Mathematics Commons^™

Mathematics In Motion: Linear Systems Of Differential Equations On The Differential Analyzer, Devon A. Tivener

Theses, Dissertations and Capstones

In this work, I will provide an introduction to the dierential analyzer, a machine designed to solve dierential equations through a process called mechanical integration. I will give a brief historical account of dierential analyzers of the past, and discuss the Marshall University Dierential Analyzer Project. The goal of this work is to provide an analysis of solutions of systems of dierential equations using a dierential analyzer. In particular, we are interested in the points at which these systems are in equilibrium and the behavior of solutions that start away from equilibrium. After giving a description of linear systems of …

On Residual Lifetimes Of K-Out-Of-N Systems With Nonidentical Components, Subhash C. Kochar, Maochao Xu

Mathematics and Statistics Faculty Publications and Presentations

In this article, mixture representations of survival functions of residual lifetimes of k-out-of-n systems are obtained when the components are independent but not necessarily identically distributed. Then we stochastically compare the residual lifetimes of k-out-of-n systems in one- and two-sample problems. In particular, the results extend some results in Li and Zhao [14], Khaledi and Shaked [13], Sadegh [17], Gurler and Bairamov [7] and Navarro, Balakrishnan, and Samaniego [16]. Applications in the proportional hazard rates model are presented as well.

Methods Of Variational Analysis In Pessimistic Bilevel Programming, Samarathunga M. Dassanayaka

Wayne State University Dissertations

Bilevel programming problems are of growing interest both from theoretical and practical points of view. These models are used in various applications, such as economic planning, network design, and so on. The purpose of this dissertation is to study the pessimistic (or strong) version of bilevel programming problems in finite-dimensional spaces. Problems of this type are intrinsically nonsmooth (even for smooth initial data) and can be treated by using appropriate tools of modern variational analysis and generalized differentiation developed by B. Mordukhovich.

This dissertation begins with analyzing pessimistic bilevel programs, formulation of the problems, literature review, practical application, existence of …

Numerical Solution Of The Five-Moment Ideal Two-Fluid Equations In One Dimension, Marcus Scott

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Plasmas are frequently treated as a single conducting fluid and modeled using the equations of magnetohydrodynamics. However, this regime works better for low-frequency plasmas. High-frequency plasmas may be modeled using the principles of kinetic theory. For plasmas with frequencies between these two extremes, a two-fluid approach can yield better results. In 2006, Ammar Hakim mathematically modeled a plasma with a set of equations called the five-moment ideal two-fluid equations. An attempt is made reproduce those results. A derivation of this set of equations by taking moments of the Boltzmann equation is presented. Electric and magnetic fields contribute to the source …

Simulating Power For One-Way Anova By Using Non-Normal Error Distributions, Caixia Xu

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Usually we assume that the distribution of the additive errors in a one-way ANOVA linear model is normal. However, exceptions to this assumption about the error distribution may exist. In such cases, we might consider non-normal error distributions, but proceed with the "usual" ANOVA F-test analyses. This study focuses on simulating power for one-way ANOVA when using non-normal error distributions.

Effects Of Multitemperature Nonequilibrium On Compressible Homogeneous Turbulence, Wei Liao, Yan Peng, Li-Shi Luo

Mathematics & Statistics Faculty Publications

We study the effects of the rotational-translational energy exchange on the compressible decaying homogeneous isotropic turbulence (DHIT) in three dimensions through direct numerical simulations. We use the gas-kinetic scheme coupled with multitemperature nonequilibrium based on the Jeans-Landau-Teller model. We investigate the effects of the relaxation time of rotational temperature, Z_R, and the initial ratio of the rotational and translational temperatures, T_R0 / T_L0, on the dynamics of various turbulence statistics including the kinetic energy K (t), the dissipation rate ε (t), the energy spectrum E (k,t), the root mean square of the velocity divergence θ′ …

Global Caccioppoli-Type And Poincar ´E Inequalities With Orlicz Norms, Ravi P. Agarwal, Shusen Ding

Mathematics and System Engineering Faculty Publications

We obtain global weighted Caccioppoli-type and Poincaré inequalities in terms of Orlicz norms for solutions to the nonhomogeneous A -harmonic equation d A(x,d)=B(x,d).

The Fibonacci Sequence, Arik Avagyan

A with Honors Projects

A review was made of the Fibonacci sequence, its characteristics and applications.

Variational Analysis In Parametric Optimization, Yen Nhi Nguyen Thi

Wayne State University Dissertations

The dissertation is devoted to the development of variational analysis and generalized differentiation in infinite dimensions. We derive new calculus rules for both first-order partial subdifferentials and second-order partial subdifferentials in the framework of general Banach spaces as well as more developed rules in the framework of Asplund spaces. This calculus is applied in the study of sensitivity analysis for solution maps to the parameterized generalized equations in Asplund spaces, where both bases and fields are parameter-dependent multifunctions. We analyze the parametric sensitivity of either stationary points or stationary point multiplier multifunctions associated with parameterized optimization problems under consideration. The …

On The Convergence Of Greedy Algorithms For Initial Segments Of The Haar Basis, S J. Dilworth, E Odell, Th Schlumprecht, Andras Zsak

Faculty Publications

We consider the X-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in Lp[0, 1] (1< p < 1) then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases.

Local Versus Global Search In Channel Graphs, A.H. Hunter, Nicholas Pippenger

All HMC Faculty Publications and Research

Previous studies of search in channel graphs has assumed that the search is global; that is, that the status of any link can be probed by the search algorithm at any time. We consider for the first time local search, for which only links to which an idle path from the source has already been established may be probed. We show that some well known channel graphs may require exponentially more probes, on the average, when search must be local than when it may be global.

Voting In Agreeable Societies, Deborah E. Berg '06, Serguei Norine, Francis E. Su, Robin Thomas, Paul Wollan

All HMC Faculty Publications and Research

No abstract provided in this article.

Early Intervention In College Mathematics Courses: A Component Of The Stem Rrg Program Funded By The Us Department Of Education, Rohitha Goonatilake, Eduardo Chappa

The Mathematics Enthusiast

Student preparedness in entry level college mathematics courses has decreased in the past. In order for students to be successful in these courses, early intervention is required. Texas A&M International University (TAMIU) has implemented an early intervention program, the Mathematics Enrichment Program (MEP), which will target freshman students entering College Algebra courses in Spring 2009. This project is part of the STEM Recruitment, Retention, and Graduation program, recently funded by the US Department of Education. This paper will highlight the components of the project, most importantly the extent of the intervention, how the project is planned, and preliminary results.

New Year Tidings, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Leading Learning Within A Plc: Implementing New Mathematics Content, Ann Heirdsfield, Janeen Lamb, Gayle Spry

The Mathematics Enthusiast

This paper does two things. Firstly, it examines the literature that coalesces around theoretical models of teacher professional development (PD) within a professional learning community (PLC). Secondly, these models are used to analyse support provided to two year 3 teachers, while implementing the draft Queensland mathematics syllabus. The findings from this study suggest that the development of this small PLC extended the teachers’ Zone of Enactment which in turn led to teacher action and reflection. This was demonstrated by the teachers leading their own learning as well as that of their students.

Tme Volume 7, Number 1

The Mathematics Enthusiast

No abstract provided.

Calculating The Time Constant Of An Rc Circuit, Sean Dunford

Undergraduate Journal of Mathematical Modeling: One + Two

In this experiment, a capacitor was charged to its full capacitance then discharged through a resistor. By timing how long it took the capacitor to fully discharge through the resistor, we can determine the RC time constant using calculus.

Social Network Gaming Trends, Michael Gathwright

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project was to determine how long the social network game Scratch-Offs, created by game development company Spice Rack Media, will remain financially viable. The game Scratch-Offs is a freeware game (users pay nothing for the actual software) and is funded through micro transactions (users must pay small amounts of money to play actual games). This implies a relationship between total games played and revenue earned. Using data provided by Spice Rack, we were able to develop an exponential equation that accurately depicts usage trends over time. This equation was used to determine the date Scratch-Offs will …

The Progression Of Sequential Reactions, Jack Mcgeachy

Undergraduate Journal of Mathematical Modeling: One + Two

Sequential reactions consist of linked reactions in which the product of the first reaction becomes the substrate of a second reaction. Sequential reactions occur in industrially important processes, such as the chlorination of methane. A generalized series of three sequential reactions was analyzed in order to determine the times at which each chemical species reaches its maximum. To determine the concentration of each species as a function of time, the differential rate laws for each species were solved. The solution of each gave the concentration curve of the chemical species. The concentration curves of species A₁ and A_{2 …}

Quantum Mechanical Example Of Anti-Tunneling, Tim Mitchell

Undergraduate Journal of Mathematical Modeling: One + Two

The probability of a particle being reflected by a semi-infinite energy barrier was solved using Schrödinger's equations that describe the quantum mechanical behavior of the particle. The continuity of the functions at the origin allowed the wave functions and their respective derivatives to be equated. Solution of the resulting system yielded values A₁ and B₁ which were used to calculate the reflection coefficient, (B₁/A₁)². The conclusions obtained from these results stated that the particle would be reflected by the barrier when E