Applied Mathematics Commons^™

Boundary Value Problems Of Nabla Fractional Difference Equations, Abigail M. Brackins

Department of Mathematics: Dissertations, Theses, and Student Research

In this dissertation we develop the theory of the nabla fractional self-adjoint difference equation,

∇_a^ν(p∇y)(t)+q(t)y(ρ(t)) = f(t),

where 0 < ν < 1.We begin with an introduction to the nabla fractional calculus. In the second chapter, we show existence and uniqueness of the solution to a fractional self-adjoint initial value problem. We find a variation of constants formula for this fractional initial value problem, and use the variation of constants formula to derive the Green's function for a related boundary value problem. We study the Green's function and its properties in several settings. For a simplified boundary value problem, we show that the Green's function is nonnegative and we find its maximum and the maximum of its integral. For a boundary value problem with generalized boundary conditions, we find the Green's function and show that it is a generalization of the first Green's function. In the third chapter, we use the Contraction Mapping Theorem to prove existence and uniqueness of a positive solution to a forced self-adjoint fractional difference equation with a finite limit. We explore modifications to the forcing term and modifications to the space of functions in which the solution exists, and we provide examples to demonstrate the use of these theorems.

Advisers: Lynn Erbe and Allan Peterson

The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs

Department of Mathematics: Dissertations, Theses, and Student Research

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can - in principle - be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects …

Multi-Sensory Emotion Recognition With Speech And Facial Expression, Qingmei Yao

Dissertations

Emotion plays an important role in human beings’ daily lives. Understanding emotions and recognizing how to react to others’ feelings are fundamental to engaging in successful social interactions. Currently, emotion recognition is not only significant in human beings’ daily lives, but also a hot topic in academic research, as new techniques such as emotion recognition from speech context inspires us as to how emotions are related to the content we are uttering.

The demand and importance of emotion recognition have highly increased in many applications in recent years, such as video games, human computer interaction, cognitive computing, and affective computing. …

Prediction Of Time-To-Graduation For Stem Hispanic Undergraduate Students, Gejun Zhu

Theses and Dissertations - UTB/UTPA

In this thesis, we study the time-to-graduation problem for STEM Hispanic undergraduate students. The response, time-to-graduation, was treated in two different ways: as a binary variable with graduated (by the 6th year) and not-graduated values, and as an ordinal variable with values year-4, year-5, year-6, and not-graduate. Mathematics education plays critical role in students’ timely graduation, especially for STEM students. We used students records data obtained from The University of Texas-Pan American to illustrate how mathematics background factors (including SAT math score, ACT math score, TASP math score) and mathematics performance variables (including mathematics GPA, number of dropped mathematics courses, …

Development And Applications Of The Expanded Equivalent Fluid Method, Bharath Kumar Kandula

Dissertations

Ocean acoustics is the study of sound in the oceans. Electromagnetic waves attenuate rapidly in the water medium. Sound is the best means to transmit information underwater. Computational numerical simulations play an important role in ocean acoustics. Simulations of acoustic propagation in the oceans are challenging due to the complexities involved in the ocean environment. Different methods have been developed to simulate underwater sound propagation. The Parabolic-Equation (PE) method is the best choice in several ocean acoustic problems. In shallow water acoustic experiments, sound loses some of its energy when it interacts with the bottom. An equivalent fluid technique was …

Level Stripping Of Genus 2 Siegel Modular Forms, Rodney Keaton

All Dissertations

In this Dissertation we consider stripping primes from the level of genus 2 cuspidal Siegel eigenforms. Specifically, given an eigenform of level Nlr which satisfies certain mild conditions, where l is a prime not dividing N, we construct an eigenform of level N which is congruent to our original form. To obtain our results, we use explicit constructions of Eisenstein series and theta functions to adapt ideas from a level stripping result on elliptic modular forms. Furthermore, we give applications of this result to Galois representations and provide evidence for an analog of Serre's conjecture in the genus 2 case.

Convergence Of A Reinforcement Learning Algorithm In Continuous Domains, Stephen Carden

All Dissertations

In the field of Reinforcement Learning, Markov Decision Processes with a finite number of states and actions have been well studied, and there exist algorithms capable of producing a sequence of policies which converge to an optimal policy with probability one. Convergence guarantees for problems with continuous states also exist. Until recently, no online algorithm for continuous states and continuous actions has been proven to produce optimal policies. This Dissertation contains the results of research into reinforcement learning algorithms for problems in which both the state and action spaces are continuous. The problems to be solved are introduced formally as …

One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov

Articles

In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.

Numerical Simulations Of Traffic Flow Models, Puneet Lakhanpal

UNLV Theses, Dissertations, Professional Papers, and Capstones

Traffic flow has been considered to be a continuum flow of a compressible liquid having a certain density profile and an associated velocity, depending upon density, position and time. Several one-equation and two-equation macroscopic continuum flow models have been developed which utilize the fluid dynamics continuity equation and help us find analytical solutions with simplified initial and boundary conditions. In this thesis, the one-equation Lighthill Witham and Richards (LWR) model combined with the Greenshield's model, is used for finding analytical and numerical solutions for four problems: Linear Advection, Red Traffic Light turning into Green, Stationary Shock and Shock Moving towards …

Mathematical Equations And System Identification Models For A Portable Pneumatic Bladder System Designed To Reduce Human Exposure To Whole Body Shock And Vibration, Ezzat Aziz Ayyad

UNLV Theses, Dissertations, Professional Papers, and Capstones

A mathematical representation is sought to model the behavior of a portable pneumatic foam bladder designed to mitigate the effects of human exposure to shock and whole body random vibration. Fluid Dynamics principles are used to derive the analytic differential equations used for the physical equations Model. Additionally, combination of Wiener and Hammerstein block oriented representation techniques have been selected to create system identification (SID) block oriented models. A number of algorithms have been iterated to obtain numerical solutions for the system of equations which was found to be coupled and non-linear, with no analytic closed form solution. The purpose …

Several Functional Equations Defined On Groups Arising From Stochastic Distance Measures., Heather B. Hunt

Electronic Theses and Dissertations

Several functional equations related to stochastic distance measures have been widely studied when defined on the real line. This dissertation generalizes several of those results to functions defined on groups and fields. Specifically, we consider when the domain is an arbitrary group, G, and the range is the field of complex numbers, C. We begin by looking at the linear functional equation f(pr, qs)+f(ps, qr) = 2f(p, q)+2f(r, s) for all p, q, r, s, € G. The general solution f : G x G → C is given along with a few specific examples. Several generalizations of this equation …

Magnetoviscous Effects Of Magnetized Particle Threads In Magnetized Ferrofluid, Alexander Francis Cali

Theses, Dissertations and Culminating Projects

The magnetoviscous effect of applied fields on ferrofluids has been utilized in many applications in which the ferrofluid must remain in a fixed position while this effect on ferrofluids in motion has yet to be rigorously explored. In light of potential biomedical applications such as drug targeting, experiments were conducted to probe the rheology of ferrofluids on the micrometer scale. A non-conducting glass sphere of diameter 550 μm is dropped into a cylindrical container of magnetized ferrofluid of inner diameter 5.2 mm. This was repeated for two applied field strengths (980 gauss and 480 gauss) and over multiple angles with …

Grobner Bases: Degree Bounds And Generic Ideals, Juliane Golubinski Capaverde

All Dissertations

In this thesis, we study two problems related to Gröbner basis theory: degree bounds for general ideals and Gröbner bases structure for generic ideals. We start by giving an introduction to Gröbner bases and their basic properties and presenting a recent algorithm by Gao, Volny and Wang. Next, we survey degree bounds for the ideal membership problem, the effective Nullstellensatz, and polynomials in minimal Gröbner bases. We present general upper bounds, and bounds for several classes of special ideals. We provide classical examples showing some of these bounds cannot be improved in general. We present a comprehensive study of a …

On Numerical Algorithms For Fluid Flow Regularization Models, Abigail Bowers

All Dissertations

This thesis studies regularization models as a way to approximate a flow simulation at a lower computational cost. The Leray model is more easily computed than the Navier-Stokes equations (NSE), and it is more computationally attractive than the NS-α regularization because it admits a natural linearization which decouples the mass/momentum system and the filter system, allowing for efficient and stable computations. A major disadvantage of the Leray model lies in its inaccuracy. Thus, we study herein several methods to improve the accuracy of the model, while still retaining many of its attractive properties. This thesis is arranged as follows. Chapter …

A Women In Mathematics, Computer Science, And Physics Course, Jim Crumley, Kristen Nairn, Lynn Ziegler, Pamela L. Bacon, Yu Zhang

MapCores Faculty Publications

Increasing women's participation is a concern in disciplines beyond
physics. As part of our Mathematics, Physics, Computer Science
Research Scholars (MapCores) program, we teach a women in science
class covering these three areas. Our course is a special version of
our college's first year seminar, which is a course designed to
prepare our students to read, write, and speak at a college-level. We
structure our FYS to promote academic confidence and interest in our
disciplines for the women in MapCores. It covers not only contributions
that women have made and barriers that women face in these
disciplines, but also research …

Variable Viscosity Condition In The Modeling Of A Slider Bearing, Kedar Nath Uprety, S.C. Mancas

Publications

To reduce tear and wear of machinery lubrication is essential. Lubricants form a layer between two surfaces preventing direct contact and reduce friction between moving parts and hence reduce wear. In this short letter the lubrication of two slider bearings with parallel and nonparallel is studied. First, we show that bearings with parallel plates cannot support any load. For bearings with nonparallel plates we are interested on how constant and temperature dependent viscosity affects the properties of the bearings. Also, a critical temperature for which the bearings would fail due to excess in temperature is found for both latter cases. …

What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, John Tabak

Journal of Interpretation

Courses and seminars in higher mathematics are some of the most challenging assignments faced by academic interpreters. Difficulties interpreting higher mathematics can adversely impact the academic and professional aspirations of deaf mathematics students and professionals. This paper discusses the nature of higher mathematics with the goal of identifying what distinguishes higher mathematics from other subjects; it then reviews the history of attempts to sign/interpret higher mathematics with particular attention to current challenges associated with expressing higher mathematics in sign. The final part of the paper discusses strategies for more effectively expressing higher mathematics in American Sign Language.

A Comparison Of Five Malaria Transmission Models: Benchmark Tests And Implications For Disease Control, Dorothy I. Wallace, Ben S. Southworth, Xun Shi, Jonathan W. Chipman, Andrew K. Githeko

Dartmouth Scholarship

Background: Models for malaria transmission are usually compared based on the quantities tracked, the form taken by each term in the equations, and the qualitative properties of the systems at equilibrium. Here five models are compared in detail in order to develop a set of performance measures that further illuminate the differences among models.

Methods: Five models of malaria transmission are compared. Parameters are adjusted to correspond to similar biological quantities across models. Nine choices of parameter sets/initial conditions are tested for all five models. The relationship between malaria incidence in humans and (1) malaria incidence in vectors, (2) man-biting …

Analysis Of A Mathematical Model For The Heave Motion Of A Micro Aerial Vehicle With Flexible Wings Having Non-Local Damping Effects, Jonathan B. Walters

Doctoral Dissertations

In this work we analyze a one dimensional model for a flexible wing micro aerial vehicle which can undergo heaving motion. The vehicle is modeled with a non-local type of internal damping known as spatial hysteresis as well as viscous external damping. We present a rigorous theoretical analysis of the model proving that the linearly approximated system is well-posed and the first order feedback system operators generate exponentially stable C0–semigroups.

Furthermore, we present numerical simulations of control designs used on the linearly approximated model to control the associated nonlinear model in two different strategies. The first strategy used to …

Using Second-Order Probabilities To Make Maximum Entropy Approach To Copulas More Reasonable, Hung T. Nguyen, Vladik Kreinovich, Berlin Wu

Departmental Technical Reports (CS)

Copulas are a general way of describing dependence between two or more random variables. When we only have partial information about the dependence, i.e., when several different copulas are consistent with our knowledge, it is often necessary to select one of these copulas. A frequently used method of selecting this copula is the maximum entropy approach, when we select a copula with the largest entropy. However, in some cases, the maximum entropy approach leads to an unreasonable selection -- e.g., even if we know that the two random variables are positively correlated, the maximum entropy approach completely ignores this information. …