Applied Mathematics Commons^™

Elementary-Level Mathematics Content In Comic Book Format, Bruce Kessler, Janet Tassell, Mary Evans, Cathy Willoughby, Melissa Zimmer

Mathematics Faculty Publications

No abstract provided.

Extending The Support Theorem To Infinite Dimensions, Jeremy J. Becnel

Faculty Publications

The Radon transform is one of the most useful and applicable tools in functional analysis. First constructed by John Radon in 1917 [9] it has now been adapted to several settings. One of the principle theorems involving the Radon transform is the Support Theorem. In this paper, we discuss how the Radon transform can be constructed in the white noise setting. We also develop a Support Theorem in this setting.

Generalized Probabilistic Bowling Distributions, Jennifer Lynn Hohn

Masters Theses & Specialist Projects

Have you ever wondered if you are better than the average bowler? If so, there are a variety of ways to compute the average score of a bowling game, including methods that account for a bowler’s skill level. In this thesis, we discuss several different ways to generate bowling scores randomly. For each distribution, we give results for the expected value and standard deviation of each frame's score, the expected value of the game’s final score, and the correlation coefficient between the score of the first and second roll of a single frame. Furthermore, we shall generalize the results in …

Pain As A Predictor Of Depression Treatment Outcomes In Women With Childhood Sexual Abuse, Ellen L. Poleshuck, Nancy L. Talbot, Haiyan Su, Xin Tu, Linda Chaudron, Stephanie Gamble, Donna E. Giles

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Objectives: Childhood sexual abuse (CSA) increases risk for both depression and pain in women. Pain is associated with worse depression treatment response. The contribution of pain to depression treatment outcomes in women with histories of CSA is unknown. This study examined whether clinically significant pain would be associated with worse depression and functioning outcomes among women with CSA histories treated with interpersonal psychotherapy. Method: Participants were 66 women with major depression and CSA who presented to a community mental health center. An interpersonal psychotherapy protocol planned for 14 weekly sessions followed by 2 biweekly sessions. Patients were classified as experiencing …

On Elliptic Curves, Modular Forms, And The Distribution Of Primes, Ethan Smith

All Dissertations

In this thesis, we present four problems related to elliptic curves, modular forms, the distribution of primes, or some combination of the three. The first chapter surveys the relevant background material necessary for understanding the remainder of the thesis. The four following chapters present our problems of interest and their solutions. In the final chapter, we present our conclusions as well as a few possible directions for future research.
Hurwitz class numbers are known to have connections to many areas of number theory. In particular, they are intimately connected to the theory of binary quadratic forms, the structure of imaginary …

Migration And Mixing Between Populations In Disease Models, David Burger

Theses, Dissertations and Culminating Projects

The goal of this thesis is to model the spread of disease between populations and find ways to prevent its continued epidemic. This thesis studies disease spread as a function of migration in epidemiological models. The models are constructed using the compartmental approach, and we compare discrete and continuous time approximations. In the discrete model, we will look at ways that induced migration can cause an epidemic case to turn into a dieout case. It will be shown that migration can only effect the size of an outbreak, but cannot create or destroy one. For the continuous cases, we will …

Patch Models And Applications On The Spread Of Avian Influenza, Kimberly Rude

Theses, Dissertations and Culminating Projects

The avian influenza virus (AIV) is an infectious disease that predominantly affects birds. Economic losses due to large-scale deaths of domestic poultry as a result of past outbreaks have been devastating. Additionally, there is major concern about the spread of the virus to humans. The virus has spread to humans in the past, but has not yet been known to spread beyond one human. Since influenza viruses are known to mutate easily, there is serious concern that the virus could mutate into a strain that can be transmitted easily to and among humans.

There has been much speculation that migratory …

Metric Regularity And Lipschitzian Stability Of Parametric Variational Systems, Francisco J. Aragón Artacho, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns the study of variational systems described by parameterized generalized equations/variational conditions important for many aspects of nonlinear analysis, optimization, and their applications. Focusing on the fundamental properties of metric regularity and Lipschitzian stability, we establish various qualitative and quantitative relationships between these properties for multivalued parts/fields of parametric generalized equations and the corresponding solution maps for them in the framework of arbitrary Banach spaces of decision and parameter variables.

A Dual Algorithm For The Weighted Euclidean Distance Min-Max Location Problem In R^2 And R^3, Andrea Smith

All Theses

A dual approach algorithm is given for the solution of the weighted min-max location problem with Euclidean distance in R^2 and R^3. Each subproblem is solved using a directional search procedure and by taking advantage of its geometric structure. An algebraic replacement rule is employed to update the subproblem.

Construction Of A Dimension Two Rank One Drinfeld Module, Catherine Trentacoste

All Theses

Consider F_r[t] where r = pm for some prime p and m in the natural numbers. Let f(t) be an irreducible square-free polynomial with even degree in F_r[t] so that the leading coeffcient is not a square
mod F_r. Let A = L = F_r[t][\sqrt{f(t)}].
We will examine the basic set-up required for a dimension two rank one Drinfeld module over L along with an explanation of our choice of f(t). In addition we will show the construction for the exponential function.

Binary Quadratic Forms Over F[T] And Principal Ideal Domains, Jeff Beyerl

All Theses

This paper concerns binary quadratic forms over F[T]. It develops theory analogous to the theory of binary quadratic forms over the integers. Most although not all of the results are almost identical, while some of the proofs require different techniques.
In particular, the form class group is determined when the form takes values in a principal ideal domain, and the ideal class group (and class group isomorphism) is determined when the form takes values in F[T].

Ethnomathematics In The Dominican Republic: A Mathematics Education Approach To Knowledge And Emancipation, Sofia Pablo-Hoshino

Renée Crown University Honors Thesis Projects - All

This focus of this project was to look at the extent to which ethnomathematics is being used in the mathematics curriculum in theDominican Republic. Broadly described, ethnomathematics emphasizes that the culture, history, and experiences of the students are significant and therefore should be infused into the mathematics curriculum.

I read articles and books as well as traveled to theDominican Republicto conduct qualitative research. I interviewed 32 professionals consisting of mathematics teachers, mathematics professors, and mathematics education professors from theSantiagoandSanto Domingoareas. I then volunteered at the Dominican Republic Education and Mentoring (DREAM) Project where I was able to observe and participate …

Analytical Upstream Collocation Solution Of A Quadratic Forced Steady-State Convection-Diffusion Equation, Eric Paul Smith

Boise State University Theses and Dissertations

In this thesis we present the exact solution to the Hermite collocation discretization of a quadratically forced steady-state convection-diffusion equation in one spatial dimension with constant coeffcients, defined on a uniform mesh, with Dirichlet boundary conditions. To improve the accuracy of the method we use \upstream weighting" of the convective term in an optimal way. We also provide a method to determine where the forcing function should be optimally sampled. Computational examples are given, which support and illustrate the theory of the optimal sampling of the convective and forcing term.

Tight Lower Bound For The Sparse Travelling Salesman Problem, Fredrick Mtenzi

Conference papers

The Sparse Travelling Salesman Problem (Sparse TSP) which is a variant of the classical Travelling Salesman Problem (TSP) is the problem of finding the shortest route of the salesman when visiting cities in a region making sure that each city is visited at least once and returning home at the end. In the Sparse TSP, the distance between cities may not obey the triangle inequality; this makes the use of algorithms and formulations designed for the TSP to require modifications in order to produce near-optimal results. A lower bound for optmisation problems gives us the quality guarantee of the near-optimal …

Intersections And Representations Of Graphs, John Light

All Dissertations

Given two graphs G and H sharing the same vertex set, the edge-intersection spectrum of G and H is the set of possible
sizes of the intersection of the edge sets of both graphs. For example,
the spectrum of two copies of the cycle C₅ is {0, 2, 3, 5}, and the spectrum of two copies of the star K_1,r is {1, r}. The intersection spectrum was initially studied for designs by Lindner and Fu and others and was originally extended to graphs by Eric Mendelsohn. Several examples are studied, both when G and H are isomorphic and …

New Directions In Multivariate Public Key Cryptography, Raymond Heindl

All Dissertations

Most public key cryptosystems used in practice are based on integer factorization or discrete logarithms (in finite fields or elliptic curves). However, these systems suffer from two potential drawbacks. First, they must use large keys to maintain security, resulting in decreased efficiency. Second, if large enough quantum computers can be built, Shor's algorithm will render them completely insecure.
Multivariate public key cryptosystems (MPKC) are one possible alternative. MPKC makes use of the fact that solving multivariate polynomial systems over a finite field is an NP-complete problem, for which it is not known whether there is a polynomial algorithm on quantum …

Covariant Relativistic Quantum Mechanics Analysis Of A Linearly Accelerated Scalar Particle, Karol Mcdonald

Doctoral

A covariant formalism of Relativistic Quantum Mechanics is demonstrated, through it's de- velopment and application. The Relativistic Case is shown to follow a similar structure to the established Non-Relativistic formalism. Reasons for preferring the new covariant formalism over the established method are presented. Solutions to the case of a scalar particle in a one-dimensional field are presented. The Relativistic Energy Eigenfunction is derived. Results are generated from initial Gaussian states via a Green's Function method. A Green's Function for the system is derived and applied. The solution to the Quantum System is shown to follow a scaled version of the …

Noisy Signal Recovery Via Iterative Reweighted L1-Minimization, Deanna Needell

CMC Faculty Publications and Research

Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate even in the presence of noise. Recent a modified version of this method, reweighted L1-minimization, has been suggested. Although no provable results have yet been attained, empirical studies have suggested the reweighted version outperforms the standard method. Here we analyze the reweighted L1-minimization method in the noisy case, and provide provable results showing an improvement in the error bound over the standard bounds.

Using Maxwells Z Model To Determine Lunar Mare Lava Thickness, Autumn Wille

Honors Capstones

Capstone submitted as a graduate requirement for the BSU Honors Program.

Weak Sharp Minima On Riemannian Manifolds, Chong Li, Boris S. Mordukhovich, Jinhua Wang, Jen-Chih Yao

Mathematics Research Reports

This is the first paper dealing with the study of weak sharp minima for constrained optimization problems on Riemannian manifolds, which are important in many applications. We consider the notions of local weak sharp minima, boundedly weak sharp minima, and global weak sharp minima for such problems and obtain their complete characterizations in the case of convex problems on finite-dimensional Riemannian manifolds and their Hadamard counterparts. A number of the results obtained in this paper are also new for the case of conventional problems in linear spaces. Our methods involve appropriate tools of variational analysis and generalized differentiation on Riemannian …

Fractional Calculus: Definitions And Applications, Joseph M. Kimeu

Masters Theses & Specialist Projects

No abstract provided.

Spatiotemporal Structure Of Pulsating Solitons In The Cubic-Quintic Ginzburg-Landau Equation: A Novel Variational Formulation, S.C. Mancas, S. Roy Choudhury

Publications

Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic–quintic Ginzburg–Landau Equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are …

Modeling Hiv Drug Resistance, Mingfu Zhu

All Dissertations

Despite the development of antiviral drugs and the optimization of therapies, the emergence of drug resistance remains one of the most challenging issues for successful treatments of HIV-infected patients. The availability of massive HIV drug resistance data provides us not only exciting opportunities for HIV research, but also the curse of high dimensionality.
We provide several statistical learning methods in this thesis to analyze sequence data from different perspectives. We propose a hierarchical random graph approach to identify possible covariation among residue-specific mutations. Viral progression pathways were inferred using an EM-like algorithm in literature, and we present a normalization method …

Communication Across Random Landings, Kerron Joseph, Jay Walbran

Undergraduate Research Conference

The idea to do this project began with a simple question: Suppose that people carrying communication radios parachute out of a plane, if each device has a certain range, what is the probability that once everyone lands they will be able to communicate. To study this problem I assumed that the spot where each individual lands is normally distributed.

We discuss the different ways the communication radios can work. In particular we examine the situation where all the radios have to be within a certain radius r to operate correctly and the situation where the radios work on a relay …

Determining The Orbit Locations Of Turkish Airborne Early Warning And Control Aircraft Over The Turkish Air Space, Nebi Sarikaya

Theses and Dissertations

The technology improvement affects the military needs of individual countries. The new doctrine of defense for many countries emphasizes detecting threats as far away as you can from your homeland. Today, the military uses both ground RADAR and Airborne Early Warning and Control (AEW&C) Aircraft. AEW&C aircraft has become vital to detect low altitude threats that a ground RADAR cannot detect because of obstacles on the earth. Turkey has ordered four AEW&C aircraft for her air defense system because of the lack of complete coverage by ground RADAR. This research provides optimal orbit locations that can be updated according to …

Probabilistic Estimation Of Rare Random Collisions In 3-Space, Timothy Holzmann

Theses and Dissertations

A study of risk assessment for artillery fire randomly colliding with fixed wing aircraft is presented. The research lends itself to a general study of collision models. Current models of object collisions fall under one of three categories: the historical model, the gas particle model, and the satellite model. These three vary in data requirements and mathematical representation of the impact event. The gas particle model is selected for its flexibility and robust estimation. However, current mathematical development in the literature does not include certain spatial and dynamic components necessary for a general encounter (collision) model. These are derived in …

A Wigner Distribution Analysis Of One Dimensional Scattering, Brent R. Lacy

Theses and Dissertations

We applied the Wigner Distribution Function, a distribution function of time and frequency based on an initial function of either of those variables, to a series of time based correlation functions. These time based correlation functions were the result of a 1-dimensional free particle wave packet, the reactant wave function, which had propagated through a quantum potential well and then had components of the reactant wave function that exited the opposite side of the well auto-correlated in time with a stationary 1-dimensional free particle wave packet, the product wave function. This process was undertaking in order to generate a 3-dimensional …

Characterizing And Detecting Unrevealed Elements Of Network Systems, James A. Leinart

Theses and Dissertations

This dissertation addresses the problem of discovering and characterizing unknown elements in network systems. Klir (1985) provides a general definition of a system as “... a set of some things and a relation among the things" (p. 4). A system, where the `things', i.e. nodes, are related through links is a network system (Klir, 1985). The nodes can represent a range of entities such as machines or people (Pearl, 2001; Wasserman & Faust, 1994). Likewise, links can represent abstract relationships such as causal influence or more visible ties such as roads (Pearl, 1988, pp. 50-51; Wasserman & Faust, 1994; Winston, …

Quantification Of Mandatory Sustainment Requirements, Joe M. Blackman

Theses and Dissertations

To emphasize the importance of sustainment, the DoD Joint Requirements Oversight Council addressed sustained Materiel readiness and established a mandatory Key Performance Parameter (KPP) for Materiel Availability; it also established supporting Key System Attributes (KSAs) for Materiel Reliability and Ownership Cost (Chairman of the Joint Chiefs of Staff Manual (CJCSM) 3170.01C, 2007). Current guidance requires two numbers: a threshold value and an objective value (Chairman of the Joint Chiefs of Staff Manual (CJCSM) 3170.01C, 2007). No distinction is made between the approaches in establishing these values for major system acquisitions, versus smaller, modification-focused efforts for existing systems. The Joint Staff …

Efficient Evaluation Of Ranking Procedures When The Number Of Units Is Large With Application To Snp Identification, Thomas A. Louis, Ingo Ruczinski

Johns Hopkins University, Dept. of Biostatistics Working Papers

Simulation-based assessment is a popular and frequently necessary approach to evaluation of statistical procedures. Sometimes overlooked is the ability to take advantage of underlying mathematical relations and we focus on this aspect. We show how to take advantage of large-sample theory when conducting a simulation using the analysis of genomic data as a motivating example. The approach uses convergence results to provide an approximation to smaller-sample results, results that are available only by simulation. We consider evaluating and comparing a variety of ranking-based methods for identifying the most highly associated SNPs in a genome-wide association study, derive integral equation representations …