Mathematics Commons^™

Euler’S Calculation Of The Sum Of The Reciprocals Of Squares, Kenneth M. Monks

Calculus

No abstract provided.

Reduction Of Order: Analytical Solution Of Film Formation In The Electrostatic Rotary Bell Sprayer, Mark Doerre, Nelson Akafuah

Institute of Research for Technology Development Faculty Publications

This brief paper explains the slight differences in governing equations for a fluid film in a spinning cone, and the mechanism that reduces the order of a solution. Spinning cones with a centrally supplied fluid that spreads over its inner surface as a thin film have been the subject of interest for many years. Though often cast as a mathematical analysis, understanding this process is important, especially in the application of automotive painting. The analysis consists of a system of equations obtained from the Navier–Stokes equations along with simple boundary conditions that describe radial and tangential momentum conservation. Solutions to …

Math Careers And Alumni, University Of Mississippi. Department Of Mathematics

Faculty and Student Publications

A selection of program graduates answer questions about why they chose to study Math at the University of Mississippi.

• Adrian Wilson Cartier
• Josephine Howard
• Donald Cole
• Carla Cotwright-Williams
• Ken Lackey
• Skylyn Irby
• Adam Broome
• Samuel S. Watson
• Cheryl White

Development Of A Karst Tourism Management Index To Assess Tourism-Driven Degradation Of Protected Karst Sites, Keith R. Semler

Masters Theses & Specialist Projects

The intent of this research was to create and evaluate a karst tourism management index (KTMI). This index is intended to be a new management tool designed to quantify environmental disturbances caused specifically by tourism activities in karst regions, particularly show caves and springs. In an effort to assess the effectiveness of the index as a management tool in karst terrains, after development, the index was applied to six case study sites. A review of the management policies at each study site was conducted with the use of standard policy critique methods and semistructured interviews with managers at the study …

Properties Of Functionally Alexandroff Topologies And Their Lattice, Jacob Scott Menix

Masters Theses & Specialist Projects

This thesis explores functionally Alexandroff topologies and the order theory asso- ciated when considering the collection of such topologies on some set X. We present several theorems about the properties of these topologies as well as their partially ordered set.

The first chapter introduces functionally Alexandroff topologies and motivates why this work is of interest to topologists. This chapter explains the historical context of this relatively new type of topology and how this work relates to previous work in topology. Chapter 2 presents several theorems describing properties of functionally Alexandroff topologies ad presents a characterization for the functionally Alexandroff topologies …

Tracing Cyclic Homology Pairings Under Twisting Of Graded Algebras, Sayan Chakraborty, Makoto Yamashita

Journal Articles

We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the Gauss–Manin connection on periodic cyclic cohomology in terms of the cup product action of group cohomology.

Extensions Of The Power Group Enumeration Theorem, Shawn Jeffrey Green

Theses and Dissertations

The goal of this paper is to develop extensions of Polya enumeration methods which count orbits of functions. De Bruijn, Harary, and Palmer all worked on this problem and created generalizations which involve permuting the codomain and domain of functions simultaneously. We cover their results and specifically extend them to the case where the group of permutations need not be a direct product of groups. In this situation, we develop a way of breaking the orbits into subclasses based on a characteristic of the functions involved. Additionally, we develop a formula for the number of orbits made up of bijective …

Using Literature To Engage Students Mathematically, Ann Wheeler, Joe Champion, Holly Dybvig

Mathematics Faculty Publications and Presentations

In this article, the authors share two lessons that incorporate children’s literature with the Pythagorean theorem and area to engage preservice teachers (PSTs) mathematically. Sample responses, example texts, and future work are discussed.

A Nonlinear Parallel Model For Reversible Polymer Solutions In Steady And Oscillating Shear Flow, Erik Tracey Palmer

Theses and Dissertations

A mathematical model for reversible polymers in steady and oscillating shear flows is presented. Using a mean-field approach, the behavior of the polymer network is characterized by a finitely extensible nonlinear elastic bead-spring model that stochastically transitions between dumbbell states to represent attachments, detachments and loops. An efficient parallel scheme for computation on GPUs utilizes populations of over a million dumbbells to characterize steady, large and small amplitude oscillatory shear (SAOS) flows in Brownian dynamics simulations. In steady-shear a novel attachment species transition function enables shear thickening and shear thinning by the adjustment of either attachment or detachment parameters. Three …

An Implementation Of The Kapustin-Li Formula, Jessica Otis

Theses and Dissertations

Let R be a regular local ring and take ! to be an isolated singularity on R. Taking Z/2-graded R-modules, X and Y , a matrix factorization of ω is a pair of morphisms (ϕ, ψ) such that ϕ⃝◦ψ = ω and ψ⃝◦ϕ = ω are satisfied in the diagram X ϕ → Y ψ→ X. We will discuss the category of matrix factorizations of ! in R and lead into the homotopy category of matrix factorizations as well as its historical development. Finally, we will conclude with the statement …

On Continuous Images Of Ultra-Arcs, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Any space homeomorphic to one of the standard subcontinua of the Stone-Čech remainder of the real half-line is called an ultra-arc. Alternatively, an ultra-arc may be viewed as an ultracopower of the real unit interval via a free ultrafilter on a countable set. It is known that any continuum of weight is a continuous image of any ultra-arc; in this paper we address the problem of which continua are continuous images under special maps. Here are some of the results we present.

Active Prelude To Calculus, Matthew Boelkins

Open Textbooks

Active Prelude to Calculus is designed for college students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes how it is important in calculus. This text is written in the spirit of Active Calculus and is especially ideal for students who will eventually study calculus from that text. The reader will find that …

Mittag–Leffler Stability Of Systems Of Fractional Nabla Difference Equations, Paul W. Eloe, Jaganmohan Jonnalagadda

Mathematics Faculty Publications

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

Long-Dose Intensive Therapy Is Necessary For Strong, Clinically Significant, Upper Limb Functional Gains And Retained Gains In Severe/Moderate Chronic Stroke, Janis J. Daly, Jessica P. Mccabe, John P. Holcomb, Michelle Monkiewicz, Jennifer Gansen, Svetlana Pundik

Mathematics and Statistics Faculty Publications

Background. Effective treatment methods are needed for moderate/severely impairment chronic stroke. Objective. The questions were the following: (1) Is there need for long-dose therapy or is there a mid-treatment plateau? (2) Are the observed gains from the prior-studied protocol retained after treatment? Methods. Single-blind, stratified/randomized design, with 3 applied technology treatment groups, combined with motor learning, for long-duration treatment (300 hours of treatment). Measures were Arm Motor Ability Test time and coordination-function (AMAT-T, AMAT-F, respectively), acquired pre-/posttreatment and 3-month follow-up (3moF/U); Fugl-Meyer (FM), acquired similarly with addition of mid-treatment. Findings. There was no group difference in …

Sequential Survival Analysis With Deep Learning, Seth William Glazier

Theses and Dissertations

Survival Analysis is the collection of statistical techniques used to model the time of occurrence, i.e. survival time, of an event of interest such as death, marriage, the lifespan of a consumer product or the onset of a disease. Traditional survival analysis methods rely on assumptions that make it difficult, if not impossible to learn complex non-linear relationships between the covariates and survival time that is inherent in many real world applications. We first demonstrate that a recurrent neural network (RNN) is better suited to model problems with non-linear dependencies in synthetic time-dependent and non-time-dependent experiments.

A Zero-Suppressed Binary Decision Diagram Approach For Constrained Path Enumeration, Renzo Roel P. Tan, Jun Kawahara, Agnes Garciano, Immanuel Sin

Mathematics Faculty Publications

Combinatorial optimization over graphs has been the subject of research. Recently, the solution of such problems by enumeration using a compact data structure called the zero-suppressed binary decision diagram was proposed and studied. The paper augments the existing frontier-based search method of construction and puts forth a technique for accommodating additional constraints during computation. The shortest and longest path problems for the Osaka Metro transit network are simultaneously solved as demonstration. Furthermore, a comparison of the approach with a conventional integer programming method is presented towards justifying the effectiveness of the algorithm.

Algebraic Topics In The Classroom – Gauss And Beyond, Lisa Krance

Masters Essays

No abstract provided.

Introduction Of Infinite Series In High School Level Calculus, Ericka Bella

Masters Essays

No abstract provided.

A Few Problems On The Steiner Distance And Crossing Number Of Graphs, Josiah Reiswig

Theses and Dissertations

We provide a brief overview of the Steiner ratio problem in its original Euclidean context and briefly discuss the problem in other metric spaces. We then review literature in Steiner distance problems in general graphs as well as in trees.

Given a connected graph G we examine the relationship between the Steiner k-diameter, sdiam_k(G), and the Steiner k-radius, srad_k(G). In 1990, Henning, Oellermann and Swart [Ars Combinatoria 12 13-19, (1990)] showed that for any connected graph G, sdiam₃(G) ≤(8/5)srad₃(G) and …

Unconditionally Energy Stable Linear Schemes For A Two-Phase Diffuse Interface Model With Peng-Robinson Equation Of State, Chenfei Zhang

Theses and Dissertations

Many problems in the fields of science and engineering, particularly in materials science and fluid dynamic, involve flows with multiple phases and components. From mathematical modeling point of view, it is a challenge to perform numerical simulations of multiphase flows and study interfaces between phases, due to the topological changes, inherent nonlinearities and complexities of dealing with moving interfaces.

In this work, we investigate numerical solutions of a diffuse interface model with Peng-Robinson equation of state. Based on the invariant energy quadratization approach, we develop first and second order time stepping schemes to solve the liquid-gas diffuse interface problems for …

Finding Resolutions Of Mononomial Ideals, Hannah Melissa Kimbrell

Theses and Dissertations

In this paper we present two different combinatorial approaches to finding resolutions of polynomial ideals. Their goal is to get resolutions that are as small as possible while still preserving the structure of the zeroth syzygy module. Then we present the idea of a differential graded algebra and discuss when the minimal resolutions of a polynomial ideals admits such a structure.

New Modified Singh-Maddala Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a new five-parameter extended Burr XII model called new modified Singh-Maddala (NMSM) is developed from cumulative hazard function of the modified log extended integrated beta hazard (MLEIBH) model. The NMSM density function is left-skewed, right-skewed and symmetrical. The Lambert W function is used to study descriptive measures based on quantile, moments, and moments of order statistics, incomplete moments, inequality measures and residual life function. Different reliability and uncertainty measures are also theoretically established. The NMSM distribution is characterized via different techniques and its parameters are estimated using maximum likelihood method. The simulation studies are performed on the …

The Odd Nadarajah-Haghighi Family Of Distributions: Properties And Applications, Abraão D.C. Nascimento, Kássio F. Silva, Gauss M. Cordeiro, Morad Alizadeh, Haitham M. Yousof, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

We study some mathematical properties of a new generator of continuous distributions called the Odd Nadarajah-Haghighi (ONH) family. In particular, three special models in this family are investigated, namely the ONH gamma, beta and Weibull distributions. The family density function is given as a linear combination of exponentiated densities. Further, we propose a bivariate extension and various characterization results of the new family. We determine the maximum likelihood estimates of ONH parameters for complete and censored data. We provide a simulation study to verify the precision of these estimates. We illustrate the performance of the new family by means of …

Reduction Of The Kp Hierarchy, Adrian Eugenio Torres

Theses and Dissertations

This thesis will delve into the Kadomtsev-Petviashvili equation or KP equation and it's hierarchy. More specifically, the solition theory around it. To do so, we first explore the soliton theory for the Korteweg de-Vries equation or KdV equation by analysing it through the inverse scattering transform method and presenting it's soliton solutions. Second, we will introduce, Hirota's bilinear form, and understand its main idea. Third, introduce Sato Theory, and use it to formulate the KP hierarchy, via using pseudo-differential operators, presenting the lax operator, the dressing operator, Sato’s equation, and the zero curvature equation (Zakharov-Shabat Equation). Fourth, find the general …

Polymer Stress Growth In Viscoelastic Fluids In Oscillating Extensional Flows With Applications To Micro-Organism Locomotion, Becca Thomases, Robert D. Guy

Mathematics Sciences: Faculty Publications

Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers. We use a series of related theoretical investigations to probe the origin of these concentrated stresses. First the polymer stress is computed analytically at a given oscillating extensional stagnation point in a viscoelastic fluid. The analysis identifies a Deborah number (De) dependent Weissenberg number (Wi) transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. Next, stress and velocity are found from numerical simulations in an oscillating 4-roll mill …

Loose Legendrian And Pseudo-Legendrian Knots In 3-Manifolds, Patricia Cahn, Vladimir Chernov

Mathematics Sciences: Faculty Publications

We prove a complete classification theorem for loose Legendrian knots in an oriented 3-manifold, generalizing results of Dymara and DingGeiges. Our approach is to classify knots in a 3-manifold M that are transverse to a nowhere-zero vector field V up to the corresponding isotopy relation. Such knots are called V -transverse. A framed isotopy class is simple if any two V -transverse knots in that class which are homotopic through V -transverse immersions are V -transverse isotopic. We show that all knot types in M are simple if any one of the following three conditions hold: 1. M is closed, …

Developing Understanding Of The Chain Rule, Implicit Differentiation, And Related Rates: Towards A Hypothetical Learning Trajectory Rooted In Nested Multivariation, Haley Paige Jeppson

Theses and Dissertations

There is an overemphasis on procedures and manipulation of symbols in calculus and not enough emphasis on conceptual understanding of the subject. Specifically, students struggle to understand and correctly apply concepts in calculus such as the chain rule, implicit differentiation, and related rates. Students can learn mathematics more deeply when they make connections between different mathematical ideas. I have hypothesized that students can make powerful connections between the chain rule, implicit differentiation, and related rates through the mathematical concept of nested multivariation. Based on this hypothesis, I created a hypothetical learning trajectory (HLT) rooted in nested multivariation for students to …

Hyperparameters For Dense Neural Networks, Christopher James Hettinger

Theses and Dissertations

Neural networks can perform an incredible array of complex tasks, but successfully training a network is difficult because it requires us to minimize a function about which we know very little. In practice, developing a good model requires both intuition and a lot of guess-and-check. In this dissertation, we study a type of fully-connected neural network that improves on standard rectifier networks while retaining their useful properties. We then examine this type of network and its loss function from a probabilistic perspective. This analysis leads to a new rule for parameter initialization and a new method for predicting effective learning …

On The Instabilities And Transitions Of The Western Boundary Current, Daozhi Han, Marco Hernandez, Quan Wang

Mathematics and Statistics Faculty Research & Creative Works

We study the stability and dynamic transitions of the western boundary currents in a rectangular closed basin. By reducing the infinite dynamical system to a finite dimensional one via center manifold reduction, we derive a non-dimensional transition number that determines the types of dynamical transition. We show by careful numerical evaluation of the transition number that both continuous transitions (supercritical Hopf bifurcation) and catastrophic transitions (subcritical Hopf bifurcation) can happen at the critical Reynolds number, depending on the aspect ratio and stratification. The regions separating the continuous and catastrophic transitions are delineated on the parameter plane.

A Numerical Solution Of Fredholm Integral Equations Of The Second Kind Based On Tight Framelets Generated By The Oblique Extension Principle, Mutaz Mohammad

All Works

© 2019 by the authors. In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate.