Applied Mathematics Commons^™

Simulations And Queueing Theory: The Effects Of Randomly Bypassing Security, Emily Ortmann

Masters Theses & Doctoral Dissertations

We discuss queueing theory in the setting of airport security and customs. By developing queueing simulations based on mathematical models, we explore a variety of questions related to optimal queue design with respect to efficiency, feasibility, priority, and other prescribed/variable constraints.

Simulations And Queueing Theory: The Effects Of Priority And Vip Thresholds, Laura Schuck

Masters Theses & Doctoral Dissertations

Everyone has experienced waiting in lines, whether it is at the airport, the grocery store, or somewhere in-between. By developing queueing simulations based on mathematical models of airport security and customs, we explore a variety of questions related to optimal queue design with respect to efficiency, feasibility, priority, and other prescribed/variable constraints.

Swelling As A Stabilizing Mechanism During Ion Bombardment Of Thin Films: An Analytical And Numerical Study, Jennifer M. Swenson

Mathematics Theses and Dissertations

Irradiation of semiconductor surfaces often leads to the spontaneous formation of rippled structures at certain irradiation angles. However, at high enough energies, these structures are observed to vanish for all angles, despite the absence of any identified, universally-stabilizing physical mechanisms in operation. Here, we examine the effect on pattern formation of radiation-induced swelling, which has been excluded from prior treatments of stress in irradiated films. After developing a suitable continuum model, we perform a linear stability analysis to determine its effect on stability. Under appropriate simplifying assumptions, we find swelling indeed to be stabilizing at wavenumbers typical of experimental observations. …

Lozenge Tilings Of A Halved Hexagon With An Array Of Triangles Removed From The Boundary, Tri Lai

Department of Mathematics: Faculty Publications

Proctor's work on staircase plane partitions yields an enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi recently extended this tiling enumeration to a halved hexagon with a triangle removed from the boundary. In this paper, we prove a generalization of the results of Proctor and Rohatgi by enumerating lozenge tilings of a halved hexagon in which an array of an arbitrary number of adjacent triangles has been removed from the boundary.

Pricing Asian Options: Volatility Forecasting As A Source Of Downside Risk, Adam T. Diehl

Undergraduate Economic Review

Asian options are a class of derivative securities whose payoffs average movements in the underlying asset as a means of hedging exposure to unexpected market behavior. We find that despite their volatility smoothing properties, the price of an Asian option is sensitive to the choice of volatility model employed to price them from market data. We estimate the errors induced by two common schemes of forecasting volatility and their potential impact upon trading.

General Stochastic Integral And Itô Formula With Application To Stochastic Differential Equations And Mathematical Finance, Jiayu Zhai

LSU Doctoral Dissertations

A general stochastic integration theory for adapted and instantly independent stochastic processes arises when we consider anticipative stochastic differential equations. In Part I of this thesis, we conduct a deeper research on the general stochastic integral introduced by W. Ayed and H.-H. Kuo in 2008. We provide a rigorous mathematical framework for the integral in Chapter 2, and prove that the integral is well-defined. Then a general Itô formula is given. In Chapter 3, we present an intrinsic property, near-martingale property, of the general stochastic integral, and Doob-Meyer's decomposition for near-submartigales. We apply the new stochastic integration theory to several …

Improving Annual Fixed Wing Maintenance Cost Estimates Through Cost Estimating Relationships, Kirsten Bunecke

Theses and Dissertations

The Air Force executes its mission primarily through the use of fixed-wing aircrafts. Maintaining these aircrafts represents approximately one-third of annual Operating and Support costs; which in turn, make up the majority of Life Cycle Costs. The current approach to estimating aircraft maintenance costs does not take into consideration programmatic data available in the Air Force Total Ownership Cost (AFTOC) database. The four maintenance cost subcategories researched in this thesis are Consumable Materials and Repair Parts, Depot Level Repairables (DLRs), Depot Maintenance, and Contractor Logistic Support. Each of these cost categories must first be standardized to be able to compare …

Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng

Theses and Dissertations

Solutions to the one-dimensional and two-dimensional nonlinear Schrodinger (NLS) equation are obtained numerically using methods based on radial basis functions (RBFs). Periodic boundary conditions are enforced with a non-periodic initial condition over varying domain sizes. The spatial structure of the solutions is represented using RBFs while several explicit and implicit iterative methods for solving ordinary differential equations (ODEs) are used in temporal discretization for the approximate solutions to the NLS equation. Splitting schemes, integration factors and hyperviscosity are used to stabilize the time-stepping schemes and are compared with one another in terms of computational efficiency and accuracy. This thesis shows …

Analysis Of Temperature And Humidity Effects On Horizontal Photovoltaic Panels, Corey J. Booker

Theses and Dissertations

The United States Air Force seeks to address power grid vulnerability and bolster energy resilience through the use of renewable energy sources. Air Force Institute of Technology engineers designed and manufactured control systems to monitor power production from the most widely-used silicon-based solar cells at 38 testing locations around the globe spanning the majority of climate types. Researchers conducted multivariate regression analysis to establish a statistical relationship between photovoltaic power output, ambient temperature, and humidity pertaining to monocrystalline and polycrystalline photovoltaic panels. Formulated models first characterized power output globally, then by specific climate type with general inaccuracy. Location-specific models are …

An Analysis Of The Estimate At Complete For Department Of Defense Contracts, Deborah B. Kim

Theses and Dissertations

When contractors provide timely and reliable information on the status of a contract, both contractors and government program offices can provide an accurate estimate of a contract’s completion costs. This research shows that the cumulative cost performance indices provided by contractors and program offices are high and less accurate than those of previous years and/or that a significant amount of ACWP is being documented in the final portion of a contract. The high performance indices resulted in EACs that were low-balled during the majority of a contract’s life which shows a need to improve the use of EVM metrics for …

Lightning Prediction Using Artificial Neural Networks And Electric Field Mill Data, Daniel E. Hill

Theses and Dissertations

Electric Field Mills (EFMs) located in the region surrounding Cape Canaveral record the electrification of the atmosphere near them. Research studying how these sensors could improve lightning warnings has had mixed results. This paper used a Convolutional Recurrent Neural Network (CRNN) and data from 30 EFMs from May-July of 2012-2016. The mean was calculated for every 60 second period and 30 minutes of this summarized data was used to create a lightning prediction with a warning period of 15 minutes. This method achieved a True Positive Rate (TPR) of 77.6%, a False Positive Rate (FPR) of 8.3%, a False Discovery …

Modeling Multimodal Failure Effects Of Complex Systems Using Polyweibull Distribution, Daniel A. Timme

Theses and Dissertations

The Department of Defense (DoD) enlists multiple complex systems across each of their departments. Between the aging systems going through an overhaul and emerging new systems, quality assurance to complete the mission and secure the nation‘s objectives is an absolute necessity. The U.S. Air Force‘s increased interest in Remotely Piloted Aircraft (RPA) and the Space Warfighting domain are current examples of complex systems that must maintain high reliability and sustainability in order to complete missions moving forward. DoD systems continue to grow in complexity with an increasing number of components and parts in more complex arrangements. Bathtub-shaped hazard functions arise …

Analysis Of A Medical Center's Cardiac Risk Screening Protocol Using Propensity Score Matching, Jake E. Johnson

Theses and Dissertations

Researchers at the University of Maryland Medical Center in Baltimore have developed a cardiac risk stratification protocol in the hopes of reducing the time-from arrival-to-first-operation for geriatric orthopedic patients. They collected observational data for two years prior to and following the October 2014 implementation of the new screening protocol. Therefore, advanced analytical techniques are required to isolate the treatment effect of the new screening protocol. Propensity score matching (PSM) is used to handle the observational data in order to reduce the bias attributable to the confounding covariates. In addition to PSM, various regression techniques are used to help the researchers …

Lie Sphere Geometry And Dupin Hypersurfaces, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

These notes were originally written for a short course held at the Institute of Mathematics and Statistics, University of São Paulo, S.P. Brazil, January 9–20, 2012. The notes are based on the author’s book [17], Lie Sphere Geometry With Applications to Submanifolds, Second Edition, published in 2008, and many passages are taken directly from that book. The notes have been updated from their original version to include some recent developments in the field.

A hypersurface Mⁿ⁻¹ in Euclidean space Rⁿ is proper Dupin if the number of distinct principal curvatures is constant on M^{n−1 …}

Spacetime Numerical Techniques For The Wave And Schrödinger Equations, Paulina Ester Sepùlveda Salas

Dissertations and Theses

The most common tool for solving spacetime problems using finite elements is based on semidiscretization: discretizing in space by a finite element method and then advancing in time by a numerical scheme. Contrary to this standard procedure, in this dissertation we consider formulations where time is another coordinate of the domain. Therefore, spacetime problems can be studied as boundary value problems, where initial conditions are considered as part of the spacetime boundary conditions.

When seeking solutions to these problems, it is natural to ask what are the correct spaces of functions to choose, to obtain wellposedness. This motivates the study …

Real Solution Of Dae And Pdae System, Zahra Mohammadi, Greg Reid

Western Research Forum

General systems of differential equations don't have restrictions on the number or type of equations. For example, they can be over or under-determined, and also contain algebraic constraints (e.g. algebraic equations such as in Differential-Algebraic equations (DAE) and Partial differential algebraic equations (PDAE). Increasingly such general systems arise from mathematical modeling of engineering and science problems such as in multibody mechanics, electrical circuit design, optimal control, chemical kinetics and chemical control systems. In most applications, only real solutions are of interest, rather than complex-valued solutions. Much progress has been made in exact differential elimination methods, which enable characterization of all …

Asymptotic Estimate Of Variance With Applications To Stochastic Differential Equations Arises In Mathematical Neuroscience, Mahbubur Rahman 6203748

Showcase of Faculty Scholarly & Creative Activity

Approximation of stochastic differential equations (SDEs) with parametric noise plays an important role in a range of application areas, including engineering, mechanics, epidemiology, and neuroscience. A complete understanding of SDE theory with perturbed noise requires familiarity with advanced probability and stochastic processes. In this paper, we derive an asymptotic estimate of variance, and it is shown that numerical method gives a useful step toward solving SDEs with perturbed noise. Our goal is to diffuse the results to an audience not entirely familiar with functional notations or semi-group theory, but who might nonetheless be interested in the practical simulation of dynamical …

Stability Of Solitary And Cnoidal Traveling Wave Solutions For A Fifth Order Korteweg-De Vries Equation, Ronald Adams, S.C. Mancas

Publications

We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains of cnoidal waves for nonzero boundary conditions are analyzed using stability theorems, which rely on the positivity properties of the Fourier transforms. We show that all families of solutions considered here are (orbitally) stable.

Essentials Of Structural Equation Modeling, Mustafa Emre Civelek

Zea E-Books Collection

Structural Equation Modeling is a statistical method increasingly used in scientific studies in the fields of Social Sciences. It is currently a preferred analysis method, especially in doctoral dissertations and academic researches. However, since many universities do not include this method in the curriculum of undergraduate and graduate courses, students and scholars try to solve the problems they encounter by using various books and internet resources.

This book aims to guide the researcher who wants to use this method in a way that is free from math expressions. It teaches the steps of a research program using structured equality modeling …

Short-Time Expansions For Call Options On Leveraged Etfs Under Exponential Lévy Models With Local Volatility, José E. Figueroa-López, Ruoting Gong, Matthew Lorig

Mathematics Faculty Research

In this article, we consider the small-time asymptotics of options on a leveraged exchange-traded fund (LETF) when the underlying exchange-traded fund (ETF) exhibits both local volatility and jumps of either finite or infinite activity. We show that leverage modifies the drift, volatility, jump intensity, and jump distribution of a LETF in addition to inducing the possibility of default, even when the underlying ETF price remains strictly positive. Our main results are closed-form expressions for the leading-order terms of off-the-money European call and put LETF option prices near expiration, with explicit error bounds. These results show that the price of an …

P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing

Honors Scholars & Undergraduate Research Poster Symposium Programs

Rising sea surface temperatures (SSTs) in the Pacific Northwest lead to food resource reductions for surface-feeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egg-laying synchrony in the colony. We study the long-term effects of climate change on population dynamics and survival by considering a simplified, cross-season model that incorporates both of these behaviors in addition to density-dependent and environmental effects. We show that cannibalism can lead to backward bifurcations and strong Allee effects, allowing the population to survive at lower resource levels than would be possible otherwise.

Mathemagics, Arthur Benjamin

Dalrymple Lecture Series

Dr. Arthur Benjamin is the Smallwood Family Professor of Mathematics at Harvey Mudd College in Claremont, California. He is also a professional magician, and in his entertaining and fast-paced performance, Dr. Benjamin will demonstrate how to mentally add and multiply numbers faster than a calculator, how to figure out the day of the week of any date in history, and other amazing feats of mind.

Quasi-Static Nonlinear Analysis Of A Celestial Icosahedron Shaped Vacuum Lighter Than Air Vehicle, Kyle D. Moore

Theses and Dissertations

Due to the many drawbacks associated with a traditional lighter than air vehicle (LTAV), there is a desire for a LTAV which generates lift from an internal vacuum. To date, two feasible designs (the icosahedron and the hexakis icosahedron) for this so called vacuum lighter than air vehicle (VLTAV) have been studied at the Air Force Institute of Technology (AFIT). This research looks to show the feasibility of a new design for a VLTAV, the celestial icosahedron. This research includes a boundary condition study which proves the symmetric nature of the celestial icosahedron's frame with laterally constrained and unconstrained vertices. …

Numerical Simulation Of Energy Localization In Dynamic Materials, Arkadi Berezovski, Mihhail Berezovski

Publications

Dynamic materials are artificially constructed in such a way that they may vary their characteristic properties in space or in time, or both, by an appropriate arrangement or control. These controlled changes in time can be provided by the application of an external (non-mechanical) field, or through a phase transition. In principle, all materials change their properties with time, but very slowly and smoothly. Changes in properties of dynamic materials should be realized in a short or quasi-nil time lapse and over a sufficiently large material region. Wave propagation is a characteristic feature for dynamic materials because it is also …

Screening Algorithm Based On The Color Halftone Fluorescent Printing And Its Application In Packaging Design, Hu Yaojian, Liu Juan, Wang Ruojing, Zhong Yunfei

Journal of Applied Packaging Research

Abstract：This paper analyzed the characteristics of colorless fluorescent ink and the existing color separation theory, so that colored additive method should be used in printing color pattern with colorless fluorescent ink as well as three-color screening separation type (red, green and blue). Considering the exhibition of the tone, this paper selected dot parallel screening method. At the same time, through comparing the properties of different dots, this paper adopted a special method of AM screening, using regular triangle as the basic dot model to a threshold matrix of AM screening. Finally, designing a screening algorithm which best suit the …

Indicators For Early Assessment Of Palliative Care In Lung Cancer Patients: A Population Study Using Linked Health Data, Maria Kelly, Katie M. O'Brien, Michael Lucey, Kerri Clough-Gorr, Ailish Hannigan

Department of Mathematics Publications

Analysing linked, routinely collected data may be useful to identify characteristics of patients with suspected lung cancer who could benefit from early assessment for palliative care. The aim of this study was to compare characteristics of newly diagnosed lung cancer patients dying within 30 days of diagnosis (short term survivors) with those surviving more than 30 days. To identify indicators for early palliative care assessment we distinguished between characteristics available at diagnosis (age, gender, smoking status, marital status, comorbid disease, admission type, tumour stage and histology) from those available post diagnosis. A second aim was to examine the association between …

Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, Q. Zhong, Demetrios N. Christodoulides, M. Khajavikhan, K. G. Makris, Ramy El-Ganainy

Department of Physics Publications

We investigate the extreme dynamics of non-Hermitian systems near higher-order exceptional points in photonic networks constructed using the bosonic algebra method. We show that strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. By using complementary numerical and analytical approaches, we show that, in the parity-time (PT) phase near exceptional points, the logarithm of the maximum optical power amplification scales linearly with the order of the exceptional point. We focus in our discussion on photonic systems, but we note that our results apply to other …

Examples Of Finite Free Complexes Of Small Rank And Small Homology, Srikanth B. Iyengar, Mark E. Walker

Department of Mathematics: Faculty Publications

In this paper we construct counterexamples to five related conjectures concerning the rank an homology of finite free complexes over commuatitive noetherian rings, and, in particular, over group algebras of elementary abelian groups.

Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier

Electronic Theses and Dissertations

Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …

Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper studies the migration of double imaginary roots of the systems’ characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right halfplane, and the other moves to the left half-plane. When the parameters move into the …