Applied Mathematics Commons^™

Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle

Masters Theses & Specialist Projects

The Bernoulli distribution is a basic, well-studied distribution in probability. In this thesis, we will consider repeated Bernoulli trials in order to study runs of identical outcomes. More formally, for t ∈ N, we let Xt ∼ Bernoulli(p), where p is the probability of success, q = 1 − p is the probability of failure, and all Xt are independent. Then Xt gives the outcome of the tth trial, which is 1 for success or 0 for failure. For n, m ∈ N, we define Tn to be the number of trials needed to first observe n …

Controllability And Observability Of The Discrete Fractional Linear State-Space Model, Duc M. Nguyen

Masters Theses & Specialist Projects

This thesis aims to investigate the controllability and observability of the discrete fractional linear time-invariant state-space model. First, we will establish key concepts and properties which are the tools necessary for our task. In the third chapter, we will discuss the discrete state-space model and set up the criteria for these two properties. Then, in the fourth chapter, we will attempt to apply these criteria to the discrete fractional model. The general flow of our objectives is as follows: we start with the first-order linear difference equation, move on to the discrete system, then the fractional difference equation, and finally …

A Mathematical Analysis Of The Game Of Chess, John C. White

Selected Honors Theses

This paper analyzes chess through the lens of mathematics. Chess is a complex yet easy to understand game. Can mathematics be used to perfect a player’s skills? The work of Ernst Zermelo shows that one player should be able to force a win or force a draw. The work of Shannon and Hardy demonstrates the complexities of the game. Combinatorics, probability, and some chess puzzles are used to better understand the game. A computer program is used to test a hypothesis regarding chess strategy. Through the use of this program, we see that it is detrimental to be the first …

Near-Optimal Control Of Switched Systems With Continuous-Time Dynamics Using Approximate Dynamic Programming, Tohid Sardarmehni

Mechanical Engineering Research Theses and Dissertations

Optimal control is a control method which provides inputs that minimize a performance index subject to state or input constraints [58]. The existing solutions for finding the exact optimal control solution such as Pontryagin’s minimum principle and dynamic programming suffer from curse of dimensionality in high order dynamical systems. One remedy for this problem is finding near optimal solution instead of the exact optimal solution to avoid curse of dimensionality [31]. A method for finding the approximate optimal solution is through Approximate Dynamic Programming (ADP) methods which are discussed in the subsequent chapters.

In this dissertation, optimal switching in switched …

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.

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 …

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 …}

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 …

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.

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 …

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, …

Ns-Cross Entropy-Based Magdm Under Single-Valued Neutrosophic Set Environment, Florentin Smarandache, Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy

Branch Mathematics and Statistics Faculty and Staff Publications

A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties. Also we define weighted NS-cross entropy measure and investigate its basic properties. We develop a novel multi-attribute group decision-making (MAGDM) strategy that is free from the drawback of asymmetrical behavior and undefined phenomena. It is …

Summary Of The Special Issue “Neutrosophic Information Theory And Applications” At “Information” Journal, Florentin Smarandache, Jun Ye

Branch Mathematics and Statistics Faculty and Staff Publications

Over a period of seven months (August 2017–February 2018), the Special Issue dedicated to “Neutrosophic Information Theory and Applications” by the “Information” journal (ISSN 2078-2489), located in Basel, Switzerland, was a success. The Guest Editors, Prof. Dr. Florentin Smarandache from the University of New Mexico (USA) and Prof. Dr. Jun Ye from the Shaoxing University (China), were happy to select—helped by a team of neutrosophic reviewers from around the world, and by the “Information” journal editors themselves—and publish twelve important neutrosophic papers, authored by 27 authors and coauthors. There were a variety of neutrosophic topics studied and used by the …

Neutrosophic Soft Rough Graphs With Application, Florentin Smarandache, Muhammad Akram, Hafsa M. Malik, Sundas Shahzadi

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In …

Nn-Harmonic Mean Aggregation Operators-Based Mcgdm Strategy In A Neutrosophic Number Environment, Florentin Smarandache, Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri

Branch Mathematics and Statistics Faculty and Staff Publications

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and …

Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood

Journal of Humanistic Mathematics

In Andy Weir’s novel The Martian, the characters encounter high-stakes, life-or-death situations, in which they must make choices based on their assessment of risk and likely outcomes. They have different reactions to risky situations, based on their approaches to assessing risk and their perspectives on the stakes involved. In this paper, we examine the ways that characters in The Martian intuitively assess risk and compare them to mathematical analysis of the situations in the book.

Theoretical Open-Loop Model Of Respiratory Mechanics In The Extremely Preterm Infant, Laura Ellwein Fix, Joseph Khoury, Russell R. Moores Jr., Lauren Linkous, Matthew Brandes, Henry J. Rozycki

Mathematics and Applied Mathematics Publications

Non-invasive ventilation is increasingly used for respiratory support in preterm infants, and is associated with a lower risk of chronic lung disease. However, this mode is often not successful in the extremely preterm infant in part due to their markedly increased chest wall compliance that does not provide enough structure against which the forces of inhalation can generate sufficient pressure. To address the continued challenge of studying treatments in this fragile population, we developed a nonlinear lumped-parameter respiratory system mechanics model of the extremely preterm infant that incorporates nonlinear lung and chest wall compliances and lung volume parameters tuned to …

Examples Of The Birkhoff Theorem And Its Generalizations, Charles G. Torre

Tutorials on... in 1 hour or less

In this worksheet I demonstrate three versions of Birkhoff's theorem, which is a characterization of spherically symmetric solutions of the Einstein equations. The three versions considered here correspond to taking the "Einstein equations" to be: (1) the vacuum Einstein equations; (2) the Einstein equations with a cosmological constant (3) the Einstein-Maxwell equations. I will restrict my attention to 4-dimensional spacetimes.

How To Make Tetrads, Charles G. Torre

How to... in 10 minutes or less

This is a worksheet which demonstrates tools for creating orthonormal and null tetrads for a given spacetime.

Symmetric Criticality In General Relativity, Charles G. Torre

Research Vignettes

In this worksheet I explore the local Lagrangian version of the Principle of Symmetric Criticality (PSC) due to Anderson, Fels, and Torre], which asserts the commutativity of the processes (i) of symmetry reduction (for finding group-invariant fields) and (ii) forming Euler-Lagrange equations. There are two obstructions to PSC, which I will call the Lie algebra obstruction and the isotropy obstruction. In this worksheet I will illustrate these obstructions in the General Theory of Relativity.

Existing And Regularity Of Minimizers For Nonlocal Energy Functionals, Mikil D. Foss, Petronela Radu, Cory Wright

Department of Mathematics: Faculty Publications

In this paper, we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics [19] or nonlocal diffusion models [1]. We derive nonlocal versions of the Euler-Lagrange equations under two sets of growth assumptions for the integrand. Existence of minimizers is shown for integrands with joint convexity (in the function and nonlocal gradient components). By using the convolution structure, we show regularity of solutions for certain Euler-Lagrange equations. No growth assumptions are needed for the existence and regularity of minimizers results, in contrast with the classical theory.

Switching Diffusion Systems With Past-Dependent Switching Having A Countable State Space, Hai Dang Nguyen

Wayne State University Dissertations

Emerging and existing applications in wireless communications, queueing networks, biological models, financial engineering, and social networks demand the

mathematical modeling and analysis of hybrid models in which continuous dynamics and discrete events coexist.

Assuming that the systems are in continuous times,

stemming from stochastic-differential-equation-based models and random discrete events,

switching diffusions come into being. In such systems, continuous states and discrete events

(discrete states)

coexist and interact.

A switching diffusion is a two-component process $(X(t),\alpha(t))$, a continuous component and a discrete component taking values in a discrete set (a set consisting of isolated points).

When the discrete component takes a …

Optimal Supply Delivery Under Military Specific Constraints, Talena Fletcher

College of Graduate Studies: Theses & Dissertations

Through-out military history, the need to safely and effectively allocate resources to various military operations was a task of extreme importance. Satisfying the needs of multiple consumers by optimally pairing with appropriate suppliers falls into the category of vehicle routing problems (VRP), which has been intensively studied over the years. In general, finding the optimal solution to VRP is known to be NP-hard. The proposed solutions rely on mathematical programming and the size of the problems that can be optimally solved is typically limited. In military settings, balancing the needs of multiple consumers with the current operational environment has always …

Direct Immunoassays And Their Performance: Theoretical Modelling Of The Effects Of Antibody Orientation And Associated Kinetics, Dana Mackey, Eilis Kelly, Robert Nooney, Richard O'Kennedy

Articles

The orientation and activity of antibodies immobilized on solid surfaces are of direct relevance to many immunosensing applications. We therefore investigate a mathematical model which estimates the fraction of antibodies which are available for reaction in a randomly adsorbed sample. Numerical simulations are presented which highlight the separate effects of antibody orientation, accessibility and loss of binding ability on the amount of captured antigen. The assay response can then be expressed as a function of total antibody density and used for optimizing the surface coverage strategy under various conditions.

Diagnostic Effects Of An Early Mastery Activity In College Algebra And Precalculus, Nathan Wakefield, Joe Champion, Jessalyn Bolkema, Douglas Dailey

Department of Mathematics: Faculty Publications

The purpose of this study was to investigate implementation of an early intervention mastery activity during the first two weeks of college algebra and precalculus courses at a large U.S. public university. Statistical modeling of (N = 935) students’ performance in the courses, including a logistic regression model of pass/fail course achievement with students’ high school rank, ACT Mathematics scores, and performance on the intervention as explanatory variables, suggested significant independent differences in course performance across performance levels on the early mastery activity. An evaluation of diagnostic validity for the model yielded a 19% false negative rate (predicted to …

Numerical Simulation For A Rising Bubble Interacting With A Solid Wall: Impact, Bounce, And Thin Film Dynamics, Changjuan Zhang, Jie Li, Li-Shi Luo, Tiezheng Qian

Mathematics & Statistics Faculty Publications

Using an arbitrary Lagrangian-Eulerian method on an adaptive moving unstructured mesh, we carry out numerical simulations for a rising bubble interacting with a solid wall. Driven by the buoyancy force, the axisymmetric bubble rises in a viscous liquid toward a horizontal wall, with impact on and possible bounce from the wall. First, our simulation is quantitatively validated through a detailed comparison between numerical results and experimental data. We then investigate the bubble dynamics which exhibits four different behaviors depending on the competition among the inertial, viscous, gravitational, and capillary forces. A phase diagram for bubble dynamics has been produced using …

Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell

Theses and Dissertations--Mathematics

In this dissertation, we first provide a short introduction to qualitative homogenization of elliptic equations and systems. We collect relevant and known results regarding elliptic equations and systems with rapidly oscillating, periodic coefficients, which is the classical setting in homogenization of elliptic equations and systems. We extend several classical results to the so called case of perforated domains and consider materials reinforced with soft inclusions. We establish quantitative H¹-convergence rates in both settings, and as a result deduce large-scale Lipschitz estimates and Liouville-type estimates for solutions to elliptic systems with rapidly oscillating periodic bounded and measurable coefficients. Finally, …

Concavity In Fractional Calculus, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

No abstract provided.