Physical Sciences and Mathematics Commons^™

Automorphisms Of Graph Curves On K3 Surfaces, Joshua C. Ferrerra

Electronic Theses and Dissertations

We examine the automorphism group of configurations of rational curves on $K3$ surfaces. We use the properties of finite automorphisms of $\PP^1$ to examine what restrictions a given elliptic fibration imposes on the possible finite order non-symplectic automorphisms of the $K3$ surface. We also examine the fixed loci of these automorphisms, and construct an explicit fibration to demonstrate the process.

Graphs Of Classroom Networks, Rebecca Holliday

Electronic Theses and Dissertations

In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism …

Solutions Of Inequality Constrained Spline Optimization Problems With The Active Set Method, Joshua A. Holloway

Electronic Theses and Dissertations

We solve the problem of finding a near-interpolant curve, subject to constraints, which minimizes the bending energy of the curve. Using B-splines as our tools, we give a brief overview of spline properties and develop several different cases of inequality constrained optimization problems of this type. In particular, we develop the active set method and use it to solve these problems, emphasizing the fact that this algorithm will converge to a solution in finite iterations. Our solution will solve an open problem regarding near-interpolant spline curves. Furthermore, we supplement this with an iterative technique for better choosing data sites so …

Improved Full-Newton-Step Infeasible Interior-Point Method For Linear Complementarity Problems, Mustafa Ozen

Electronic Theses and Dissertations

In this thesis, we present an improved version of Infeasible Interior-Point Method (IIPM) for monotone Linear Complementarity Problem (LCP). One of the most important advantages of this version in compare to old version is that it only requires feasibility steps. In the earlier version, each iteration consisted of one feasibility step and some centering steps (at most three in practice). The improved version guarantees that after one feasibility step, the new iterated point is feasible and close enough to central path. Thus, the centering steps are eliminated. This improvement is based on the Lemma(Roos, 2015). Thanks to this lemma, proximity …

Labeled Trees And Spanning Trees: Computational Discrete Mathematics And Applications, Demet Yalman

Electronic Theses and Dissertations

In this thesis, we examine two topics. In the first part, we consider Leech tree which is a tree of order n with positive integer edge weights such that the weighted distances between pairs of vertices are exactly from 1 to n choose 2. Only five Leech trees are known and some non-existence results have been presented through the years. Variations of Leech trees such as the minimal distinct distance trees and modular Leech trees have been considered in recent years. In this thesis, such Leech-type questions on distances between leaves are studied as well as some other labeling questions …

Enumerating Graphs Using Integrals From Quantum Field Theory, William A. Coggins

Electronic Theses and Dissertations

Enumerating graphs is a relatively new subfield of mathematics. In this thesis, we will discuss a enumerative method that derives from Quantum Field Theory. We begin with the basic ideas of Calculus and extend them into a enumerative method that will allow us to classify graphs embedded on surfaces.

Bayesian Inference Of The Weibull-Pareto Distribution, James Dow

Electronic Theses and Dissertations

The Weibull distribution has many applications in various topics. Some of these topics include survival analysis, reliability engineering, general insurance, electrical engineering, and industrial engineering. The Weibull distribution was further extended by the Weibull-Pareto distribution. A desirable property this distribution has is its shape can skew being able to better model left or right skewed data. Examples of skewed data include human longevity and actuarial data. In this work a hierarchical Bayesian model was developed using the Weibull-Pareto distribution.

Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford

Electronic Theses and Dissertations

Chemical graph theory began as a way for mathematicians to bring together the areas of the Physical Sciences and Mathematics. Through its use, mathematicians are able to model chemical systems, predict their properties as well as structure-property relationships. In this dissertation, we consider two questions involving chemical graph theory and its applications. We first look at tree-like polyphenyl systems, which form an important family of compounds in Chemistry, particularly in Material Science. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are …

Comparing K Population Means With No Assumption About The Variances, Tony Yaacoub

Electronic Theses and Dissertations

In the analysis of most statistically designed experiments, it is common to assume equal variances along with the assumptions that the sample measurements are independent and normally distributed. Under these three assumptions, a likelihood ratio test is used to test for the difference in population means. Typically, the assumption of independence can be justified based on the sampling method used by the researcher. The likelihood ratio test is robust to the assumption of normality. However, the equality of variances is often difficult to justify. It has been found that the assumption of equal variances cannot be made even after transforming …

Adaptive State Feedback Control Of Lorenz Systems To Its Non-Trivial Equilibrium, Anh V. Tran

Electronic Theses and Dissertations

The complex Lorenz system is a simplified nonlinear dynamical system, which is derived from the Navier-Stokes equations that govern a closed thermal convection loop. The Lorenz system is chaotic for large Rayleigh number. In this chaotic regime, we implement a linear state feedback controller to stabilize the state trajectory at its original nontrivial equilibrium. The state variable for feedback is easily measurable. The system is proved to be globally asymptotically stable with a optimal feedback gain. The stability bound is improved over the previous result. We also established globally stability of the adaptively control system, where the system parameters are …

Polymorphic Data Modeling, Steven R. Benson

Electronic Theses and Dissertations

There are currently no data modeling standards for modeling NoSQL document store databases. This work proposes a standard to fill the void. The proposed standard is based on our new data modeling pattern named The Polymorphic Table Pattern. The pattern embraces the “schemaless” nature of document store NoSQL while allowing the data modeler to use his or her existing skillsets. The concepts of our proposed modeling have been demonstrated against MongoDB.

Exponentially Weighted Moving Average Charts For Monitoring The Process Generalized Variance, Anna Khamitova

Electronic Theses and Dissertations

The exponentially weighted moving average chart based on the sample generalized variance is studied under the independent multivariate normal model for the vector of quality measurements. The performance of the chart is based on an analysis of the chart's initial and steady-state run length distributions. The three methods that are commonly used to determinate run length distribution, simulation, the integral equation method, and the Markov chain approximation are discussed. The integral equation and Markov chain approaches are analytical methods that require a nu- merical method for determining the probability density and cumulative distribution functions describing the distribution of the sample …

Generalized Weibull And Inverse Weibull Distributions With Applications, Valeriia Sherina

Electronic Theses and Dissertations

In this thesis, new classes of Weibull and inverse Weibull distributions including the generalized new modified Weibull (GNMW), gamma-generalized inverse Weibull (GGIW), the weighted proportional inverse Weibull (WPIW) and inverse new modified Weibull (INMW) distributions are introduced. The GNMW contains several sub-models including the new modified Weibull (NMW), generalized modified Weibull (GMW), modified Weibull (MW), Weibull (W) and exponential (E) distributions, just to mention a few. The class of WPIW distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Frechet distributions as special cases. Included …

Selection Of Step Size For Total Variation Minimization In Ct, Anna N. Yeboah

Electronic Theses and Dissertations

Medical image reconstruction by total variation minimization is a newly developed area in computed tomography (CT). In compressed sensing literature, it hasbeen shown that signals with sparse representations in an orthonormal basis may be reconstructed via l1-minimization. Furthermore, if an image can be approximately modeled to be piecewise constant, then its gradient is sparse. The application of l1-minimization to a sparse gradient, known as total variation minimization, may then be used to recover the image. In this paper, the steepest descent method is employed to update the approximation of the image. We propose a way to estimate an optimal step …

An Investigation Of Sensitivity Of An F Test In Locating Change Points In Linear Regression, Jing Sun

Electronic Theses and Dissertations

Change point is a statistic phenomenon, which has many direct applications in climatology, bioinformatics, finance, oceanography and medical imaging. In this thesis, we investigate the sensitivity of the F-test for detecting change points in linear regression, using a two-phase linear regression model. it offers an effective method to detect "undocumented" change points using a form of an F-test. Using simulated data, we explore its sensitivity and accuracy with respect t different parameters in the model.

Elements Of Convergence Approach Theory, William D. Trott

Electronic Theses and Dissertations

We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.

Statistical Analysis Of Unreplicated Factorial Designs Using Contrasts, Meixi Yang

Electronic Theses and Dissertations

Factorial designs can have a large number of treatments due to the number of factors and the number of levels of each factor. The number of experimental units required for a researcher to conduct a $k$ factorial experiment is at least the number of treatments. For such an experiment, the total number of experimental units will also depend on the number of replicates for each treatment. The more experimental units used in a study the more the cost to the researcher. The minimum cost is associated with the case in which there is one experimental unit per treatment. That is, …

A Constructive Proof Of The Borel-Weil Theorem For Classical Groups, Kostiantyn Timchenko

Electronic Theses and Dissertations

The Borel-Weil theorem is usually understood as a realization theorem for representations that have already been shown to exist by other means (``Theorem of the Highest Weight''). In this thesis we turn the tables and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\lambda$, for each dominant integral form $\lambda$ on the Lie algebra of a maximal torus of $G$.

Precise Partitions Of Large Graphs, Pouria Salehi Nowbandegani

Electronic Theses and Dissertations

First by using an easy application of the Regularity Lemma, we extend some known results about cycles of many lengths to include a specified edge on the cycles. The results in this chapter will help us in rest of this thesis. In 2000, Enomoto and Ota posed a conjecture on the existence of path decomposition of graphs with fixed start vertices and fixed lengths. We prove this conjecture when |G| is large. Our proof uses the Regularity Lemma along with several extremal lemmas, concluding with an absorbing argument to retrieve misbehaving vertices. Furthermore, sharp minimum degree and degree sum conditions …

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva

Electronic Theses and Dissertations

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

Generalized Classes Of Distributions With Applications To Income And Lifetime Data, Shujiao Huang

Electronic Theses and Dissertations

In this thesis, new classes of distributions namely: exponentiated Kumaraswamy-Dagum (EKD), Log-exponentiated Kumaraswamy-Dagum (Log-EKD), McDonald Log-logistic (McLLog) and Gamma-Dagum (GD) distributions are presented. A thorough and comprehensive investigation of these classes of distributions is conducted. Mathematical properties of these classes of distributions including series expansion, hazard and reverse hazard functions, moments, generating functions, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics, moments of order statistics and entropies are presented. Estimation of parameters of these distributions via maximum likelihood technique, Fisher information and asymptotic confidence intervals are given. Maximum likelihood estimation of the parameters of the exponentiated …

Generating Surfaces Of Variable Eccentricity Within A Ray Tracer, Joshua A. Smith

Electronic Theses and Dissertations

Polynomial surfaces used in ray tracing have recently been improved upon allowing for three dimensional applications. Among these are surfaces that have a varying eccentricity. This paper will discuss a method for finding real roots of polynomials [allowing us to create these surfaces]. First, we will give the reader a basic comprehension of the workings of a ray tracer, a general understanding of three dimensional polynomial surfaces, how this newly implemented root finder functions, and how these concepts enable us to create surfaces of variable eccentricity. Then, examples will be provided to demonstrate the capabilities of the program.

Statistical Properties Of The Mc-Dagum And Related Distributions, Sasith Rajasooriya

Electronic Theses and Dissertations

In this thesis, we present a new class of distributions called Mc-Dagum distribution. This class of distributions contains several distributions such as beta-Dagum, beta-Burr III, beta-Fisk and Dagum distributions as special cases. The hazard function, reverse hazard function, moments and mean residual life function are obtained. Inequality measures, entropy and Fisher information are presented. Maximum likelihood estimates of the model parameters are given.

Variational Methods On Elastic Curves, Daniel D. Rocker

Electronic Theses and Dissertations

In this thesis we investigate elastic curves. These are curves with minimal bending energy as measured by the total squared curvature functional. We show that these can be computed by evolving curves in the direction of the negative gradient in certain Hilbert space settings. By discretizing the curves and using numerical integration, we compute approximate minimizers and display using computer graphics. We propose a conjecture based on the rotation number of a curve that predicts the critical point curves that minimize bending energy.

Approximate Similarity Reduction, Rui Zhang

Electronic Theses and Dissertations

The nonlinear K (n;1) equation with damping is investigated via the approximate homotopy symmetry method and approximate homotopy direct method. The approximate homotopy symmetry and homotopy similarity reduction equations of different orders are derived and the corresponding homotopy series reduction solutionsare obtained. As a result, the formal coincidence for both methods is displayed.

Using Neural Networks To Provide Local Weather Forecasts, Andrew Culclasure

Electronic Theses and Dissertations

Artificial neural networks (ANNs) have been applied extensively to both regress and classify weather phenomena. While one of the core strengths of neural networks is rendering accurate predictions with noisy datasets, there is currently not a significant amount of research focusing on whether ANNs are capable of producing accurate forecasts of relevant weather variables from small-scale, imperfect datasets. Also, there is not a significant amount of research focusing on the forecasting performance of neural networks applied to weather datasets that have been temporally rolled-up from a base dataset. In this paper, a survey of existing research on applying ANNs to …

Numerical Solutions To The Gross-Pitaevskii Equation For Bose-Einstein Condensates, Luigi Galati

Electronic Theses and Dissertations

In this thesis we compare various potential operators for the two-dimensional (2D) Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates. Both the 2D and the 1D models are scaled to get a three parameter model. Smoothness of initial conditions is considered and choice of method (Split-Step Fourier method with Strang Splitting) is justied. Numerical simulations provide graphical evidence of properties of both focusing and nonfocusing cases.

Accelerated Data Delivery Architecture, Michael L. Grecol

Electronic Theses and Dissertations

This paper introduces the Accelerated Data Delivery Architecture (ADDA). ADDA establishes a framework to distribute transactional data and control consistency to achieve fast access to data, distributed scalability and non-blocking concurrency control by using a clean declarative interface. It is designed to be used with web-based business applications. This framework uses a combination of traditional Relational Database Management System (RDBMS) combined with a distributed Not Only SQL (NoSQL) database and a browser-based database. It uses a single physical and conceptual database schema designed for a standard RDBMS driven application. The design allows the architect to assign consistency levels to entities …

Cusum Generalized Variance Charts, Yuxiang Li

Electronic Theses and Dissertations

The commonly recommended charts for monitoring the mean vector are affected by a shit in the covariance matrix. As in the univariate case, a chart for monitoring for a change in the covariance matrix should be examined first before examining the chart used to monitor for a change in the mean vector.

Computational Fluid Dynamics (Cfd) Modeling Of A Laboratory Scale Coal Gasifier, Kiel S. Schultheiss

Electronic Theses and Dissertations

Furthering gasification technology is an essential part of advancing clean coal technologies. In order to seek insight into the appropriate operations for the formation of synthetic gas (syngas) a numerical simulation was performed to predict the phenomena of coal gasification in a laboratory scale entrained-flow coal gasifier. The mesh for the model was developed with ICEM CFD software and the chemical and physical phenomena were modeled using the fluid flow solver ANSYS FLUENT. Mesh independence was verified. The model was validated with experimental data from several studies performed on a laboratory scale gasifier.

Systematic examination of the model was performed …