Physical Sciences and Mathematics Commons^™

Stochastic Modeling And Analysis Of Energy Commodity Spot Price Processes, Olusegun Michael Otunuga

USF Tampa Graduate Theses and Dissertations

Supply and demand in the World oil market are balanced through responses to price movement with considerable complexity in the evolution of underlying supply-demand

expectation process. In order to be able to understand the price balancing process, it is important to know the economic forces and the behavior of energy commodity spot price processes. The relationship between the different energy sources and its utility together with uncertainty also play a role in many important energy issues.

The qualitative and quantitative behavior of energy commodities in which the trend in price of one commodity coincides with the trend in price of …

Topological Data Analysis Of Properties Of Four-Regular Rigid Vertex Graphs, Grant Mcneil Conine

USF Tampa Graduate Theses and Dissertations

Homologous DNA recombination and rearrangement has been modeled with a class of four-regular rigid vertex graphs called assembly graphs which can also be represented by double occurrence words. Various invariants have been suggested for these graphs, some based on the structure of the graphs, and some biologically motivated.

In this thesis we use a novel method of data analysis based on a technique known as partial-clustering analysis and an algorithm known as Mapper to examine the relationships between these invariants. We introduce some of the basic machinery of topological data analysis, including the construction of simplicial complexes on a data …

A Maximum Principle In The Engel Group, James Klinedinst

USF Tampa Graduate Theses and Dissertations

In this thesis, we will examine the properties of subelliptic jets in the Engel group of step 3. Step-2 groups, such as the Heisenberg group, do not provide insight into the general abstract calculations. This thesis then, is the first explicit non-trivial computation of the abstract results.

On The Classification Of Groups Generated By Automata With 4 States Over A 2-Letter Alphabet, Louis Caponi

USF Tampa Graduate Theses and Dissertations

The class of groups generated by automata have been a source of many counterexamples in group theory. At the same time it is connected to other branches of mathematics, such as analysis, holomorphic dynamics, combinatorics, etc. A question that naturally arises is finding the ways to classify these groups. The task of a complete classification and understanding at the moment seems to be too ambitious, but it is reasonable to concentrate on some smaller subclasses of this class. One approach is to consider groups generated by small automata: the automata with k states over d-letter alphabet (so called, (k,d)-automata) with …

Properties Of Graphs Used To Model Dna Recombination, Ryan Arredondo

USF Tampa Graduate Theses and Dissertations

A model for DNA recombination uses 4-valent rigid vertex graphs,

called assembly graphs. An assembly graph,

similarly to the projection of knots, can be associated with an

unsigned Gauss code, or double occurrence word.

We define biologically motivated reductions that act on double

occurrence words and, in turn, on their associated assembly graphs. For

every double occurrence word w there is a sequence of reduction

operations that may be applied to w so that what remains is the

empty word, [epsilon]. Then the nesting index of a word w,

denoted by NI(w), is defined to to be …

Topological Degree And Variational Inequality Theories For Pseudomonotone Perturbations Of Maximal Monotone Operators, Teffera Mekonnen Asfaw

USF Tampa Graduate Theses and Dissertations

Let X be a real reflexive locally uniformly convex

Banach space with locally uniformly convex dual space X^*

. Let G be a

bounded open subset of X. Let T:X⊃ D(T)⇒ 2X^*

be maximal

monotone and S: X ⇒ 2X^*

be bounded

pseudomonotone and such that 0 notin cl((T+S)(D(T)∩partG)). Chapter 1 gives general introduction and mathematical prerequisites. In

Chapter 2 we develop a homotopy invariance and uniqueness results for the degree theory constructed by Zhang and Chen for multivalued (S₊) perturbations of

maximal monotone operators. Chapter 3 is devoted to the construction of a new …

A Study Of Permutation Polynomials Over Finite Fields, Neranga Fernando

USF Tampa Graduate Theses and Dissertations

Let p be a prime and q = p^k. The polynomial g_n,q isin F_p[x] defined by the functional equation Sigma_{a isin Fq} (x+a)ⁿ = g_n,q(x^q- x) gives rise to many permutation polynomials over finite fields. We are interested in triples (n,e;q) for which g_n,q is a permutation polynomial of F_q^e. In Chapters 2, 3, and 4 of this dissertation, we present many new families of permutation polynomials in the form of g_n,q. The permutation behavior of g_n,q is becoming increasingly more …

Boolean Partition Algebras, Joseph Anthony Van Name

USF Tampa Graduate Theses and Dissertations

A Boolean partition algebra is a pair $(B,F)$ where $B$ is a Boolean

algebra and $F$ is a filter on the semilattice of partitions of $B$ where $\bigcup F=B\setminus\{0\}$. In this dissertation, we shall investigate the algebraic theory of Boolean partition algebras and their connection with uniform spaces. In particular, we shall show that the category of complete non-Archimedean uniform spaces

is equivalent to a subcategory of the category of Boolean partition algebras, and notions such as supercompleteness

of non-Archimedean uniform spaces can be formulated in terms of Boolean partition algebras.

Analytic Functions With Real Boundary Values In Smirnov Classes EP, Lisa De Castro

USF Tampa Graduate Theses and Dissertations

This thesis concerns the classes of analytic functions on bounded, n-connected domains known as the Smirnov classes E^p, where p > 0. Functions in these classes satisfy a certain growth condition and have a relationship to the more well known classes of functions known as the Hardy classes H^p. In this thesis I will show how the geometry of a given domain will determine the existence of non-constant analytic functions in Smirnov classes that possess real boundary values. This is a phenomenon that does not occur among functions in the Hardy classes.

The preliminary and background information …

Optimization In Non-Parametric Survival Analysis And Climate Change Modeling, Iuliana Teodorescu

USF Tampa Graduate Theses and Dissertations

Many of the open problems of current interest in probability and statistics involve complicated data

sets that do not satisfy the strong assumptions of being independent and identically distributed. Often,

the samples are known only empirically, and making assumptions about underlying parametric

distributions is not warranted by the insufficient information available. Under such circumstances,

the usual Fisher or parametric Bayes approaches cannot be used to model the data or make predictions.

However, this situation is quite often encountered in some of the main challenges facing statistical,

data-driven studies of climate change, clinical studies, or financial markets, to name a few. …

Towards Interference-Immune And Channel-Aware Multicarrier Schemes: Filters, Lattices, And Interference Issues, Alphan Sahin

USF Tampa Graduate Theses and Dissertations

In this dissertation, multicarrier schemes are reviewed within the framework of Gabor Systems. Their fundamental elements; what to transmit, i.e., symbols, how to transmit, i.e., filters or pulse shape, and where/when to transmit, i.e., lattices are investigated extensively. The relations between different types of multicarrier schemes are discussed.

Within the framework of Gabor systems, a new windowing approach, edge windowing, is developed to address the out-of-band (OOB) radiation problem of orthogonal frequency division multiplexing (OFDM) based multicarrier schemes. To the best of our knowledge, for the first time, the diversity on the range of the users is exploited to suppress …

Nonlinear Techniques For Stochastic Systems Of Differential Equations, Tadesse G. Zerihun

USF Tampa Graduate Theses and Dissertations

Two of the most well-known nonlinear methods for investigating nonlinear dynamic processes in sciences and engineering are nonlinear variation of constants parameters and comparison method. Knowing the existence of solution process, these methods provide a very powerful tools for investigating variety of problems, for example, qualitative and quantitative properties of solutions, finding error estimates between solution processes of stochastic system and the corresponding nominal system, and inputs for the designing engineering and industrial problems. The aim of this work is to systematically develop mathematical tools to undertake the mathematical frame-work to investigate a complex nonlinear nonstationary stochastic systems of differential …

Modeling State Transitions With Automata, Egor Dolzhenko

USF Tampa Graduate Theses and Dissertations

Models based on various types of automata are ubiquitous in modern science. These models allow reasoning about deep theoretical questions and provide a basis for the development of efficient algorithms to solve related computational problems. This work discusses several types of automata used in such models, including cellular automata and mandatory results automata.

The first part of this work is dedicated to cellular automata. These automata form an important class of discrete dynamical systems widely used to model physical, biological, and chemical processes. Here we discuss a way to study the dynamics of one-dimensional cellular automata through the theory of …

On Algorithmic Fractional Packings Of Hypergraphs, Jill Dizona

USF Tampa Graduate Theses and Dissertations

Let F₀ be a fixed k-uniform hypergraph, and let H be a given k-uniform hypergraph on n vertices. An F₀-packing of H is a family F of edge-disjoint copies of F₀ which are subhypergraphs in H. Let n_F0(H) denote the maximum size |F| of an F₀-packing F of H. It is well-known that computing n_F0(H) is NP-hard for nearly any choice of F₀.

In this thesis, we consider the special case when F₀ is a linear hypergraph, that is, when no two edges …

Wronskian, Grammian And Pfaffian Solutions To Nonlinear Partial Differential Equations, Alrazi Abdeljabbar

USF Tampa Graduate Theses and Dissertations

It is significantly important to search for exact soliton solutions to nonlinear partial differential equations (PDEs) of mathematical physics. Transforming nonlinear PDEs into bilinear forms using the Hirota differential operators enables us to apply the Wronskian and Pfaffian techniques to search for exact solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation with not only constant coefficients but also variable coefficients under a certain constraint

(u_t + α ₁(t)u_xxy + 3α ₂(t)u_xu_y)_x +α ₃ (t)u_ty -α ₄(t)u_zz + α ₅(t)(u_x + α ₃(t)u_y) = …

Pfaffian And Wronskian Solutions To Generalized Integrable Nonlinear Partial Differential Equations, Magdy Asaad

USF Tampa Graduate Theses and Dissertations

The aim of this work is to use the Pfaffian technique, along with the Hirota bilinear method to construct different classes of exact solutions to various of generalized integrable nonlinear partial differential equations. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.

The derivation and solutions of integrable nonlinear partial differential equations in two spatial dimensions have been …

Team-Teaching Experiences Of A Mathematician And A Mathematics Teacher Educator: An Interpretative Phenomenological Case Study, Sarah K. Bleiler

USF Tampa Graduate Theses and Dissertations

In recent years, experts and organizations involved in mathematics education have emphasized the importance of collaboration between mathematicians and mathematics teacher educators as a means of improving the professional preparation of mathematics teachers. While several such collaborative endeavors have been documented in the extant literature, most research reports have focused on the products, rather than the process, of collaboration. The purpose of this interpretative phenomenological case study is to gain an understanding of the lived experiences of a mathematician and a mathematics teacher educator as they engaged in a team-teaching collaboration within the context of prospective secondary mathematics teacher preparation. …

Self-Assembly Of Self-Similar Structures By Active Tiles, Daria Karpenko

USF Tampa Graduate Theses and Dissertations

The natural capacity of DNA for molecular self-assembly has already been exploited to create DNA based tiles which can self-assemble into nano-scale arrays and carry out nano-scale computation. Thus far, however, all such self-assembly has been passive, in the sense that the binding capacities of a tile are never altered throughout the assembly. The idea of active tiles, tiles that can send signals to each other and activate latent binding sites, has been proposed but never incorporated into a formal model. Here, I present an extension of the existent abstract tile assembly model by defining an active tile assembly and …

Hamiltonian Sets Of Polygonal Paths In 4-Valent Spatial Graphs, Tilahun Abay Muche

USF Tampa Graduate Theses and Dissertations

Spatial graphs with 4–valent rigid vertices and two single valent endpoints, called assembly graphs, model DNA recombination processes that appear in certain species of ciliates. Recombined genes are modeled by certain types of paths in an assembly graph that make a ”oper pendicular ” turn at each 4–valent vertex of the graph called polygonal paths. The assembly number of an assembly graph is the minimum number of polygonal paths that visit each vertex exactly once. In particular, an assembly graph is called realizable if the graph has a Hamiltonian polygonal path.

An assembly graph ɣ^{^} obtained from a given …

Multi-Time Scales Stochastic Dynamic Processes: Modeling, Methods, Algorithms, Analysis, And Applications, Jean-Claude Pedjeu

USF Tampa Graduate Theses and Dissertations

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model is formulated and it leads to a system of multi-time scale stochastic differential equations. The classical Picard-Lindel\"{o}f successive approximations scheme is expended to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this generates to a problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations. To illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are exhibited. Without loss in generality, …

Stochastic Hybrid Dynamic Systems: Modeling, Estimation And Simulation, Daniel Siu

USF Tampa Graduate Theses and Dissertations

Stochastic hybrid dynamic systems that incorporate both continuous and discrete dynamics have been an area of great interest over the recent years. In view of applications, stochastic hybrid dynamic systems have been employed to diverse fields of studies, such as communication networks, air traffic management, and insurance risk models. The aim of the present study is to investigate properties of some classes of stochastic hybrid dynamic systems.

The class of stochastic hybrid dynamic systems investigated has random jumps driven by a non-homogeneous Poisson process and deterministic jumps triggered by hitting the boundary. Its real-valued continuous dynamic between jumps is described …

Integrable Couplings Of The Kaup-Newell Soliton Hierarchy, Mengshu Zhang

USF Tampa Graduate Theses and Dissertations

By enlarging the spatial and temporal spectral problems within a certain Lie algebra, a hierarchy of integrable couplings of the Kaup-Newell soliton equations is constructed. The recursion operator of the resulting hierarchy of integrable couplings is explicitly computed. The integrability of the new coupling hierarchy is exhibited by showing the existence of infinitely many commuting symmetries.

Bi-Integrable And Tri-Integrable Couplings And Their Hamiltonian Structures, Jinghan Meng

USF Tampa Graduate Theses and Dissertations

An investigation into structures of bi-integrable and tri-integrable couplings is undertaken. Our study is based on semi-direct sums of matrix Lie algebras. By introducing new classes of matrix loop Lie algebras, we form new Lax pairs and generate several new bi-integrable and tri-integrable couplings of soliton hierarchies through zero curvature equations. Moreover, we discuss properties of the resulting bi-integrable couplings, including infinitely many commuting symmetries and conserved densities. Their Hamiltonian structures are furnished by applying the variational identities associated with the presented matrix loop Lie algebras.

The goal of this dissertation is to demonstrate the efficiency of our approach and …

Fundamental Transversals On The Complexes Of Polyhedra, Joy D'Andrea

USF Tampa Graduate Theses and Dissertations

We present a formal description of `Face Fundamental Transversals' on the faces of the Complexes of polyhedra (meaning threedimensional polytopes). A Complex of a polyhedron is the collection of the vertex points of the polyhedron, line segment edges and polygonal faces of the polyhedron. We will prove that for the faces of any 3-dimensional complex of a polyhedron under face adjacency relations, that a `Face Fundamental Transversal' exists, and it is a union of the connected orbits of faces that are intersected exactly once. While exploring the problem of finding a face fundamental transversal, we have found a partial result …

Problems In Classical Potential Theory With Applications To Mathematical Physics, Erik Lundberg

USF Tampa Graduate Theses and Dissertations

In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters.

Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem).

Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is …

Generalizations Of A Laplacian-Type Equation In The Heisenberg Group And A Class Of Grushin-Type Spaces, Kristen Snyder Childers

USF Tampa Graduate Theses and Dissertations

In [2], Beals, Gaveau and Greiner find the fundamental solution to a 2-Laplace-type equation in a class of sub-Riemannian spaces. This fundamental solution is based on the well-known fundamental solution to the p-Laplace equation in Grushin-type spaces [4] and the Heisenberg group [6]. In this thesis, we look to generalize the work in [2] for a p-Laplace-type equation. After discovering that the "natural" generalization fails, we find two generalizations whose solutions are based on the fundamental solution to the p-Laplace equation.

Minimal And Symmetric Global Partition Polynomials For Reproducing Kernel Elements, Mario Jesus Juha

USF Tampa Graduate Theses and Dissertations

The Reproducing Kernel Element Method is a numerical technique that combines finite element and meshless methods to construct shape functions of arbitrary order and continuity, yet retains the Kronecker-δ property. Central to constructing these shape functions is the construction of global partition polynomials on an element. This dissertation shows that asymmetric interpolations may arise due to such things as changes in the local to global node numbering and that may adversely affect the interpolation capability of the method. This issue arises due to the use in previous formulations of incomplete polynomials that are subsequently non-affine invariant. This dissertation lays out …

Automorphism Groups Of Quandles, Jennifer Macquarrie

USF Tampa Graduate Theses and Dissertations

This thesis arose from a desire to better understand the structures of automorphism groups and inner automorphism groups of quandles. We compute and give the structure of the automorphism groups of all dihedral quandles. In their paper Matrices and Finite Quandles, Ho and Nelson found all quandles (up to isomorphism) of orders 3, 4, and 5 and determined their automorphism groups. Here we find the automorphism groups of all quandles of orders 6 and 7. There are, up to isomoprhism, 73 quandles of order 6 and 289 quandles of order 7.

Parametric And Bayesian Modeling Of Reliability And Survival Analysis, Carlos A. Molinares

USF Tampa Graduate Theses and Dissertations

The objective of this study is to compare Bayesian and parametric approaches to determine the best for estimating reliability in complex systems. Determining reliability is particularly important in business and medical contexts. As expected, the Bayesian method showed the best results in assessing the reliability of systems.

In the first study, the Bayesian reliability function under the Higgins-Tsokos loss function using Jeffreys as its prior performs similarly as when the Bayesian reliability function is based on the squared-error loss. In addition, the Higgins-Tsokos loss function was found to be as robust as the squared-error loss function and slightly more efficient. …

Topics In Random Knots And R-Matrices From Frobenius Algebras, Enver Karadayi

USF Tampa Graduate Theses and Dissertations

In this dissertation, we study two areas of interest in knot theory: Random knots in the unit cube, and the Yang-Baxter solutions constructed from Frobenius algebras.

The study of random knots can be thought of as a model of DNA strings situated in confinement. A random knot with n vertices is a polygonal loop formed by selecting n distinct points in the unit cube, for a positive integer n, and connecting these points by straight line segments successively, such that the last point selected is joined with the first one. We present a step by step description of our algorithm …