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 2016

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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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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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Sobriety in Delta not Sober, Joe Mashburn

Submissions from 2014

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

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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

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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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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An Order Model for Infinite Classical States, Joe Mashburn

Submissions from 2007

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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 2000

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

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 1995

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

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 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