Mathematics Commons^™

Oscillation Criteria For Third-Order Functional Differential Equations With Damping, Martin Bohner, Said R. Grace, Irena Jadlovska

Mathematics and Statistics Faculty Research & Creative Works

This paper is a continuation of the recent study by Bohner et al [9] on oscillation properties of nonlinear third order functional differential equation under the assumption that the second order differential equation is nonoscillatory. We consider both the delayed and advanced case of the studied equation. The presented results correct and extend earlier ones. Several illustrative examples are included.

Connecting Models Of Configuration Spaces: From Double Loops To Strings, Jason M. Lucas

Open Access Dissertations

Foundational to the subject of operad theory is the notion of an En operad, that is, an operad that is quasi-isomorphic to the operad of little n-cubes Cn. They are central to the study of iterated loop spaces, and the specific case of n = 2 is key in the solution of the Deligne Conjecture. In this paper we examine the connection between two E 2 operads, namely the little 2-cubes operad C 2 itself and the operad of spineless cacti. To this end, we construct a new suboperad of C2, which we name the operad of tethered …

Size Variables In Audit Fee Models: An Examination Of The Effects Of Alternative Mathematical Transformations, Charles Cullinan, Hui Du, Xiaochuan Zheng

Accounting Department Faculty Journal Articles

We consider the mathematical transformations used for assets of different valuation complexity in audit fee models. These mathematical transformations (such as logs and square roots) relate to the non-linear relationship between client size and audit fees. We use closed-end mutual fund audits to examine this question because virtually all fund assets are reported at fair value. We find that more complexly valued assets are less likely to follow the traditional log transformation because the presence of these assets has a stronger relationship with audit fees that is not fully captured by the coefficient on the logged variable alone. The significance …

An Update On A Few Permanent Conjectures, Fuzhen Zhang

Mathematics Faculty Articles

We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We also raise a few new questions for future study. (†conjectures have been recently settled negatively.)

Reproductive Numbers For Periodic Epidemic Systems, Christopher David Mitchell

Mathematics Dissertations - Archive

When using mathematics to study epidemics, often times the goal is to deter- mine when an infection can invade and persist within a population. This can be done in a variety of ways but the most common is to use threshold quantities called reproductive numbers. For models with only one infection, the basic reproductive number (BRN) is used to determine the stability of the disease-free equilibrium. For many years this was done solely for autonomous systems; however, many diseases exhibit seasonal behavior. If this seasonality is incorporated into models, it gives nonautonomous systems, which while more accurate in their description, …

Numerical Construction Of Diffeomorphism And The Applications To Grid Generation And Image Registration, Xi Chen

Mathematics Dissertations - Archive

Diffeomorphism is an active research topic in differential geometry. In this area, the existence and construction of diffeomorphism under certain constraints is an interesting and meaningful task. J. Moser first proved the existence of diffeomorphism under a Jacobian determinant constraint. Later, Dr. Liao along with his co-authors, proposed the deformation method to construct diffeomorphisms. A div-curl system is created in the construction of diffeomorphisms. Since the Jacobian determinant has a direct physical meaning in grid generation, i.e. the grid cell size, the deformation method was applied successfully to grid generation and adaptation problems. In this dissertation, we review the deformation …

Editorial, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Tme Volume 13, Number 3

The Mathematics Enthusiast

No abstract provided.

The Secret Life Of 1/N: A Journey Far Beyond The Decimal Point, Christopher Lyons

The Mathematics Enthusiast

The decimal expansions of the numbers 1/n (such as 1/3 = .03333..., 1/7 = 0.142857...) are most often viewed as tools for approximating quantities to a desired degree of accuracy. The aim of this exposition is to show how these modest expressions in fact have much more to offer, particularly in the case when the expansions are infinitely long. First we discuss how simply asking about the period (that is, the length of the repeating sequence of digits) of the decimal expansion of 1/n naturally leads to more sophisticated ideas from elementary number theory, as well as to …

The History Of Algorithmic Complexity, Audrey A. Nasar

The Mathematics Enthusiast

This paper provides a historical account of the development of algorithmic complexity in a form that is suitable to instructors of mathematics at the high school or undergraduate level. The study of algorithmic complexity, despite being deeply rooted in mathematics, is usually restricted to the computer science curriculum. By providing a historical account of algorithmic complexity through a mathematical lens, this paper aims to equip mathematics educators with the necessary background and framework for incorporating the analysis of algorithmic complexity into mathematics courses as early on as algebra or pre-calculus.

Integral Of Radical Trigonometric Functions Revisited, Natanael Karjanto, Binur Yermukanova

The Mathematics Enthusiast

This article revisits an integral of radical trigonometric functions. It presents several methods of integration where the integrand takes the form 1+/- sin x or 1+/- cos x. The integral has applications in Calculus where it appears as the length of cardioid represented in polar coordinates.

Mathematical Problem-Solving Via Wallas’ Four Stages Of Creativity: Implications For The Undergraduate Classroom, Milos Savic

The Mathematics Enthusiast

The central theme in this article is that certain problem-solving frameworks (e.g., Polya, 1957; Carlson & Bloom, 2005) can be viewed within Wallas’ four stages of mathematical creativity. The author attempts to justify the previous claim by breaking down each of Wallas’ four components (preparation, incubation, illumination, verification) using both mathematical creativity and problem-solving/proving literature. Since creativity seems to be important in mathematics at the undergraduate level (Schumacher & Siegel, 2015), the author then outlines three observations about the lack of fostering mathematical creativity in the classroom. Finally, conclusions and future research are discussed, with emphasis on using technological advances …

Plato On The Foundations Of Modern Theorem Provers, Ines Hipolito

The Mathematics Enthusiast

Is it possible to achieve such a proof that is independent of both acts and dispositions of the human mind? Plato is one of the great contributors to the foundations of mathematics. He discussed, 2400 years ago, the importance of clear and precise definitions as fundamental entities in mathematics, independent of the human mind. In the seventh book of his masterpiece, The Republic, Plato states “arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument” (525c). In the light of this …

Is There A Symmetric Version Of Hindman's Theorem?, Ethan Akin, Eli Glasner

Mathematics and Statistics Faculty Research & Creative Works

We show that there does not exist a symmetric version of Hindman's Theorem, or more explicitly, that the property of containing a symmetric IP-set is not divisible. We consider several related dynamics questions.

Ε-Kernel Coresets For Stochastic Points, Haitao Wang, Lingxiao Huang, Jian Li, Jeff Mark Phillips

Computer Science Faculty and Staff Publications

With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over such data. In this paper, we initiate the study of constructing epsilon-kernel coresets for uncertain points. We consider uncertainty in the existential model where each point's location is fixed but only occurs with a certain probability, and the locational model where each point has a probability distribution describing its location. An epsilon-kernel coreset approximates the width of a point set in any direction. We consider approximating the …

An Investigation Into Lagrangian Coherent Structure Detection For Low Reynolds Number Flows, Kyle Fitzsimmons

Theses, Dissertations and Culminating Projects

In order to better understand and make use of complex fluid systems, regions of similar behavior can be categorized, thus reducing the problem to one of identifying the important structures within the fluid system, and examining their interaction. An important category of fluid structures are those known as Lagrangian Coherent Structures. An experimental setup has been constructed in order to study methods for improving the detection of Lagrangian Coherent Structures, and experimental data has been analyzed in order to verify the experimental setup. Several modifications to the basic gyre flow have been analyzed in order to provide direction, and a …

Applications Of The Homotopy Analysis Method To Optimal Control Problems, Shubham Singh

Open Access Theses

Traditionally, trajectory optimization for aerospace applications has been performed using either direct or indirect methods. Indirect methods produce highly accurate solutions but suer from a small convergence region, requiring initial guesses close to the optimal solution. In past two decades, a new series of analytical approximation methods have been used for solving systems of dierential equations and boundary value problems.

The Homotopy Analysis Method (HAM) is one such method which has been used to solve typical boundary value problems in nance, science, and engineering. In this investigation, a methodology is created to solve indirect trajectory optimization problems using the Homotopy …

Oscillation Of Quenched Slowdown Asymptotics Of Random Walks In Random Environment In Z, Sung Won Ahn

Open Access Dissertations

We consider a one dimensional random walk in a random environment (RWRE) with a positive speed limn→∞ (Xn/) = υα > 0. Gantert and Zeitouni showed that if the environment has both positive and negative local drifts then the quenched slowdown probabilities P ω(Xn < xn) with x∈ (0,υα) decay approximately like exp{- n1-1/s} for a deterministic s > 1. More precisely, they showed that n -γ log Pω(Xn < xn) converges to 0 or -∞ depending on whether γ > 1 - 1/s or γ < 1 - 1/ s. In this paper, …

Maximum Empirical Likelihood Estimation In U-Statistics Based General Estimating Equations, Lingnan Li

Open Access Dissertations

In the first part of this thesis, we study maximum empirical likelihood estimates (MELE's) in U-statistics based general estimating equations (UGEE's). Our technical maneuver is the jackknife empirical likelihood (JEL) approach. We give the local uniform asymptotic normality condition for the log-JEL for UGEE's. We derive the estimating equations for finding MELE's and provide their asymptotic normality. We obtain easy MELE's which have less computational burden than the usual MELE's and can be easily implemented using existing software. We investigate the use of side information of the data to improve efficiency. We exhibit that the MELE's are fully efficient, and …

Rees Algebras And Iterated Jacobian Duals, Vivek Mukundan

Open Access Dissertations

Consider the rational map Ψ : [Special characters omitted.] where the fi's are homogeneous forms of the same degree in the homogeneous coordinate ring R = k[ x1,…,xd] of [Special characters omitted.]. Assume that I = (f 1,…,fm) is a height 2 perfect ideal in the polynomial ring R. In this context, the coordinate ring of the graph of Ψ is the Rees algebra of I and the co-ordinate ring of the image of Ψ is the special fiber ring. We study two settings. The first setting is when I is almost …