNF Graduate Theses and Dissertations

We study the hypercube and the associated subconstituent algebra. Let Q_D denote the hypercube with dimension D and let X denote the vertex set of Q_D. Fix a vertex x in X. We denote by A the adjacency matrix of Q_D and by A* = A*(x) the diagonal matrix with yy-entry equal to D − 2i, where i is the distance between x and y. The subconstitutent algebra T = T(x) of Q_D with respect to x is generated by A and A* . We show that A 2A* − 2AA*A + A*A 2 = 4A* A*2A − 2A*AA* + …

Maximality And Applications Of Subword-Closed Languages, Rhys Davis Jones

UNF Graduate Theses and Dissertations

Characterizing languages D that are maximal with the property that D^* ⊆ S^⊗ is an important problem in formal language theory with applications to coding theory and DNA codewords. Given a finite set of words of a fixed length S, the constraint, we consider its subword closure, S^⊗, the set of words whose subwords of that fixed length are all in the constraint. We investigate these maximal languages and present characterizations for them. These characterizations use strongly connected components of deterministic finite automata and lead to polynomial time algorithms for generating such languages. We prove that …

Harmonic Morphisms With One-Dimensional Fibres And Milnor Fibrations, Murphy Griffin

UNF Graduate Theses and Dissertations

We study a problem at the intersection of harmonic morphisms and real analytic Milnor fibrations. Baird and Ou establish that a harmonic morphism from G: \mathbb{R}^m \setminus V_G \rightarrow \mathbb{R}^n\setminus \{0\} defined by homogeneous polynomials of order p retracts to a harmonic morphism \psi|: S^{m-1} \setminus K_\epsilon \rightarrow S^{n-1} that induces a Milnor fibration over the sphere. In seeking to relax the homogeneity assumption on the map G, we determine that the only harmonic morphism $\varphi: \mathbb{R}^m \setminus V_G \rightarrow S^{m-1}\K_\epsilon$ that preserves \arg G is radial projection. Due to this limitation, we confirm Baird and Ou's result, yet establish …

On Representations Of The Jacobi Group And Differential Equations, Benjamin Webster

UNF Graduate Theses and Dissertations

In PDEs with nontrivial Lie symmetry algebras, the Lie symmetry naturally yield Fourier and Laplace transforms of fundamental solutions. Applying this fact we discuss the semidirect product of the metaplectic group and the Heisenberg group, then induce a representation our group and use it to investigate the invariant solutions of a general differential equation of the form .

Self-Assembly Of Dna Graphs And Postman Tours, Katie Bakewell

UNF Graduate Theses and Dissertations

DNA graph structures can self-assemble from branched junction molecules to yield solutions to computational problems. Self-assembly of graphs have previously been shown to give polynomial time solutions to hard computational problems such as 3-SAT and k-colorability problems. Jonoska et al. have proposed studying self-assembly of graphs topologically, considering the boundary components of their thickened graphs, which allows for reading the solutions to computational problems through reporter strands. We discuss weighting algorithms and consider applications of self-assembly of graphs and the boundary components of their thickened graphs to problems involving minimal weight Eulerian walks such as the Chinese Postman Problem and …

The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen

UNF Graduate Theses and Dissertations

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method …

Transitions In Line Bitangency Submanifolds For A One-Parameter Family Of Immersion Pairs, William Edward Olsen

UNF Graduate Theses and Dissertations

Consider two immersed surfaces M and N. A pair of points (p,q) in M x N is called a line bitangency if there is a common tangent line between them. Furthermore, we define the line bitangency submanifold as the union of all such pairs of points in M x N. In this thesis we investigate the dynamics of the line bitangency submanifold in a one-parameter family of immersion pairs. We do so by translating one of the surfaces and studying the wide range of transitions the submanifold may undertake. We then characterize these transitions by the local geometry of each …

Singular Value Inequalities: New Approaches To Conjectures, Peter Chilstrom

UNF Graduate Theses and Dissertations

Singular values have been found to be useful in the theory of unitarily invariant norms, as well as many modern computational algorithms. In examining singular value inequalities, it can be seen how these can be related to eigenvalues and how several algebraic inequalities can be preserved and written in an analogous singular value form. We examine the fundamental building blocks to the modern theory of singular value inequalities, such as positive matrices, matrix norms, block matrices, and singular value decomposition, then use these to examine new techniques being used to prove singular value inequalities, and also look at existing conjectures.

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 …

A Comparison Of Methods For Generating Bivariate Non-Normally Distributed Random Variables, Jaimee E. Stewart

UNF Graduate Theses and Dissertations

Many distributions of multivariate data in the real world follow a non-normal model with distributions being skewed and/or heavy tailed. In studies in which multivariate non-normal distributions are needed, it is important for simulations of those variables to provide data that is close to the desired parameters while also being fast and easy to perform. Three algorithms for generating multivariate non-normal distributions are reviewed for accuracy, speed and simplicity. They are the Fleishman Power Method, the Fifth-Order Polynomial Transformation Method, and the Generalized Lambda Distribution Method. Simulations were run in order to compare the three methods by how well they …

Tests For Correlation On Bivariate Nonnormal Distributions, Louanne Margaret Beversdorf

UNF Graduate Theses and Dissertations

Many samples in the real world are very small in size and often do not follow a normal distribution. Existing tests for correlation have restrictions on the distribution of data and sample sizes, therefore the current tests cannot be used in some real world situations.

In this thesis, two tests are considered to test hypotheses about the population correlation coefficient. The tests are based on statistics transformed by a saddlepoint approximation and by Fisher's Z-transformation. The tests are conducted on small samples of bivariate nonnormal data and found to perfom well.

Simulations were run in order to compare the type …

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 …

The Kronecker Product, Bobbi Jo Broxson

UNF Graduate Theses and Dissertations

This paper presents a detailed discussion of the Kronecker product of matrices. It begins with the definition and some basic properties of the Kronecker product. Statements will be proven that reveal information concerning the eigenvalues, singular values, rank, trace, and determinant of the Kronecker product of two matrices. The Kronecker product will then be employed to solve linear matrix equations. An investigation of the commutativity of the Kronecker product will be carried out using permutation matrices. The Jordan - Canonical form of a Kronecker product will be examined. Variations such as the Kronecker sum and generalized Kronecker product will be …

Applications Of Stochastic Calculus To Finance, Scott Stelljes

UNF Graduate Theses and Dissertations

Stochastic Calculus has been applied to the problem of pricing financial derivatives since 1973 when Black and Scholes published their famous paper "The Pricing of Options and Corporate Liabilities" in the Joumal of Political Economy. The purpose of this thesis is to show the mathematical principles underlying the methods applied to finance and to present a new model of the stock price process.

As part of this paper, we present proofs of Ito's Formula and Girsanov's Theorem which are frequently used in financial applications. We demonstrate the application of these theorems to calculating the fair price of a European call …

Robust I-Sample Analysis Of Means Type Randomization Tests For Variances, Anthony Joseph Bernard

UNF Graduate Theses and Dissertations

The advent of powerful computers has brought about the randomization technique for testing statistical hypotheses. Randomization tests are based on shuffles or rearrangements of the (combined) sample. Putting each of the I samples "in a bowl" forms the combined sample. Drawing samples "from the bowl" forms a shuffle. Shuffles can be made with or without replacement.

In this thesis, analysis of means type randomization tests will be presented to solve the homogeneity of variance problem. An advantage of these tests is that they allow the user to graphically present the results via a decision chart similar to a Shewhart control …

An Efficient Implementation Of The Transportation Problem, Alissa Michele Sustarsic

UNF Graduate Theses and Dissertations

The transportation problem is a special type of linear program in which the objective is to minimize the total cost of shipping a single commodity from a number of sources (m) to a number of destinations or sinks (n).

Because of the special structure of the transportation problem, a special algorithm can be designed to find an optimal solution efficiently. Due to the large amount of information in the problem, judicious storage and management of the data are essential requirements of any viable implementation of the transportation algorithm.

Using sparse matrix techniques to store the solution …

A Bayesian Meta-Analysis Using The Gibbs Sampler, Shannon Marie Fair

UNF Graduate Theses and Dissertations

A meta-analysis is the combination of results from several similar studies, conducted by different scientists, in order to arrive at a single, overall conclusion. Unlike common experimental procedures, the data used in a meta-analysis happen to be the descriptive statistics from the distinct individual studies.

In this thesis, we will consider two regression studies performed by two scientists. These studies have one common dependent variable, Y, and one or more independent common variables, X. A regression of Y on X with other independent variables is carried out on both studies. We will estimate the regression coefficients of X …

Monte Carlo Methods For Confidence Bands In Nonlinear Regression, Shantonu Mazumdar

UNF Graduate Theses and Dissertations

Confidence Bands for Nonlinear Regression Functions can be found analytically for a very limited range of functions with a restrictive parameter space. A computer intensive technique, the Monte Carlo Method will be used to develop an algorithm to find confidence bands for any given nonlinear regression functions with a broader parameter space.

The logistic regression function with one independent variable and two parameters will be used to test the validity and efficiency of the algorithm. The confidence bands for this particular function have been solved for analytically by Khorasani and Milliken (1982). Their derivations will be used to test the …

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.

A Study Of The Two Major Causes Of Neonatal Deaths: Perinatal Conditions And Congenital Anomalies, Felipe Lorenzo-Luaces

UNF Graduate Theses and Dissertations

Infant mortality is a public health concern in the United states. We concentrate on neonatal mortality for its high accountability of infant mortality. In this paper we study the neonatal mortality of Florida's 1989 live birth cohort.

The data has been analyzed for two major causes of deaths: perinatal conditions and congenital anomalies. We use the KAPLAN-MEIER method to estimate the survival probabilities. For each cause, data were fit to the Weibull models and Extreme Value models to estimate the parameters of the survival curves. The results indicate that primary factors for each cause of neonatal deaths are very low …

A Relationship Between The Fibonacci Sequence And Cantor's Ternary Set, John David Samons

UNF Graduate Theses and Dissertations

The Fibonacci sequence and Cantor's ternary set are two objects of study in mathematics. There is much theory published about these two objects, individually. This paper provides a fascinating relationship between the Fibonacci sequence and Cantor's ternary set. It is a fact that every natural number can be expressed as the sum of distinct Fibonacci numbers. This expression is unique if and only if no two consecutive Fibonacci numbers are used in the expression--this is known as Zekendorf's representation of natural numbers. By Zekendorf's representation, a function F from the natural numbers into [0,0.603] will be defined which has the …

Density Of The Numerators Or Denominators Of A Continued Fraction, Seyed J. Vafabakhsh

UNF Graduate Theses and Dissertations

Let A = {a_n}^∞_{n = 1} be a sequence of positive integers. There are two related sequences P_n and Q_n obtained from A by taking partial convergents out of the number [0; a₁, a₂, ..., a_n, ...], where P_n and Q_n are the numerators and denominators of the finite continued fraction [0; a₁, a₂, ...,a_n].

Let P(n) be the largest positive integer k , such that P_k ≤ n. The sequence Q(n …

Regression Trees Versus Stepwise Regression, Mary Christine Jacobs

UNF Graduate Theses and Dissertations

Many methods have been developed to determine the "appropriate" subset of independent variables in a multiple variable problem. Some of the methods are application specific while others have a wide range of uses. This study compares two such methods, Regression Trees and Stepwise Regression. A simulation using a known distribution is used for the comparison. In 699 out of 742 cases the Regression Tree method gave better predictors than the Stepwise Regression procedure.

A Study Of The Survival Rate Of The Hepatitis B Virus, James Abraham Houck Iii

UNF Graduate Theses and Dissertations

Hepatitis B virus (HBV) is one of many viruses transmitted through the blood or body fluids. This paper concentrates on a mathematical study of the survival rate of HBV. Using data which includes the survival time for individuals who were diagnosed as being affected by HBV and those who died from HBV, we fit non-linear models to study the survival time for people affected by the virus. Survival probabilities suggest an exponential curve for the survival time. We also consider a pure death process which is a stochastic model for the survival time of the individuals affected. Our results show …