Physical Sciences and Mathematics Commons^™

Counting Threshold Graphs And Finding Inertia Sets, Christopher Abraham Guzman

Theses and Dissertations

This thesis is separated into two parts: threshold graphs and inertia sets. First we present an algorithmic approach to finding the minimum rank of threshold graphs and then progress to counting the number of threshold graphs with a specific minimum rank. Second, we find an algorithmic and more automated way of determining the inertia set of graphs with seven or fewer vertices using theorems and lemmata found in previous papers. Inertia sets are a relaxation of the inverse eigenvalue problem. Instead of determining all the possible eigenvalues that can be obtained by matrices with a specific zero/nonzero pattern we restrict …

Record Linkage, Stasha Ann Bown Larsen

Theses and Dissertations

This document explains the use of different metrics involved with record linkage. There are two forms of record linkage: deterministic and probabilistic. We will focus on probabilistic record linkage used in merging and updating two databases. Record pairs will be compared using character-based and phonetic-based similarity metrics to determine at what level they match. Performance measures are then calculated and Receiver Operating Characteristic (ROC) curves are formed. Finally, an economic model is applied that returns the optimal tolerance level two databases should use to determine a record pair match in order to maximize profit.

Minimum Rank Problems For Cographs, Nicole Andrea Malloy

Theses and Dissertations

Let G be a simple graph on n vertices, and let S(G) be the class of all real-valued symmetric nxn matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The smallest rank achieved by a matrix in S(G) is called the minimum rank of G, denoted mr(G). The maximum nullity achieved by a matrix in S(G) is denoted M(G). For each graph G, there is an associated minimum rank class, MR(G) consisting of all matrices A in S(G) with rank A = mr(G). Although no restrictions are applied to the diagonal entries of …

An Experimental Investigation Characterizing The Tribological Performance Of Natural And Synthetic Biolubricants Composed Of Carboxylic Acids For Energy Conservation And Sustainability, Carlton Jonathan Reeves

Theses and Dissertations

Over the last several decades the lubrication industry has been striving to bring bio-based lubricants known as biolubricants to prominence. The reasons for the increased environmental initiatives are due to depletion of oil reserves, increases in oil price, stringent government regulations on petroleum-based oils, and most importantly, concerns for protecting the environment. With an estimated, 50% of all lubricants entering the environment and much of these being composed of toxic mineral oils, biolubricants have begun to witness a resurgence. This experimental investigation seeks to develop a new class of ecofriendly biolubricants that are less toxic to the environment, derived from …

A Crowdsourced Hail Dataset: Potential, Biases, And Inaccuracies, Joseph Robert Pehoski

Theses and Dissertations

Hail is a substantial severe weather hazard in the USA, with significant damage to property and

crops occurring annually. Traditional methods of forecasting hail size have limited accuracy, and despite

improvements in remote sensing of precipitation, the fall characteristics of hail make quantification of

hail imprecise. Research into hail is ongoing, but traditional hail datasets have known biases and low

spatiotemporal resolution. The increased usage of smartphones creates the opportunity to use a

crowdsourced dataset provided by the Precipitation Identification Near the Ground (PING) program, a

program developed by the National Severe Storms Laboratory. PING data is compared to approximate …

Extremal Results For Peg Solitaire On Graphs, Aaron D. Gray

Electronic Theses and Dissertations

In a 2011 paper by Beeler and Hoilman, the game of peg solitaire is generalized to arbitrary boards. These boards are treated as graphs in the combinatorial sense. An open problem from that paper is to determine the minimum number of edges necessary for a graph with a fixed number of vertices to be solvable. This thesis provides new bounds on this number. It also provides necessary and sufficient conditions for two families of graphs to be solvable, along with criticality results, and the maximum number of pegs that can be left in each of the two graph families.

Magic Squares Of Squares Of Order 4 Over Certain Finite Fields, Drew O’Neill

Theses, Dissertations and Culminating Projects

A magic square of order n over a commutative ring R is an n x n matrix such that all the rows, columns, and the two diagonals add up to a fixed sum, which is called the magic sum. If all of the numbers in a magic square are perfect squares in R, it is called a magic square of squares. The rings under consideration in this thesis are either Z or Zp where p is a prime. In this thesis I present methods of constructing magic squares of squares of order 4 from selected ones of order 3. A …

Survival Analysis Of Cardiovascular Diseases, Yuanxin Hu

All Theses and Dissertations (ETDs)

No abstract provided.

Application Of Linear Sequences To Cryptography, Amanda C. Yeates

Honors Theses

Cryptography is the study of a centuries–old technique of secretly transferring information between parties. Linear recurrences were the chosen method of encryption and decryption in the thesis. The Fibonacci sequence, with its Zeckendorf representation, allows for the flexibility of encoding any number desired based on a particular encoding technique used in the film Sherlock Holmes: A Game of Shadows. The main goal is to find other linear recurrences that possess characteristics similar to the Fibonacci sequence to use as suitable substitutes for encoding. Different sequences were analyzed based on a number of criteria. In order for a sequence to be …

The Computation Of Fluid Velocity In A Closed Cavity With A Moving Lid, Daniel A. Montez

Theses and Dissertations - UTB/UTPA

We consider a cavity filled with fluid whose three sides are stationary and the lid at the top is moving at a constant speed. The flow in the cavity is modeled using the conservation of mass and momentum equations with proper boundary conditions. We compute the fluid velocity for the steady state case using the finite element method. We seek the weak formulation and develop a finite element model based on the Galerkin method. Furthermore we use the penalty function method to modify our weak formulation to eliminate the pressure. The Gaussian quadrature method is used to evaluate our integrals …

Viscosity Dependence Of Faraday Wave Formation Thresholds, Lisa Michelle Slaughter

Physics

This experiment uses an electromagnetic shaker to produce standing wave patterns on the surface of a vertically oscillating sample of silicon liquid. These surface waves, known as Faraday waves, form shapes such as squares, lines, and hexagons. They are known to be dependent upon the frequency and amplitude of the forcing as well as on the viscosity and depth of the liquid in the dish. At a depth of 4mm and for various silicon liquids having kinematic viscosities of 10, 20, and 38 cSt, we determined the acceleration at which patterns form for frequencies between 10 and 60 Hz. For …

On High-Performance Parallel Fixed-Point Decimal Multiplier Designs, Ming Zhu

UNLV Theses, Dissertations, Professional Papers, and Capstones

High-performance, area-efficient hardware implementation of decimal multiplication is preferred to slow software simulations in a number of key scientific and financial application areas, where errors caused by converting decimal numbers into their approximate binary representations are not acceptable.

Multi-digit parallel decimal multipliers involve two major stages: (i) the partial product generation (PPG) stage, where decimal partial products are determined by selecting the right versions of the pre-computed multiples of the multiplicand, followed by (ii) the partial product accumulation (PPA) stage, where all the partial products are shifted and then added together to obtain the final multiplication product. In this thesis, …

Estimation Of Travel Time Based On Vehicle-Tracking Models, Anuj Nayyar

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis we study the travel time problem based on the known traffic density model. Using the conservation law, we model the travel time function by a boundary value problem of a non homogeneous linear hyperbolic equation. The equation is transformed into an initial value hyperbolic equation, and the well-posedness of the problem is discussed. The mathematical analysis for both density and travel problems are given. We also derive the analytic solutions for several special cases of traffic density. Numerical schemes are proposed for solving for travel time problem. Several numerical examples are presented and error analysis on the …

Comparison Of Mesh And Meshless Methods For Partial Differential Equations Of Galerkin Form, Wallace F. Atterberry

UNLV Theses, Dissertations, Professional Papers, and Capstones

There are two purposes of this research project. The first purpose is to compare two types of Galerkin methods: The finite element mesh method and moving least sqaures meshless Galerkin (EFG) method. The second purpose of this project is to determine if a hybrid between the mesh and meshless method is beneficial.

This manuscript will be divided into three main parts. The first part is chapter one which develops the finite element method. The second part (Chapter two) will be developing the meshless method. The last part will provide a method for combining the mesh and meshless methods for a …

Symplectomorphism Groups Of Weighted Projective Spaces And Related Embedding Spaces, Martin L. Vanhoof

Electronic Thesis and Dissertation Repository

In this thesis, we study 4-dimensional weighted projective spaces and homotopy properties of their symplectomorphism groups. Using these computations, we also investigate some homotopy theoretic properties of a few associated embedding spaces. In the classical case of the complex projective plane, Gromov observed that its symplectomorphism group is homotopy equivalent to its subgroup of Kahler isometries. We find that in the case of one singularity, the symplectomorphism group is weakly homotopy equivalent to the Kahler isometry group of a certain Hirzebruch surface, which corresponds to the resolution of the singularity. In the case of multiple singularities, the symplectomorphism groups are …

On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera

Theses and Dissertations - UTB/UTPA

The notion of an association scheme is a generalization of the concept of a group. In fact, the so-called thin association schemes correspond in a well-understood way to groups. In this thesis, we look at the structure of non-commutative association schemes of rank 6. We will show that a non-normal closed subset of a noncommutative association scheme of rank 6, must have rank 2. The so-called Coxeter schemes of rank 6 which we present in Section 4 provide examples of association schemes of rank 6 with non-normal closed subsets of rank 2. It is shown that normal closed subsets of …

A Topics Analysis Model For Health Insurance Claims, Jared Anthony Webb

Theses and Dissertations

Mathematical probability has a rich theory and powerful applications. Of particular note is the Markov chain Monte Carlo (MCMC) method for sampling from high dimensional distributions that may not admit a naive analysis. We develop the theory of the MCMC method from first principles and prove its relevance. We also define a Bayesian hierarchical model for generating data. By understanding how data are generated we may infer hidden structure about these models. We use a specific MCMC method called a Gibbs' sampler to discover topic distributions in a hierarchical Bayesian model called Topics Over Time. We propose an innovative use …

An Epidemic Model Structured By The Time Since Last Infection, Jorge Alturo Alfaro Murillo

Open Access Dissertations

Epidemiological models structured by time since infection have their origin in the seminal work of 1927 by Kermack and McKendrick. Compared to ordinary differential equations (ODE) models, they are able to capture differences in infectivity of the individuals in a more suitable manner. Their use declined in the second half of the 20th century, probably because the theory for ODE models is more robust, complete and has proved successful in providing insights and predictions for many epidemiological problems. Nevertheless, it is important to understand in what occasions the inclusion of time since infection may alter the outcomes in a significant …

Exploring The Effects Of Conversational Repair As A Scaffolding Strategy To Promote Mathematics Explanations Of Students With Learning Disabilities, Jia Liu

Open Access Dissertations

Conversational repair often occurs in conversations when people attempt to address communicative breakdowns or inaccuracy by way of repeating what have been said or putting them in another way. The review of literature on conversational repair revealed that as an important concept in pragmatic aspect of language, it is an effective strategy to improve communication of different populations with disabilities. However, it is rarely studied in the domain of mathematics and with the population with learning disabilities/difficulties (LD). In current reform-based, discourse-oriented mathematics classrooms, students with LD encounter difficulties articulating or explaining well their reasoning processes due to the mathematical …

A Jackknife Empirical Likelihood Approach To Goodness Of Fit U-Statistic Testing With Side Information, Qun Lin

Open Access Dissertations

Motivated by applications to goodness of fit U-statistics testing, the jackknife empirical likelihood of Jing, et al. (2009) is justified with an alternative approach, and the Wilks theorem for vector U-statistics is proved. This generalizes Owen's empirical likelihood theorem for a vector mean to a vector U-statistics-based mean and includes the jackknife empirical likelihood of U-statistics with side information as a special case. The results are generalized to allow for the constraints to use estimated criteria functions and for the number of constraints to grow with the sample size. The latter is needed to handle naturally occurring nuisance parameters in …

Methods For Increasing Domains Of Convergence In Iterative Linear System Solvers, David Michael Imberti

Open Access Dissertations

In this thesis, we introduce and improve various methods for increasing the domains of convergence for iterative linear system solvers. We rely on the following three approaches: making the iteration adaptive, or nesting an inner iteration inside of a previously determined outer iteration; using deflation and projections to manipulate the spectra inherent to the iteration; and/or focusing on reordering schemes. We will analyze a specific combination of these three strategies. In particular, we propose to examine the influence of nesting a Flexible Generalized Minimum Residual algorithm together with an inner Recursive Projection Method using a banded preconditioner resulting from the …

Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey

Doctoral Dissertations

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do not routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together …

Open Books On Contact Three Orbifolds, Daniel Herr

Open Access Dissertations

In 2002, Giroux showed that every contact structure had a corresponding open book decomposition. This was the converse to a previous construction of Thurston and Winkelnkemper, and made open books a vital tool in the study of contact three-manifolds. We extend these results to contact orbifolds, i.e. spaces that are locally diffeomorphic to the quotient of a contact manifold and a compatible finite group action. This involves adapting some of the main concepts and constructions of three dimensional contact geometry to the orbifold setting.

Conditional Gaussian Fluctuations And Refined Asymptotics Of The Spin In The Phase-Coexistence Region, Jingran Li

Open Access Dissertations

In this dissertation four results are presented on the fluctuations of the spin per site around the thermodynamic magnetization in the mean-field Blume-Capel model, a basic model in statistical mechanics. The first two results refine the main theorem in a 2010 paper by R. S. Ellis, J. Machta, and P. T. Otto published in Annals of Applied Probability 20 (2010) 2118-2161. This paper provides the first rigorous confirmation of the statistical mechanical theory of finite-size scaling for a mean-field model. The first main result studies the asymptotics of the centered, finite-size magnetization, giving its precise rate of convergence to 0 …

Martingale Central Limit Theorem And Nonuniformly Hyperbolic Systems, Luke Mohr

Open Access Dissertations

In this thesis we study the central limit theorem (CLT) for nonuniformly hyperbolic dynamical systems. We examine cases in which polynomial decay of correlations leads to a CLT with a non-standard scaling factor of √ n ln n. We also formulate an explicit expression for the the diffusion constant σ in situations where a return time function on the system is a certain class of supermartingale. We then demonstrate applications by exhibiting the CLT for the return time function in four classes of dynamical billiards, including one previously unproven case, the skewed stadium, as well as for the linked twist …

Twisted Weyl Group Multiple Dirichlet Series Over The Rational Function Field, Holley Ann Friedlander

Open Access Dissertations

Let K be a global field. For each prime p of K, the p-part of a multiple Dirichlet series defined over K is a generating function in several variables for the p-power coefficients. Let _ be an irreducible, reduced root system, and let n be an integer greater than 1. Fix a prime power q 2 Z congruent to 1 modulo 2n, and let Fq(T) be the field of rational functions in T over the finite field Fq of order q. In this thesis, we examine the relationship between Weyl …

Properties Of Singular Schubert Varieties, Jennifer Koonz

Open Access Dissertations

This thesis deals with the study of Schubert varieties, which are subsets of flag varieties indexed by elements of Weyl groups. We start by defining Lascoux elements in the Hecke algebra, and showing that they coincide with the Kazhdan-Lusztig basis elements in certain cases. We then construct a resolution (Z_w, π) of the Schubert variety X_w for which Rπ_*(C[l(w)]) is a sheaf on X_w whose expression in the Hecke algebra is closely related to the Lascoux element. We also define two new polynomials which coincide with the intersection cohomology Poincar\'e polynomial in …

A Study On Several Applications For Impulse Force Supporting Technique And The Controlling Problem, Dalong An

Math Theses

Motivated by the Space Elevator concept, several alternate space transportation systems are studied. Details, such as the structure, transporting capacity, and stability of the systems are explored. Further study shows that despite the difference in their structure, these transportation systems are all applications for the impulse force supporting technique. Moreover, we can show that the centrifugal force and the impulse force are merely two aspects of one kind of supporting force, each 1 of which can be used for different purposes.

Elementary Teacher Candidates' Images Of Mathematics, Diverse Students, And Teaching: An Exploratory Study With Implications For Culturally Responsive Mathematics Education, Bernd Richard Ferner

Dissertations and Theses

Children from many culturally diverse backgrounds do not achieve in mathematics at the same rates as their counterparts from the dominant White, European-American culture (Gay, 2010). This so-called achievement gap is an artifact of an educational system that continues to fail to provide equal learning opportunities to culturally diverse children (Ladson-Billings, 2006; Nieto & Bode, 2011). Teachers who employ culturally responsive teaching (Gay, 2010) may help to close this opportunity gap and hence, the achievement gap. This study investigated, "How do elementary teacher candidates perceive teaching mathematics in a multicultural environment"; Using a critical constructivism research paradigm, this qualitative instrumental …

On Degeneracies In The Family Of Fibres Of A Complex Analytic Mapping, Hadi Seyedinejad

Electronic Thesis and Dissertation Repository

Failure of some (important) properties of a holomorphic mapping manifests itself as degeneracies in the family of fibres of the mapping. Among these properties are openness and flatness. The first goal in this thesis is to develop criteria that allow one to effectively (i.e., computationally) detect such degeneracies in the family of fibres, and in addition, that are applicable to the case of mappings with singular targets. Particularly regarding flatness, no such algorithms that work in the general setting of singular targets were known before. We prove that a mapping (with a locally irreducible target) is flat (resp. open) if …