Mathematics Commons^™

Discontinuous Galerkin Finite Element Methods For Maxwell's Equations In Dispersive And Metamaterials Media, Jiajia Waters

UNLV Theses, Dissertations, Professional Papers, and Capstones

Discontinuous Galerkin Finite Element Method (DG-FEM) has been further developed in this dissertation. We give a complete proof of stability and error estimate for the DG-FEM combined with Runge Kutta which is commonly used in different fields. The proved error estimate matches those numerical results seen in technical papers. Numerical simulations of metamaterials play a very important role in the design of invisibility cloak, and sub-wavelength imaging. We propose a leap-frog discontinuous Galerkin Finite Element Method to solve the time-dependent Maxwell's equations in metamaterials. The stability and error estimate are proved for this scheme. The proposed algorithm is implemented and …

Generalizations Of Pascal's Triangle: A Construction Based Approach, Michael Anton Kuhlmann

UNLV Theses, Dissertations, Professional Papers, and Capstones

The study of this paper is based on current generalizations of Pascal's Triangle, both the expansion of the polynomial of one variable and the multivariate case. Our goal is to establish relationships between these generalizations, and to use the properties of the generalizations to create a new type of generalization for the multivariate case that can be represented in the third dimension.

In the first part of this paper we look at Pascal's original Triangle with properties and classical applications. We then look at contemporary extensions of the triangle to coefficient arrays for polynomials of two forms. The first of …

Symbolic Powers Of Ideals In K[PN], Michael Janssen

Department of Mathematics: Dissertations, Theses, and Student Research

Let I ⊆ k[P^N] be a homogeneous ideal and k an algebraically closed field. Of particular interest over the last several years are ideal containments of symbolic powers of I in ordinary powers of I of the form I^(m) ⊆ I^r, and which ratios m/r guarantee such containment. A result of Ein-Lazarsfeld-Smith and Hochster-Huneke states that, if I ⊆ k[P^N], where k is an algebraically closed field, then the symbolic power I^(Ne) is contained in the ordinary power I^e, and thus, whenever …

Traffic Modeling In Lagrangian Coordinates Using Smartphone Apps, Sergio Contreras

UNLV Theses, Dissertations, Professional Papers, and Capstones

Traditionally, one of the ways traffic flow has been studied is by using the kinematic wave model. This model is derived in the Eulerian framework by using conservation of the number of vehicles. Recently, the kinematic wave model has been transformed into Lagrangian coordinates. In this framework, the independent variables are unique

vehicles and time. The detailed change in framework, and the properties of the model in the changed framework are reviewed. Numerical results from different traffic cases are explained. Since vehicle trajectory data can be easily collected from smartphones,

a smartphone application is developed for this purpose. This data …

Uphill & Downhill Domination In Graphs And Related Graph Parameters., Jessie Deering

Undergraduate Honors Theses

Placing degree constraints on the vertices of a path allows the definitions of uphill and downhill paths. Specifically, we say that a path π = v₁, v₂,...v_k+1 is a downhill path if for every i, 1 ≤ i ≤ k, deg(v_i) ≥ deg(v_i+1). Conversely, a path π = u₁, u₂,...u_k+1 is an uphill path if for every i, 1 ≤ i ≤ k, deg(u_i) ≤ deg(u_i+1). We investigate graphical parameters related to downhill and …

Particle Dynamics And Resistivity Characteristics In Bifurcated Current Sheets, Tushar Andriyas

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Charged particle chaos and its collective effects in different magnetic geometries are investigated in a sequence of various numerical experiments. The fields generated by the particles as a result of interaction with the background electric and magnetic fields is not accounted for in the simulation. An X-line is first used to describe the geometry of the magnetotail prior to magnetic reconnection and a study of the behavior of charged particles is done from a microscopic viewpoint. Another important geometry in the magnetotail prior to substorm onset is Bifurcated Current Sheet. The same analysis is done for this configuration. The existence …

Asian Carp Could Help Us Solve Hunger Problem, Michael (Dung) Tran

Collection of Engaged Learning

Bighead carp and silver carp (Invader Species – Asian Carp) invaded the Illinois River waterway over a decade ago. Populations of these fishes have apparently grown dense in the lower and middle Illinois Rivers and both species are approaching the Chicago Area Waterway System (CAWS) and potentially making their way into Great Lakes. So far, positive DNA of Asian Carp has been found beyond the defensive electrical barrier, which means they have made their way to Great Lakes somehow. Asian Carp are fast growing, aggressive, and adaptable fish that are outcompeting native fish species for food and habitat in much …

Several Problems Concerning Multivariate Functions And Associated Operators, Kelly Ann Bickel

All Theses and Dissertations (ETDs)

This dissertation examines two distinct problems about multivariate functions and their associated operators. It first discusses the structure of Agler decompositions, which give useful ways to represent two-variable Schur functions on the bidisk using positive kernels. An elementary proof of the existence of Agler decompositions is provided, which uses special shift-invariant subspaces of the Hardy space. These shift-invariant subspaces are specific cases of Hilbert spaces that can be defined from Agler decompositions and their properties are analyzed. More specific results are obtained for certain classes of polynomials and rational inner functions.

Secondly, this dissertation examines differentiation of matrix-valued functions. Specifically, …

Image Processing Algorithms For Improving Planetary Exploration And Understanding, Ali Pouryazdanpanah

College of Engineering: Graduate Celebration Programs

• To design a fully automated tool-set that allows to detect and extract the sky region in planetary images.

• To develop the new method for rock segmentation in planetary stereo images.
• To develop the new method for shadow detection in planetary images

Mono-Sized Sphere Packing Algorithm Development Using Optimized Monte Carlo Technique, Karn Soontrapa, Yitung Chen

College of Engineering: Graduate Celebration Programs

In this research, fuel cell catalyst layer was developed using the optimized sphere packing algorithm. An optimization technique named adaptive random search technique (ARSET) was employed in this packing algorithm. The ARSET algorithm will generate the initial location of spheres and allow them to move in the random direction with the variable moving distance, randomly selected from the sampling range (a), based on the Lennard–Jones potential and Morse potential of the current and new configuration. The solid fraction values obtained from this developed algorithm are in the range of 0.610–0.624 while the actual processing time can significantly be reduced by …

Applied Analysis Of Ionic Polymer Metal-Composite Actuators, Siul Ruiz, Benjamin Mead, Woosoon Yim

College of Engineering: Graduate Celebration Programs

• IPMC is a type of smart material called an electroactive polymer
• Consists of an ionic polymer such as Nafion or Flemion and a conducive metal such as platinum or gold
• COMSOL multi-physics simulations accurately model the experimental displacement results
• Optimization performed using the multi-physics model to find the maximum deflection, force, and twisting
• Using the closed loop control system accurate IPMC tip location can be achieved
• This control system has been extended to function using a computer mouse as an input

Actual Vs. Perceived Value Of Players Of The National Basketball Association, Stephen Righini

Honors Projects in Mathematics

Over the past few decades the media has played an increasingly large role in shaping how player effectiveness in the National Basketball Association (NBA) is perceived. Several factors have caused fans, announcers, and even NBA team management to have unintentional bias toward certain players. This study aims to utilize various formulas created by NBA statisticians, called Player Raters, to identify how efficient each NBA player actually is in comparison to the rest of the league. Data from the past 12 seasons was compiled and six Player Raters were used to place values on every NBA player since the 2000-2001 season. …

Time Series Data Mining: A Retail Application Using Sas Enterprise Miner, Daniel Hebert

Honors Projects in Mathematics

Modern technologies have allowed for the amassment of data at a rate never encountered before. Organizations are now able to routinely collect and process massive volumes of data. A plethora of regularly collected information can be ordered using an appropriate time interval. The data would thus be developed into a time series. With such data, analytical techniques can be employed to collect information pertaining to historical trends and seasonality. Time series data mining methodology allows users to identify commonalities between sets of time-ordered data. This technique is supported by a variety of algorithms, notably dynamic time warping (DTW). This mathematical …

Limit Theorems For Random Billiard Models, Timothy Chumley

All Theses and Dissertations (ETDs)

The central objects of study in this dissertation are random billiard systems. These are Markov chain systems with general state spaces derived from deterministic billiard systems by selecting one or more dynamical variables and replacing them with random variables with fixed probability distributions. In particular, we study two specific model systems; one which models gas diffusion through cylindrical channels whose walls have a microscopic structure, and another which models a minimalistic heat engine. The main results for the gas diffusion model, a series of probabilistic limit theorems, allow us to express transport characteristics such as mean exit times of the …

Sorting Permutations With Finite-Depth Stacks, Timothy Goodrich, Will Olson, Ruyue Yuan

Symposium on Research and Creative Expression (SORCE)

Sorting organizes information for optimal usage, and our work examines the mathematics behind sorting with stacks. In 1968, Donald Knuth showed that a permutation is sortable in an infinite-depth stack if and only if it avoids the pattern 231; Knuth also enumerated these permutations. Twenty-five years later, Julian West extended these ideas to permutations sortable with 2 consecutive stacks. We continue this work by limiting the stack(s) to a finite depth. In particular, we completely characterize permutations sortable through a single finite-depth stack and derive a handy enumeration formula. We also apply our pattern characterization and enumeration techniques to permutations …

Simulation Modeling And Analysis Of Coal Shipping Operations, Raymond Finzel, Timothy Goodrich, Graeme Roberts

Symposium on Research and Creative Expression (SORCE)

Computer simulations are increasingly powerful and realistic models for complex real-world scenarios, and our project applies this technology to model a coal transportation case study. Given a baseline scenario of fourteen carriers transporting coal from three U.S. locations to four international locations, we optimize operations in terms of product flow, time required for shipments, and total operation costs. Implementing the case study's factors into modular code, we introduce several potential changes to current operations and develop specific scenarios. Further, in analyzing these scenarios we test for robustness and sensitivity, by changing values such as demand and bad weather occurrences, and …

Optimizing The Allocation Of Vaccines In The Presence Of Multiple Strains Of The Influenza Virus, Abby Kenyon, Ana Eveler, Tayler Grashel, Jessica Richardson

Symposium on Research and Creative Expression (SORCE)

During the annual flu season, multiple strains of the influenza virus are often present within a population. It is a significant challenge for health care administrators to determine the most effective allocation of two different vaccines to combat the various strains when treating the public. We employ a mathematical model, a system of differential equations, to find a strategy for vaccinating a population in order to minimize the number of infected individuals. We consider various strengths of transmission of the disease, availability of vaccine doses, vaccination rates, and other model parameters. This research may lead to more effective health care …

Investigating Prerequisite Grade Requirements In The Calculus Sequence, Michelle Kleckner, Lexi Paradine, Katie Merkling, Mindy Capaldi

Symposium on Research and Creative Expression (SORCE)

The Valparaiso University Mathematics and Computer Science Department has been debating a shift from a D- to a C- in the calculus sequence prerequisite grade requirement. We first researched policies at other colleges and universities. Next, we gathered data on students' self-predicted grades by distributing pre- and post-semester surveys and measuring the accuracy of the results in comparison to the actual grade data. Using the surveys, we also associated students' expectations with their majors. In the end, we investigated whether or not prerequisite grades can predict subsequent course performance. Statistical analysis of the past four years of math student data …

On The (Co)Homology Of Non-Commutative Toroidal Orbifold, Safdar Quddus

All Theses and Dissertations (ETDs)

Noncommutative torus algebra was studied in the early 80's as a fundamental example of noncommutative geometry. Connes calculated its cyclic and Hochschild cohomology. In this thesis, we study noncommutative toroidal orbifolds generated by actions of finite subgroups of S L(2,) on a noncommutative torus algebra.

In the first part, we calculate the Hochschild and cyclic homology of Γ for all finite subgroups Γ S L(2,). In the second part we analyse the cohomology of these algebras and compute the Chern-Connes pairing between the elements of and explicit cocycles discovered in our calculations. In the third part we discuss some …

A Perspective On Multiple Waves Of Influenza Pandemics, Anna Mummert, Howard Weiss, Li-Pong Long, Jose´ M. Amigo´, Xiu-Feng Wan

Mathematics Faculty Research

Background: A striking characteristic of the past four influenza pandemic outbreaks in the United States has been the multiple waves of infections. However, the mechanisms responsible for the multiple waves of influenza or other acute infectious diseases are uncertain. Understanding these mechanisms could provide knowledge for health authorities to develop and implement prevention and control strategies. Materials and Methods: We exhibit five distinct mechanisms, each of which can generate two waves of infections for an acute infectious disease. The first two mechanisms capture changes in virus transmissibility and behavioral changes. The third mechanism involves population heterogeneity (e.g., demography, geography), where …