Applied Mathematics Commons^™

On Quasilinear Parabolic Evolution Equations In Weighted Lp-Spaces Ii, Jeremy Lecrone, Mathias Wilke, Jan Prüss

Department of Math & Statistics Faculty Publications

Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in 2010, is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to reaction-diffusion problems, including Maxwell-Stefan diffusion, and to geometric evolution equations like the surface-diffusion flow or the Willmore flow. The method presented here will be applicable to other parabolic systems, including free boundary problems.

Dressing Method And Quadratic Bundles Related To Symmetric Spaces: Vanishing Boundary Conditions, Tihomir Valchev

Articles

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m) x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schroedinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.

Analytical Solution Of The Symmetric Circulant Tridiagonal Linear System, Sean A. Broughton, Jeffery J. Leader

Mathematical Sciences Technical Reports (MSTR)

A circulant tridiagonal system is a special type of Toeplitz system that appears in a variety of problems in scientific computation. In this paper we give a formula for the inverse of a symmetric circulant tridiagonal matrix as a product of a circulant matrix and its transpose, and discuss the utility of this approach for solving the associated system.

Light Pollution Research Through Citizen Science, John Kanemoto

STAR Program Research Presentations

Light pollution (LP) can disrupt and/or degrade the health of all living things, as well as, their environments. The goal of my research at the NOAO was to check the accuracy of the citizen science LP reporting systems entitled: Globe at Night (GaN), Dark Sky Meter (DSM), and Loss of the Night (LoN). On the GaN webpage, the darkness of the night sky (DotNS) is reported by selecting a magnitude chart. Each magnitude chart has a different density/number of stars around a specific constellation. The greater number of stars implies a darker night sky. Within the DSM iPhone application, a …

Kekule's Benzene Structure: A Case Study Of Teaching Usefulness Of Symmetry, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Benzene is one of the basic building blocks of organic molecules. One of the reasons for benzene's ubiquity is its unusual ring structure first discovered by Kekule in 1865. In this paper, we show that a simple symmetry-based analysis can narrow down possible benzene structures to three ring ones, including the Kekule's ring. Thus, Kekule's benzene structure provides a good pedagogical example on which one can explain usefulness of symmetries.

A Coupled Pde Model For The Morphological Instability Of A Multi-Component Thin Film During Surface Electromigration, Mahdi Bandegi

Masters Theses & Specialist Projects

In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics …

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 …

Homomorphic Encryption And The Approximate Gcd Problem, Nathanael Black

All Dissertations

With the advent of cloud computing, everyone from Fortune 500 businesses to personal consumers to the US government is storing massive amounts of sensitive data in service centers that may not be trustworthy. It is of vital importance to leverage the benefits of storing data in the cloud while simultaneously ensuring the privacy of the data. Homomorphic encryption allows one to securely delegate the processing of private data. As such, it has managed to hit the sweet spot of academic interest and industry demand. Though the concept was proposed in the 1970s, no cryptosystem realizing this goal existed until Craig …

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 …

Computational Bases For Hdiv, Alistair Bentley

All Theses

The \(H_{div}\) vector space arises in a number of mixed method formulations, particularly in fluid flow through a porous medium. First we present a Lagrangian computational basis for the Raviert-Thomas (\(RT\)) and Brezzi-Douglas-Marini (\(BDM\)) approximation subspaces of \(H_{div}\) in \(\mathbb{R}^{3}\). Second, we offer three solutions to a numerical problem that arises from the Piola mapping when \(RT\) and \(BDM\) elements are used in practice.

Vector Spaces (Appendix B), Charles G. Torre

Foundations of Wave Phenomena

Throughout this text we have noted that various objects of interest form a vector space. Here we outline the basic structure of a vector space. You may find it useful to refer to this Appendix when you encounter this concept in the text.

Taylor’S Theorem And Taylor Series (Appendix A), Charles G. Torre

Foundations of Wave Phenomena

Taylor’s theorem and Taylor’s series constitute one of the more important tools used by mathematicians, physicists and engineers. They provides a means of approximating a function in terms of polynomials.

References And Suggestions For Further Reading (Appendix C), Charles G. Torre

Foundations of Wave Phenomena

References and Suggestions for Further Reading (Appendix C)

A Soft Condensed Matter Approach Towards Mathematical Modelling Of Mass Transport And Swelling In Food Grains, Michael Chapwanya, N. Misra

Articles

Soft condensed matter (SCM) physics has recently gained importance for a large class of engineering materials. The treatment of food materials from a soft matter perspective, however, is only at the surface and is gaining importance for understanding the complex phenomena and structure of foods. In this work, we present a theoretical treatment of navy beans from a SCM perspective to describe the hydration kinetics. We solve the transport equations within a porous matrix and employ the Flory–Huggin’s equation for polymer–solvent mixture to balance the osmotic pressure. The swelling of the legume seed is modelled as a moving boundary with …

Applied Statistics In Environmental Monitoring: Case Studies And Analysis For The Michigan Bald Eagle Biosentinel Program, Katherine Leith

All Dissertations

The bald eagle (Haliaeetus leucocephalus) is an extensively researched tertiary predator. Its life history and the impact of various stressors on its reproductive outcomes have been documented in many studies, and over many years. Furthermore, the bald eagle population recovery in Michigan has been closely monitored since the 1960s, as it has continued to recover from a contaminant-induced bottleneck. Because of its position at the top of the aquatic food web and the large body of ethological knowledge, the bald eagle has become a sentinel species for the Michigan aquatic ecosystem. In April 1999, the Michigan Department of Environmental Qualtity, …

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 …

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 …

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. …

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 …

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 …

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, …

Isotropic Oscillator Under A Magnetic And Spatially Varying Electric Field, David L. Frost Mr., Frank Hagelberg

Undergraduate Honors Theses

We investigate the energy levels of a particle confined in the isotropic oscillator potential with a magnetic and spatially varying electric field. Here we are able to exactly solve the Schrodinger equation, using matrix methods, for the first excited states. To this end we find that the spatial gradient of the electric field acts as a magnetic field in certain circumstances. Here we present the changes in the energy levels as functions of the electric field, and other parameters.

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 …

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.

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. …