Applied Mathematics Commons^™

An Approximate Solution Of The Mathieu Fractional Equation By Using The Generalized Differential Transform Method (Gdtm), H. S. Najafi, S. R. Mirshafaei, E. A. Toroqi

Applications and Applied Mathematics: An International Journal (AAM)

The generalized differential transform method (GDTM) is a powerful tool for solving fractional equations. In this paper we solve the Mathieu fractional equation by this method. The approximate solutions obtained are compared with the exact solution. We also show that if both differential orders decrease, we can still have an approximate solution in the different interval of p.

Exact Solutions Of The Generalized Benjamin Equation And (3 + 1)- Dimensional Gkp Equation By The Extended Tanh Method, N. Taghizadeh, M. Mirzazadeh, S. R. Moosavi Noori

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the extended tanh method is used to construct exact solutions of the generalized Benjamin and (3 + 1)-dimensional gKP equation. This method is shown to be an efficient method for obtaining exact solutions of nonlinear partial differential equations. It can be applied to nonintegrable equations as well as to integrable ones.

Coherent Pattern Prediction In Swarms Of Delay-Coupled Agents, Luis Mier-Y-Teran-Romero, Eric Forgoston, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of the coupling amplitude. We extend these results by completely unfolding the bifurcation structure of the mean field approximation. Our analysis reveals a direct correspondence between the different dynamical behaviors found in different regions of the coupling-time delay plane with the different classes of simulated coherent swarm patterns. We derive the spatiotemporal scales of the swarm …

The Evolution Of Health Insurance In America: A Look At The Past, Present, And Future Of An Increasingly Dynamic Industry, Matthew Billas

Honors Scholar Theses

From the origins of health insurance in the form of 20^th century accident insurance to the widespread ramifications of the recent passage of the Patient Protection and Affordable Care Act (PPACA), the health insurance industry in America has undergone an unprecedented amount of change throughout its relatively short history. Over the past century, rising medical costs as well as an increased demand for medical care have led to the rapid growth of the health insurance industry. What began as a relatively simple system has grown increasingly complex with the introduction of new plan designs and increasing government reform to …

A Mathematical Model For Dengue Fever In A Virgin Environment, Jason K. Bowman

Senior Honors Projects

Dengue is a mosquito-borne viral infection found in tropical and subtropical regions around the world. The disease was named in 1779 and the first recorded epidemic of it occurred simultaneously on three continents within the following decade. Dengue is characterized by flu-like symptoms and, while its symptoms are generally reported as quite unpleasant, is rarely fatal. However, in some cases patients can contract a more serious form of the disease, known as Dengue Hemorrhagic Fever, which is far more dangerous. The World Health Organization estimates that today over 2.5 billion people are at risk for Dengue (over 40% of the …

On Nullification Of Knots And Links, Anthony Montemayor

Masters Theses & Specialist Projects

Motivated by the action of XER site-specific recombinase on DNA, this thesis will study the topological properties of a type of local crossing change on oriented knots and links called nullification.

One can define a distance between types of knots and links based on the minimum number of nullification moves necessary to change one to the other. Nullification distances form a class of isotopy invariants for oriented knots and links which may help inform potential reaction pathways for enzyme action on DNA. The minimal number of nullification moves to reach a è-component unlink will be called the è-nullification number.

This …

A Normal Truncated Skewed-Laplace Model In Stochastic Frontier Analysis, Junyi Wang

Masters Theses & Specialist Projects

Stochastic frontier analysis is an exciting method of economic production modeling that is relevant to hospitals, stock markets, manufacturing factories, and services. In this paper, we create a new model using the normal distribution and truncated skew-Laplace distribution, namely the normal-truncated skew-Laplace model. This is a generalized model of the normal-exponential case. Furthermore, we compute the true technical efficiency and estimated technical efficiency of the normal-truncated skewed-Laplace model. Also, we compare the technical efficiencies of normal-truncated skewed-Laplace model and normal-exponential model.

Design Of Orbital Maneuvers With Aeroassisted Cubesatellites, Stephanie Clark

Graduate Theses and Dissertations

Recent advances within the field of cube satellite technology has allowed for the possible development of a maneuver that utilizes a satellite's Low Earth Orbit (LEO) and increased atmospheric density to effectively use lift and drag to implement a noncoplanar orbital maneuver. Noncoplanar maneuvers typically require large quantities of propellant due to the large delta-v that is required. However, similar maneuvers using perturbing forces require little or no propellant to create the delta-v required. This research reported here studied on the effects of lift on orbital changes, those of noncoplanar types in particular, for small satellites without orbital maneuvering thrusters. …

Translation Representations And Scattering By Two Intervals, Palle Jorgensen, Steen Pedersen, Feng Tian

Mathematics and Statistics Faculty Publications

Studying unitary one-parameter groups in Hilbert space (U(t), H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L²-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U(t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator and scattering matrix. We illustrate our results in the Lax-Phillips model where (U(t), H) represents an acoustic wave equation …

Enhanced Physics Schemes For The 2d Ns-Alpha Models Of Incompressible Flow, Michael Dowling

All Theses

In this thesis, we study algorithms for the 2D NS-alpha model of incompressible flow. These schemes conserve both discrete energy and discrete enstrophy in the absence of viscous and external forces, and otherwise admit exact balances for them analogous to those of true fluid flow. This model belongs to a very small group that conserves both of these quantities in the continuous case, and in this work, we develop finite element algorithms for the vorticity-stream formulation of this model that will preserve numerical energy and enstrophy in the computed solutions.

Numerical Study For A Viscoelastic Fluid-Structure Interaction Problem, Shuhan Xu

All Theses

In this thesis, we consider a viscoelastic flow in a moving domain, which has significant applications in biology and industry. Numerical approximation schemes are developed based on the Arbitrary Lagrangian-Eulerian (ALE) formulation of the flow equations. A spatial discretization is accomplished by the finite element method, and the time descritization is carried by either the implicit Euler method or the Crank-Nicolson method. Numerical results are presented for a fluid in a moving domain, where the boundary movement is specified by a given function. Then, we extend our work to a fluid-structure interaction problem. This system consists of a two-dimensional viscoelastic …

On Factoring Hecke Eigenforms, Nearly Holomorphic Modular Forms, And Applications To L-Values, Jeff Beyerl

All Dissertations

This thesis is a presentation of some of my research activities while at Clemson University. In particular this includes joint work on the factorization of eigenforms and their relationship to Rankin- Selberg L-values, and nearly holomorphic eigenforms. The main tools used on the factorization of eigenforms are linear algebra, the j function, and the Rankin-Selberg Method. The main tool used on nearly holomorphic modular forms is the Rankin-Cohen bracket operator.

Modelling Two-Dimensional Photopolymer Patterns Produced With Multiple-Beam Holography, Dana Mackey, Tsvetanka Babeva, Izabela Naydenova, Vincent Toal

Conference papers

Periodic structures referred to as photonic crystals attract considerable interest due to their potential applications in areas such as nanotechnology, photonics, plasmonics, etc. Among various techniques used for their fabrication, multiple-beam holography is a promising method enabling defect-free structures to be produced in a single step over large areas.

In this paper we use a mathematical model describing photopolymerisation to simulate two-dimensional structures produced by the interference pattern of three noncoplanar beams. The holographic recording of different lattices is studied by variation of certain parameters such as beam wave vectors, time and intensity of illumination.

The Persistence Of Infectious Diseases In Metapopulations, Jonathan Calvin Hayes

Theses, Dissertations and Culminating Projects

Mathematical models provide a great deal of information about the dynamics of disease spread. In this paper, we use stochastic simulation to investigate spontaneous disease extinction and réintroduction in a SIR model. We begin by investigating path to extinction and time to extinction in single population models, and then expand to a multipopulation model linked with linear migration. We have found that in a single population model, it is more effective to use random pulse vaccinations less per year at a higher removal rate. We have expanded this result by developing a vaccination strategy giving one large, well timed pulse …

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 …

Pointwise Schauder Estimates Of Parabolic Equations In Carnot Groups, Heather Arielle Griffin

Graduate Theses and Dissertations

Schauder estimates were a historical stepping stone for establishing uniqueness and smoothness of solutions for certain classes of partial differential equations. Since that time, they have remained an essential tool in the field. Roughly speaking, the estimates state that the Holder continuity of the coefficient functions and inhomogeneous term implies the Holder continuity of the solution and its derivatives. This document establishes pointwise Schauder estimates for second order parabolic equations where the traditional role of derivatives are played by vector fields generated by the first layer of the Lie algebra stratification for a Carnot group. The Schauder estimates are shown …

Champion Primes For Elliptic Curves, Jason Hedetniemi

All Theses

Let E_a,b be the elliptic curve y2 = x3 + ax + b over F_p. A well known result of Hasse states that over F_p
(p+1) - 2p½ ≤ #E_a,b ≤ (p+1)+2p½
If #E_a,b = (p+1) + floor(2p½) over F_p and E_a,b is nonsingular, then we call p a champion prime for E_a,b. We will discuss methods for finding champion primes for elliptic curves. In addition, we will show that the set of elliptic curves which have a champion prime has density one.

The Number Of Ways To Write N As A Sum Of ` Regular Figurate Numbers, Seth Jacob Rothschild

Renée Crown University Honors Thesis Projects - All

See Document for Abstract

Perfect Stripes From A General Turing Model In Different Geometries, Jean Tyson Schneider

Boise State University Theses and Dissertations

We explore a striped pattern generated by a general Turing model in three different geometries. We look at the square, disk, and hemisphere and make connections between the stripes in each spatial direction. In particular, we gain a greater understanding of when perfect stripes can be generated and what causes defects in their patterns. In this investigation, we look at the difference between the solutions due to the different domain shapes. In the end, we propose a reason why stripes from a reaction-diffusion system with zero-flux boundary conditions can be perfect on a square or hemisphere, but not on a …

Valuation Of Financial Derivatives Subject To Liquidity Risk, Yanan Jiang

UNLV Theses, Dissertations, Professional Papers, and Capstones

Valuation of financial derivatives subject to liquidity risk remains an open problem in finance. This dissertation focuses on the valuation of European-style call option under limited market liquidity through the dynamic management of a portfolio of assets. We investigate liquidity from three perspectives: market breadth, depth, and immediacy. We present a general framework of valuation based on the optimal realization of a performance index relative to the set of all feasible portfolio trajectories. Numerical examples are then presented and analyzed that show option price increases as the market transitions from liquid to less liquid state. Furthermore, buying and selling activities, …

Periodic Solutions And Positive Solutions Of First And Second Order Logistic Type Odes With Harvesting, Cody Alan Palmer

UNLV Theses, Dissertations, Professional Papers, and Capstones

It was recently shown that the nonlinear logistic type ODE with periodic harvesting has a bifurcation on the periodic solutions with respect to the parameter ε:

u' = f (u) - ε h (t).

Namely, there exists an ε0 such that for 0 < ε < ε0 there are two periodic solutions, for ε = ε0 there is one periodic solution, and for ε >ε0 there are no periodic solutions, provided that....

In this paper we look at some numerical evidence regarding the behavior of this threshold for various types of harvesting terms, in particular we find evidence in the negative or a conjecture regarding the behavior of this threshold value.

Additionally, we look at analagous steady states for the reaction-diusion …

Analytic And Finite Element Solutions Of The Power-Law Euler-Bernoulli Beams, Dongming Wei, Yu Liu

Mathematics Faculty Publications

In this paper, we use Hermite cubic finite elements to approximate the solutions

of a nonlinear Euler-Bernoulli beam equation. The equation is derived

from Hollomon’s generalized Hooke’s law for work hardening materials with

the assumptions of the Euler-Bernoulli beam theory. The Ritz-Galerkin finite

element procedure is used to form a finite dimensional nonlinear program

problem, and a nonlinear conjugate gradient scheme is implemented to find

the minimizer of the Lagrangian. Convergence of the finite element approximations

is analyzed and some error estimates are presented. A Matlab finite

element code is developed to provide numerical solutions to the beam equation.

Some …

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 …

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 …

A Collection Of Problems In Combinatorics, Janine Janoski

All Dissertations

We present several problems in combinatorics including the partition function, Graph Nim, and the evolution of strings.
Let p(n) be the number of partitions of n. We say a sequence a_n is log-concave if for every n, a_n2 &ge a_n+1 a_n-1. We will show that p(n) is log-concave for n &ge 26. We will also show that for n<26, p(n) alternatively satisfies and does not satisfy the log-concave property. We include results for the Sperner property of the partition function.
The second problem we present is the game of Graph Nim. We use the Sprague-Grundy theorem to analyze modified versions of Nim played on various graphs. We include progress made towards proving that all G-paths …

An Optimization Approach To A Geometric Packing Problem, Bradley Paynter

All Dissertations

We investigate several geometric packing problems (derived from an industrial setting) that involve fitting patterns of regularly spaced disks without overlap. We first derive conditions for achieving the feasible placement of a given set of patterns and construct a network formulation that, under certain conditions, allows the calculation of such a placement. We then discuss certain related optimization problems (e.g., fitting together the maximum number of patterns) and broaden the field of application by showing a connection to the well-known Periodic Scheduling Problem. In addition, a variety of heuristics are developed for solving large-scale instances of these provably difficult packing …

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 …

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.