Faculty in the University of Dayton Department of Mathematics examine the art, science, application and philosophy of mathematics. Here, you can see a sampling of their research.

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Submissions from 2017

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Eigenstate–Specific Temperatures in Two–Level Paramagnetic Spin Lattices, Mark Masthay, Calley N. Eads, Amber N. Johnson, R. Gerald Keil, Phillip Miller, Ross E. Jones, Joe D. Mashburn, and Harry B. Fannin

Submissions from 2016

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Almost Automorphic Solutions of Delayed Neutral Dynamic Systems on Hybrid Domains, Murat Adıvar, Halis Can Koyuncuoğlu, and Youssef Raffoul

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Optimal Control Analysis of Ebola Disease with Control Strategies of Quarantine and Vaccination, Muhammad Dure Ahmad, Muhammad Usman, Adnan Khan, and Mudassar Imran

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Upper and Lower Solution Method for Boundary Value Problems at Resonance, Samerah Al Mosa and Paul W. Eloe

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Positive Solutions for a Singular Fourth Order Nonlocal Boundary Value Problem, John M. Davis, Paul W. Eloe, John R. Graef, and Johnny Henderson

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Nonlinear Interpolation and Boundary Value Problems, Paul W. Eloe and Johnny Henderson

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Convolutions and Green’s Functions for Two Families of Boundary Value Problems for Fractional Differential Equations, Paul W. Eloe and Jeffrey T. Neugebauer

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Smallest Eigenvalues for a Right Focal Boundary Value Problem, Paul W. Eloe and Jeffrey T. Neugebauer

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Modeling Factors Contributing to Injury and Fatality of Run-off-Road Crashes in Ohio, Deogratias Eustace, Omar Eid Almutairi, and Peter W. Hovey

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Asymptotically Periodic Solutions of Volterra Integral Equations, Muhammad Islam

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Existence of Periodic Solutions for a Quantum Volterra Equation, Muhammad Islam and Jeffrey T. Neugebauer

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Integration Over Curves and Surfaces Defined by the Closest Point Mapping, Catherine Kublik and Richard Tsai

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Sphere Representations, Stacked Polytopes, and the Colin de Verdière Number of a Graph, Lon Mitchell and Lynne Yengulalp

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Identification of Control Targets in Boolean Molecular Network Models via Computational Algebra, David Murrugarra, Alan Veliz-Cuba, Boris Aguilar, and Reinhard Laubenbacher

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Necessary and Sufficient Conditions for Stability of Volterra Integro-dynamic Equation Systems on Time Scales, Youssef Raffoul

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Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals, Youssef Raffoul and Habib Rai

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Theorems on Boundedness of Solutions to Stochastic Delay Differential Equations, Youssef Raffoul and Dan Ren

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Effects of Cell Cycle Noise on Excitable Gene Circuits, Alan Veliz-Cuba, Chinmaya Gupta, Matthew R. Bennett, Krešimir Josić, and William Ott

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Stochastic Models of Evidence Accumulation in Changing Environments, Alan Veliz-Cuba, Zachary P. Kilpatrick, and Krešimir Josić

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Coding Strategies, the Choquet Game and Domain Representability, Lynne Yengulalp

Submissions from 2015

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From Subcompact to Domain Representable, William Fleissner and Lynne Yengulalp

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Bounded, Asymptotically Stable, and L^1 Solutions of Caputo Fractional Differential Equations, Muhammad Islam

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Qualitative Theory of Functional Differential and Integral Equations, Muhammad Islam, Cemil Tunc, Mouffak Benchohra, Bingwen Lui, and Samir H. Saker

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Sobriety in Delta not Sober, Joe Mashburn

Submissions from 2014

Periodic and Asymptotically Periodic Solutions in Coupled Nonlinear Systems of Volterra Integro-differential Equations, Muhammad Islam and Youssef Raffoul

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Modified Homotopy Perturbation Transform Method: A Paradigm for Nonlinear Boundary Layer Problems, Yasir Khan and Muhammad Usman

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Lyapunov Functionals that Lead to Exponential Stability and Instability in Finite Delay Volterra Difference Equations, Catherine Kublik and Youssef Raffoul

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A Generalization of Poincaré-Cartan Integral Invariants of a Nonlinear Nonholonomic Dynamical System, Muhammad Usman and M. Imran

Submissions from 2013

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Every Scattered Space is Subcompact, William Fleissner, Vladimir Tkachuk, and Lynne Yengulalp

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When Cp(X) is Domain Representable, William Fleissner and Lynne Yengulalp

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Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity, Muhammad Islam

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The Effects of Variable Viscosity on the Peristaltic Flow of Non-Newtonian Fluid through a Porous Medium in an Inclined Channel with Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, and Muhammad Usman

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An Implicit Interface Boundary Integral Method for Poisson’s Equation on Arbitrary Domains, Catherine Kublik, Nicolay M. Tanushev, and Richard Tsai

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A Spectral Order for Infinite Dimensional Quantum Spaces, Joe Mashburn

Submissions from 2012

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Bounded Solutions of Almost Linear Volterra Equations, Muhammad Islam and Youssef Raffoul

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A study of the GAM approach to solve laminar boundary layer equations in the presence of a wedge, Rahmat Ali Khan and Muhammad Usman

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Eventual Periodicity of Forced Oscillations of Korteweg-de Vries Type Equation, Rahmat Ali Khan and Muhammad Usman

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A Meshless Numerical Solution of the Family of Generalized Fifth-order Korteweg-de Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, and Muhammad Usman

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Bifurcations in Steady State Solutions of a Class of Nonlinear Dispersive Wave Equation, Muhammad Usman and Paul W. Eloe

Submissions from 2011

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Research in Mathematics Educational Technology: Current Trends and Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, and David K. Pugalee

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Fully Nonlinear Boundary Value Problems with Impulse, Paul Eloe and Muhammad Usman

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Non-Normality Points of β X\X, William Fleissner and Lynne Yengulalp

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Algorithms for Area Preserving Flows, Catherine Kublik, Selim Esedoglu, and Jeffrey A. Fessler

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Prospective Teachers' Use of Representations in Solving Statistical Tasks with Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, and Robin L. Angotti

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Global Well-posedness and Asymptotic Behavior of a Class of Initial-boundary-value Problems of the KdV Equation on a Finite Domain, Ivonne Rivas, Muhammad Usman, and Bingyu Zhang

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A New Undergraduate Curriculum on Mathematical Biology at University of Dayton, Muhammad Usman and Amit Singh

Submissions from 2010

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Periodic Solutions of Neutral Delay Integral Equations of Advanced Type, Muhammad Islam, Nasrin Sultana, and James Booth

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Coarsening in High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik

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Linearly Ordered Topological Spaces and Weak Domain Representability, Joe Mashburn

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Coarser Connected Metrizable Topologies, Lynne Yengulalp

Submissions from 2009

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Forced Oscillations of the Korteweg-de Vries Equation on a Bounded Domain and their Stability, Muhammad Usman and Bingyu Zhang

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Coarser Connected Topologies and Non-Normality Points, Lynne Yengulalp

Submissions from 2008

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Qualitative Properties of Nonlinear Volterra Integral Equations, Muhammad Islam and Jeffrey T. Neugebauer

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An Order Model for Infinite Classical States, Joe Mashburn

Submissions from 2007

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Periodic Solutions of Neutral Nonlinear Systems of Differential Equations with Functional Delay, Muhammad Islam and Youssef Raffoul

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A Comparison of Three Topologies on Ordered Sets, Joe Mashburn

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A Spectral Order for Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn

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Forced Oscillations of a Class of Nonlinear Dispersive Wave Equations and their Stability, Muhammad Usman and Bingyu Zhang

Submissions from 2005

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Stability Properties of Linear Volterra Integrodifferential Equations with Nonlinear Perturbation, Muhammad Islam and Youssef Raffoul

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Boundedness and Stability in Nonlinear Delay Difference Equations Employing Fixed Point Theory, Muhammad Islam and Ernest Yankson

Submissions from 2003

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Exponential Stability in Nonlinear Difference Equations, Muhammad Islam and Youssef Raffoul

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Uniform Asymptotic Stability in Nonlinear Volterra Discrete Systems, Muhammad Islam, Youssef Raffoul, and Paul W. Eloe

Submissions from 2000

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OIF Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, and Joe D. Mashburn

Uniform Asymptotic Stability in Linear Volterra Integrodifferential Equations with Application to Delay Systems, Muhammad Islam, Paul W. Eloe, and Bo Zhang

Submissions from 1999

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On The Decomposition of Order-separable Posets of Countable Width into Chains, Gary Gruenhage and Joe Mashburn

Submissions from 1998

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Refracting System for Annular Gaussian-to-Bessel Beam Transformation, Muhammad Arif, Meer M. Hossain, Abdul Ahad S. Awwal, and Muhammad Islam

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Two-Element Refracting System for Annular Gaussian-to-Bessel Beam Transformation, Muhammad Arif, Meer M. Hossain, Abdul Ahad S. Awwal, and Muhammad Islam

Submissions from 1997

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Almost Periodic Solutions of Nonlinear Integral Equations, Muhammad Islam

Submissions from 1995

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Stability Properties and Integrability of the Resolvent of Linear Volterra Equations, Muhammad Islam and Paul W. Eloe

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A Note on Reordering Ordered Topological Spaces and the Existence of Continuous, Strictly Increasing Functions, Joe Mashburn

Submissions from 1993

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On Infinite Delay Integral Equations Having Nonlinear Perturbations, Muhammad Islam

Submissions from 1992

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Modified Signed-Digit Trinary Arithmetic Using Optical Symbolic Substitution, Muhammad Islam, A. A. S. Awwal, and Mohammad A. Karim

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Nonlinear Integrodifferential Equations and A Priori Bounds on Periodic Solutions, Muhammad Islam, T. A. Burton, and Paul W. Eloe

Submissions from 1991

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Bounded Solutions and Periodic Solutions of Volterra Equations With Infinite Delay, Muhammad Islam

Submissions from 1990

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Periodic Solutions of Linear Integrodifferential Equations, Muhammad Islam, T. A. Burton, and Paul W. Eloe

Submissions from 1989

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Countable Covers of Spaces by Migrant Sets, Zoltan Balogh, Joe Mashburn, and Peter Nyikos

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Pixley-Roy Hyperspaces of ω-graphs, Joe Mashburn

Submissions from 1988

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Periodic Solutions of Nonlinear Integral Equations, Muhammad Islam

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Periodic Solutions of Volterra Integral Equations, Muhammad Islam

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Periodic Solutions of Nonlinear Integral Equations With Infinite Memory, Muhammad Islam and Paul W. Eloe

Submissions from 1984

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A Note on Irreducibility and Weak Covering Properties, Joe Mashburn

Submissions from 1983

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The Least Fixed Point Property for ω-chain Continuous Functions, Joe Mashburn

Submissions from 1981

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Dissertation: The Least Fixed Point Property for ω-chain Continuous Functions, Joe Mashburn

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Three Counterexamples Concerning ω-Chain Continuous Functions and Fixed-point Properties, Joe Mashburn