Applied Mathematics Commons^™

Modular Forms, Elliptic Curves And Drinfeld Modules, Catherine Trentacoste

All Dissertations

In this thesis we explore three different subfields in the area of number theory. The first topic we investigate involves modular forms, specifically nearly holomorphic eigenforms. In Chapter 3, we show the product of two nearly holomorphic eigenforms is an eigenform for only a finite list of examples. The second type of problem we analyze is related to the rank of elliptic curves. Specifically in Chapter 5 we give a graph theoretical approach to calculating the size of 3-Selmer groups for a given family of elliptic curves. By calculating the size of the 3-Selmer groups, we give an upper bound …

Border Hispanics’ Physical Activity Improvement In A Chronic Disease Prevention Program, Lu Xu

Theses and Dissertations - UTB/UTPA

In seeking of effective prevention programs to improve physical activities, we want to examine the factors related to physical activities improvement in Alliance for a Healthy Border, a chronic disease prevention program with pre-post-post evaluations through 12 federally qualified community health centers serving primarily Hispanics in communities along the U.S.- Mexico border. Logistic regression was performed to examine the association between physical activity and twenty predictors at baseline. Multinomial regression was used to examine the determinants of physical activities improvement at two time points: program end and post six-months. Socio-demographic, baseline health condition factors, and determination of doing physical activity …

Mathematical Modeling Of Fluid Spills In Hydraulically Fractured Well Sites, Oluwafemi Michael Taiwo

Graduate Theses and Dissertations

Improved drilling technology and favorable energy prices have contributed to the rapid pace at which the exploitation of unconventional natural gas is taking place across the United States. As a natural gas well is being drilled, reserve pits are constructed to hold the drilling fluids and other materials returned from the drilling process. These reserve pits can fail, and when they do, plant and animal life of the surrounding area may be adversely affected. This project develops a screening tool for a suitable location for a reserve pit. This work will be a critical piece of the Infrastructure Placement Analysis …

Error Estimation Techniques To Refine Overlapping Aerial Image Mosaic Processes Via Detected Parameters, William Glenn Bond

Dissertations

In this paper, I propose to demonstrate a means of error estimation preprocessing in the assembly of overlapping aerial image mosaics. The mosaic program automatically assembles several hundred aerial images from a data set by aligning them, via image registration using a pattern search method, onto a GIS grid.

The method presented first locates the images from a data set that it predicts will not align well via the mosaic process, then it uses a correlation function, optimized by a modified Hooke and Jeeves algorithm, to provide a more optimal transformation function input to the mosaic program. Using this improved …

Generic Special Objects, Sławomir Solecki

Dalrymple Lecture Series

I will talk about mathematical objects that have two seemingly contradictory attributes. On the one hand, they are generic within a given class, in the sense that if most objects within the class have a property, then our object has it as well. So generic objects are common. On the other hand, they are very special if they exist, for example, there is always, in essence, at most one such object within a given class. Generic objects show up in various areas of mathematics, for example, in topology, geometry, and analysis. They tend to have astonishing mathematical features. Can you …

Stiefel And Grassmann Manifolds In Quantum Chemistry, Eduardo Chiumiento, Michael Melgaard

Articles

We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove thatthey are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.

Constructing Phylogenetic Trees Using Maximum Likelihood, Anna Cho

Scripps Senior Theses

Maximum likelihood methods are used to estimate the phylogenetic trees for a set of species. The probabilities of DNA base substitutions are modeled by continuous-time Markov chains. We use these probabilities to estimate which DNA bases would produce the data that we observe. The topology of the tree is also determined using base substitution probabilities and conditional likelihoods. Felsenstein [2] introduced this method of finding an estimate for the maximum likelihood phylogenetic tree. We will explore this method in detail in this paper.

A Way That Can Be Walked Is Not The Way And A Name That Can Be Named Is Not The Name: My Complex Crusade Through Systems, Nature, And Taoist Text For Solutions On Proper Leadership, Roy Leaf '12

Honor Scholar Theses

No abstract provided.

Derivation Of Hill's Equation From Scale Invariance, Andres Ortiz^, Vladik Kreinovich*

COURI Symposium Abstracts, Spring 2012

No abstract provided.

Structure For Regular Inclusions, David R. Pitts

Department of Mathematics: Faculty Publications

We study pairs (C,D) of unital C∗-algebras where D is an abelian C∗-subalgebra of C which is regular in C in the sense that the span of {v 2 C : vDv∗ [ v∗Dv D} is dense in C. When D is a MASA in C, we prove the existence and uniqueness of a completely positive unital map E of C into the injective envelope I(D) of D whose restriction to D is the identity on D. We show that the left kernel of E, L(C,D), is the unique closed two-sided ideal of C maximal with respect to having trivial …

Generating Minimal Pair-Wise Covering Test Suites, Luis C. Gutierrez ^, Martine Ceberio *

COURI Symposium Abstracts, Spring 2012

Software is ubiquitous and needs to be reliable. Software testing therefore plays an important role in software development. Proper testing a software system informs about its quality and reliability so as to prevent unexpected behavior during system execution. One of the methods to prevent failures consists in testing a system under different input values, but when all possible input values are tested, an impractical number of test cases might result. In software testing, pair-wise testing is a combinatorial technique which uses combination of pair input values to generate test cases. Using pair-wise testing dramatically reduces the number of test cases, …

Negative Curves On Algebraic Surfaces, Thomas Bauer, Brian Harbourne, Andreas Leopold Knutsen, Alex Kuronya, Stefan Muller-Stach, Xavier Roulleau, Tomasz Szemberg

Department of Mathematics: Faculty Publications

We study curves of negative self-intersection on algebraic surfaces. In contrast to what occurs in positive characteristics, it turns out that any smooth complex projective surface X with a surjective non-isomorphic endomorphism has bounded negativity (i.e., that C2 is bounded below for prime divisors C on X). We prove the same statement for Shimura curves on Hilbert modular surfaces. As a byproduct we obtain that there exist only finitely many smooth Shimura curves on a given Hilbert modular surface. We. also show that any set of curves of bounded genus on a smooth complex projective surface must have bounded negativity

R₀ Analysis Of A Spatiotemporal Model For A Stream Population, H. W. Mckenzie, Y. Jin, Jon T. Jacobsen, M. A. Lewis

All HMC Faculty Publications and Research

Water resources worldwide require management to meet industrial, agricultural, and urban consumption needs. Management actions change the natural flow regime, which impacts the river ecosystem. Water managers are tasked with meeting water needs while mitigating ecosystem impacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and we analyze them to assess the effect of water flow on population persistence. We present a new mathematical framework, based on the net reproductive rate R₀ for advection-diffusion-reaction equations and on related measures. We apply the measures to population persistence in rivers under various flow regimes. This work lays …

Mathematical Modeling Of Pipeline Features For Robotic Inspection, Yang Gao

Doctoral Dissertations

Underground pipeline systems play an indispensable role in transporting liquids in both developed and developing countries. The associated social and economic cost to repair a pipe upon abrupt failure is often unacceptable. Regular inspection is a preventative action that aims to monitor pipe conditions, catch abnormalities and reduce the chance of undesirable surprises. Robots with CCTV video cameras have been used for decades to inspect pipelines, yielding only qualitative information. It is becoming necessary and preferable for municipalities, project managers and engineers to also quantify the 3-D geometry of underground pipe networks. Existing robots equipped specialized hardware and software algorithms …

Near-Optimal Scheduling And Decision-Making Models For Reactive And Proactive Fault Tolerance Mechanisms, Nichamon Naksinehaboon

Doctoral Dissertations

As High Performance Computing (HPC) systems increase in size to fulfill computational power demand, the chance of failure occurrences dramatically increases, resulting in potentially large amounts of lost computing time. Fault Tolerance (FT) mechanisms aim to mitigate the impact of failure occurrences to the running applications. However, the overhead of FT mechanisms increases proportionally to the HPC systems' size. Therefore, challenges arise in handling the expensive overhead of FT mechanisms while minimizing the large amount of lost computing time due to failure occurrences.

In this dissertation, a near-optimal scheduling model is built to determine when to invoke a hybrid checkpoint …

The Search For An Optimal Means Of Determining The Minmax Control Parameter Using Sensitivity Analysis, John Teye Brown

Doctoral Dissertations

The use of computational methods for design and simulation of control systems allows for a cost-effective trial and error approach. In this work, we are concerned with the robust, real-time control of physical systems whose state space is infinite-dimensional. Such systems are known as Distributed Parameter Systems (DPS). A body whose state is heterogeneous is a distributed parameter. In particular, this work focuses on DPS systems that are governed by linear Partial Differential Equations, such as the heat equation. We specifically focus on the MinMax controller, which is regarded as being a very robust controller. The mathematical formulation of the …

Systems Of Nonlinear Wave Equations With Damping And Supercritical Sources, Yanqiu Guo

Department of Mathematics: Dissertations, Theses, and Student Research

We consider the local and global well-posedness of the coupled nonlinear wave equations

u_tt – Δu + g₁(u_t) = f₁(u, v)

v_tt – Δv + g₂(v_t) = f₂(u, v);

in a bounded domain Ω subset of the real numbers (Rⁿ) with a nonlinear Robin boundary condition on u and a zero boundary conditions on v. The nonlinearities f₁(u, v) and f₂(u, v) are with supercritical exponents …

Random Number Generation: Types And Techniques, David F. Dicarlo

Senior Honors Theses

What does it mean to have random numbers? Without understanding where a group of numbers came from, it is impossible to know if they were randomly generated. However, common sense claims that if the process to generate these numbers is truly understood, then the numbers could not be random. Methods that are able to let their internal workings be known without sacrificing random results are what this paper sets out to describe. Beginning with a study of what it really means for something to be random, this paper dives into the topic of random number generators and summarizes the key …

Local Histograms For Per-Pixel Classification, Melody L. Massar

Theses and Dissertations

We introduce a rigorous mathematical theory for the analysis of local histograms, and study how they interact with textures that can be modeled as occlusions of simpler components. We first show how local histograms can be computed as a system of convolutions and discuss some basic local histogram properties. We then introduce a probabilistic, occlusion-based model for textures and formally demonstrate that local histogram transforms are natural tools for analyzing the textures produced by our model. Next, we characterize all nonlinear transforms which satisfy the three key properties of local histograms and consider the appropriateness of local histogram features in …

Determining Angular Frequency From A Video With A Generalized Fast Fourier Transform, Lindsay N. Smith

Theses and Dissertations

Suppose we are given a video of a rotating object and suppose we want to determine the rate of rotation solely from the video itself and its known frame rate. In this thesis, we present a new mathematical operator called the Geometric Sum Transform (GST) that can help one determine the angular frequency of the object in question. The GST is a generalization of the discrete Fourier transform (DFT) and as such, the two transforms have much in common. However, whereas the DFT is applied to a sequence of scalars, the GST can be applied to a sequence of vectors. …