# Showcasing our scholarship.

The research and scholarly efforts of our faculty ensure that our students are educated in a vibrant and engaged environment. Recent research and scholarship projects are listed below.

## Grants

Bigelow, K. E. (Principal), **Diestelkamp, W. S.**, Krane, C. M., Pinnell, M. F.. “Multi-disciplinary STEM Grant Preparation Support in Bioengineering.” Sponsored by NSF Advance - LEADER Consortium Mini-Grant, $5,000. (December 2010 - August 2012).

**Diestelkamp, W. S.** (Other), Goldstein, D. (Principal), Krane, C. (Co-Principal). “Roles and regulation of aqua/glyceroporins in a freeze tolerant amphibian.” Sponsored by National Science Foundation, $562,269. (October 1, 2011 - September 30, 2014).

**Diestelkamp, W. S.** (Principal), Prather, J. (Principal), Swanson, C. (Principal). “Expanding the participation of two-year college faculty in Ohio NExT.” Sponsored by Mathematical Association of America, $5,000. (August 2010 - April 2013).

**Higgins, A. W.** (Co-Principal), Gallian, J. (Co-Principal), Narayan, D. (Co-Principal), Rubio, I. (Co-Principal). “Conference on Trends in Undergraduate Research in the Mathematical Sciences (TURMS).” Sponsored by Mathematical Association of America, $100,000. (October 26, 2012 - October 28, 2012).

**Krakowski, R. J.** (Supporting). “Poised for Success.” Sponsored by Ohio Department of Education - High School & Higher Education Alignment, $30,000. (January 20, 2012 - September 30, 2014).

Pinnell, M. F. (Principal), Krane, C. M. (Principal), **Diestelkamp, W. S.** (Principal). “Assessing the viscoelastic properties of porcine arteries: an integrated approach.” Sponsored by Leader Consortium - NSF Advance Program, $5,000. (January 1, 2010 - June 30, 2012).

## Invited Lectures & Addresses

**Abueida, A. A.** “Cycle Extensions in BIBD Block-Intersection Graphs.” SIAM Conference in Discrete Mathematics, Society for Industrial and Applied Mathematics, National Science Foundation, Halifax, Canada. (June 18, 2012).

**Busch, A. H., Abueida, A. A.**, Sritharan, R. Atlanta Lecture Series, Emory University, Atlanta, GA. (November 3, 2012).

Eads, C. N., **Mashburn, J. D.**, Fannin, H. B., Masthay, M. B. “Comparison of microcanonical and canonical temperatures in paramagnetic spin lattices and other two-level systems.” Midwest Thermodynamics and Statistical Mechanics Conference, National Science Foundation, Minnesota Super Computing Institute, and University of Minnesota College of Science and Engineering, Minneapolis, MN. (May 21, 2012).

**Higgins, A. W.** “Project NExT: A program of the Mathematical Association of America.” Graduate Students’ Colloquium, Department of Mathematics, University of Notre Dame, Notre Dame, IN. (November 1, 2012).

**Higgins, A. W.** “Demonic Graphs and Undergraduate Research.” Mathematics for Everyone, University of Notre Dame, Notre Dame, IN. (November 1, 2012).

**Higgins, A. W.** “Project NExT: A program of the Mathematical Association of America.” The Role of Scientific Societies in STEM Faculty Workshops, Council of Scientific Society Presidents, Washington, DC. (May 3, 2012).

**Higgins, A. W.** “Simple Surprises.” Spring Meeting 2012, Ohio Section of the Mathematical Association of America, Cincinnati, OH. (April 13, 2012).

**Higgins, A. W.** “Project NExT - what works.” Spring Opportunities, Mathematical Sciences Research Institute, Berkeley, CA. (March 14, 2012).

**Hovey, P. W.** “Reliability and Statistical Issues in Managing Aging Aircraft within the Damage Tolerant Design Framework.” Joint Statistics Meetings, American Statistical Association and other Statistical societies, San Diego, California. (July 29, 2012).

**Islam, M. N.** “Asymptotically stable solutions of a nonlinear Volterra integral equation.” Southeastern-Atlantic Regional Conference on Differential Equations, Wake Forest University, Winston Salem, North Carolina. (October 20, 2012).

**Islam, M. N.** “Bounded, L^1 and asymptotically stable solutions of a perturbed nonlinear integral equation.” The eighth international conference on differential equations and dynamical systems., University of Waterloo, Ontario, Canada. (August 3, 2012).

**Liu, R.** “Optimal Investment and Consumption in Regime-Switching Model with Transaction Costs.” Special Session on Nonlinear Stochastic Systems and Applications, The International Conference on the Theory, Methods and Applications of Nonlinear Equations, Texas A&M University-Kingsville, Kingsville, TX. (December 20, 2012).

**Liu, R.** “An Optimal Investment and Consumption Problem in Regime-Switching Model.” The 4th Annual Modeling High Frequency Data in Finance Conference, Stevens Institute of Technology, Hoboken, New Jersey. (July 21, 2012).

**Usman, M.** “A Survey of Numerical Methods for the Solution of a Cancer Cell Mutation Model.” Wright State University Colloquium. (October 26, 2012).

**Usman, M.** “Some Theoretical and Meshfree Numerical Results on a Family of a Korteweg-de Vries Equation.” Special Colloquium at Wright State University. (May 23, 2012).

**Usman, M.** “Qualitative Study of Some Nonlinear Partial Differential Equations Using CAS.” 2012 Spring Southeastern Section Meeting of American Mathematical Society, Tampa, FL. (March 11, 2012).

**Usman, M.** “Numerical Solution of Some Nonlinear Partial Differential Equations Using Radial Basis Functions.” 2012 Spring Southeastern Section Meeting of American Mathematical Society, Tampa, FL. (March 10, 2012).

## Journal Articles

**Abueida, A. A.**, Blinco, A., Clark, S., Daven, M., Eggleton, R. (2013). "Reducible and purely heterogeneous decompositions of uniform complete multigraphs into spanning trees." *Australasian Journal of Combinatorics*, 55, 145-152.

**Abueida, A. A.**, Lefevre, J., Waterhouse, M. (2012). "The spectrum of non-polychromatic equitable edge colored Steiner Triple Systems." *JCMCC*, 80, 405-414.

**Abueida, A. A.**, Rodger, C. A. (2012). "Completing a solution of the Embedding Problem for Incomplete Idempotent Latin Squares when Numerical Conditions Suffice." *Discrete Mathematics*, 312(22), 3328-3334.

**Eloe, P. W.**, Altwaty, A. (2012). "Boundary Value Problems for Impulsive Differential Equations and Avery Type Fixed Point Theorems." *Proceedings of Dynamic Systems and Applications*, 6, 27-32.

**Eloe, P. W.**, Altwaty, A. (2012). "The role of concavity in applications of Avery type fixed point theorems to higher order differential equations." *Journal of Mathematical Inequalities*, 6, 79-90.

**Eloe, P. W.**, Atici, F. M. (2012). "Gronwall’s inequality on discrete fractional calculus." *Computers & Mathematics with Applications*, 64, 3193-3200.

**Eloe, P. W.**, Avery, R., Henderson, J. (2012). "A Leggett-Williams type theorem applied to a fourth order problem." *Communications in Applied Analysis*, 16, 579-588.

**Eloe, P. W.**, Henderson, J., Khan, R. A. (2012). "Existence and uniqueness conditions for a class of (k+4j)-point nth order." *Nonlinear Dynamics and Systems Theory*, 12, 49-62.

**Eloe, P. W.**, Henderson, J., Khan, R. A. (2012). "Uniqueness implies existence and uniqueness conditions for a class of (k+j)-point boundary value problems for nth order differential equations." *Canadian Mathematical Bulletin*, 55, 285-296.

**Eloe, P. W., Usman, M.** (2012). Bifurcations in Steady State Solutions of Nonlinear Dispersive Wave Equation. Nonlinear Studies, The International Journal, 19 (2), 215-224.

**Eloe, P. W., Usman, M.** (2012). Bifurcations in Steady State Solutions of Nonlinear Dispersive Wave Equation. Nonlinear Studies, The International Journal, 19 (2), 215-224.

Flora, G., **Usman, M.** "FALSKAN: A GUI Interface for the Numerical Solution of the Falkner-Skan Problem." *Journal of Pure and Applied Mathematics: Advances and Applications*, 8 (1), 11-24.

Florescu, I., **Liu, R.**, Mariani, M. C. (2012). "Solutions to A Partial Integro-Differential Parabolic System Arising in the Pricing of Financial Options in A Regime-Switching Jump Diffusion Model." *Electronic Journal of Differential Equations*, 2012 (231), 1-12.

**Islam, M. N.**, Adivar, M., **Raffoul, Y. N.** (2012). "Separate contraction and existence of periodic solutions in totally nonlinear delay differential equations." *Hacettepe J. Math. & Stat.*, 41 (1), 1-13.

I**slam, M. N.**, Adivar, M., **Raffoul, Y. N.** (2012). "Separate contraction and existence of periodic solutions in totally nonlinear delay differential equations." *Hacettepe J. Math. & Stat.*, 41 (1), 1-13.

**Islam, M. N., Raffoul, Y. N.** (2012). "Bounded Solutions of Almost Linear Volterra Equations." *Advances in Dynamical Systems and Applications*, 7 (2), 195-205.

**Islam, M. N., Raffoul, Y. N.** (2012). "Bounded Solutions of Almost Linear Volterra Equations." *Advances in Dynamical Systems and Applications*, 7 (2), 195-205.

Khaliq, A., Kleefeld, B., **Liu, R.** (2012). "Solving complex PDE systems for pricing American options with regime-switching by efficient exponential time differencing schemes." *Numerical Methods for Partial Differential Equations*, 29(1), 320-336.

Khan, R. A., **Usman, M.** (2012). "A Study of the GAM Approach to Solve Laminar Boundary Layer Equations in the Presence of a Wedge." *Applied Mathematical Sciences*, 6 (117-120), 5947-5958.

Khan, R. A., **Usman, M.** (2012). "Eventual Periodicity of Forced Oscillations of the Korteweg-de Vries Type Equation." *Applied Mathematical Modeling*, 36 (2), 736-742.

Lee, H. S., Kersaint, G., Harper, S., **Driskell, S. O. S.**, Leatham, K. R. (2012). "Teachers’ statistical problem solving with dynamic technology: Research results across multiple institutions." *Contemporary Issues in Technology and Mathematics Teacher Education*, 12 (3).

Li, Iowa State University, M., Meeker, Iowa State University, W. Q., **Hovey, P. W.** (2012). "Joint Estimation of NDE Inspection Capability and Flaw-size Distribution for In-service Aircraft Inspections." *Research in Nondestructive Evaluation*, 23 (2), 20 pages.

**Liu, R.** (2012). "A New Tree method for Pricing Financial Derivatives in A Regime-Switching Mean-Reverting Model." *Nonlinear Analysis: Real World Applications*, 13 (6), 2609-2621.

**Mashburn, J. D.** (2012). "A Spectral Order for Infinite Dimensional Quantum Spaces." *Mathematical Structures in Computer Science*, 23 (1), 95-130.

McHugh, L., Gardstrom, S. C., Hiller, J. M., Brewer, M., **Diestelkamp, W. S.** (2012). "The Effect of Pre-Meal, Vocal Re-Creative Music Therapy on Nutritional Intake of Residents With Alzheimer’s Disease and Related Dementias: A Pilot Study." *Music Therapy Perspectives*, 30 (1), 32-42.

Mergia, W. Y., **Qumsiyeh, M.**, Eustace, D. (2012). "Exploring Factors Contributing to Injury Severity at Freeway Merging and Diverging Locations in Ohio." *Transportation Research Record*.

Mohyud-Din, S. T., Negahdary, E., **Usman, M.** (2012). "A Meshless Method of Lines for Numerical Solution of the Family of Generalized Fifth-Order Korteweg-de Vries Equations." *International Journal of Numerical Method for Heat and Fluid Flow*, 22 (5).

**Qumsiyeh, M.** (2012). "An L^2 Comparison Between the Bootstrap and the Empirical Edgeworth Expansion." *Communications in Statistics, Theory and Methods*, 41 (1-3), 251-261.

**Qumsiyeh, M., Shaughnessy, G. J.** (2012). "Comparison of Re-sampling Methods to Generalized Linear Models and Transformations in Factorial and Fractional Factorial Designs." *Journal of Modern Applied Statistical Methods*.

**Qumsiyeh, M., Shaughnessy, G. J.** (2012). "Comparison of Re-sampling Methods to Generalized Linear Models and Transformations in Factorial and Fractional Factorial Designs." *Journal of Modern Applied Statistical Methods*.

**Raffoul, Y. N.** (2012). "Discrete Population Models With Asymptotically Constant Or Periodic Solutions." *International Journal of Difference Equations*, 6 (2), 143-152.

**Raffoul, Y. N.**, Adivar, M. N. (2012). "Inequalities and exponential stability and instability in finite delay Volterra integro-differential equations." *Rendiconti del Circolo Matematico di Palermo*, 61 (3), 307-319.

**Raffoul, Y. N.**, Adivar, M. N. (2012). "Necessary and sufficient conditions for uniform stability of Volterra." Analele Stiintifice ale Universitatii Ovidius Constanta, *Seria Matematica*, XX (3), 1-13.

**Raffoul, Y. N.**, Adivar, M. N., Koyuncuoğlu, H. (2012). "Classification of positive solutions of nonlinear systems of Volterra integro-dynamic equations on time scales." *Communications in Applied Analysis*, 16 (3), 359-376.

**Raffoul, Y. N.**, Huang, Z. (2012). "Biperiodicity in Neutral-Type Delayed Difference Neural Networks." *Advances in Difference Equations*, 2012 (5), 15.

## Newsletter

**Higgins, A. W.**, Stevens, T. C. (2012). In Ivars Peterson, Lois Baron (Ed.), *Gallian and LaRose Leave Project NExT Team* (5th ed., vol. 32, pp. 20-21). Washington, DC: Mathematical Association of America.

## Other

Harper, S. R., **Driskell, S. O. S.** “Using GeoGebra to enhance prospective middle school teachers’ classification of two-dimensional shapes.” GeoGebra Institute of Ohio Midwest Regional Conference, GeoGebra Institute of Ohio, Oxford, OH. (June 11, 2012).

Harper, S. R., **Driskell, S. O. S.** “Exploring middle grades geometry using Google SketchUp.” National Council of Teachers of Mathematics Annual Conference, National Council of Teachers of Mathematics, Philadelphia, PA. (April 27, 2012).

**Higgins, A. W.** “Outlets for Undergraduate Research.” Trends in Undergraduate Research in the Mathematical Sciences, Mathematical Association of America, National Science Foundation, National Security Agency, Rosemont, IL. (October 28, 2012).

**Higgins, A. W.** “Mentoring Success Stories.” Keys to Academics’ Success: Faculty Mentoring for Success, LEADER (Launching Equity in the Academy across the Dayton Entrepreneurial Region) Consortium, Dayton, OH. (September 27, 2012).

**Higgins, A. W.** “Undergraduate Research - How to Make it Work.” Project NExT Workshop at Mathfest, Mathematical Association of America, Madison, WI. (August 3, 2012).

**Higgins, A. W.** “Undergraduate Research - How to Make it Work.” Project NExT Workshop at Mathfest, Mathematical Association of America, Madison, WI. (August 2, 2012).

**Higgins, A. W.** “Applying for Jobs.” Spring Opportunities, Mathematical Sciences Research Institute, Berkeley, CA. (March 12, 2012).

**Higgins, A. W.**, Gallian, J. “Getting Students Involved in Undergraduate Research.” Joint Mathematics Meetings, Mathematical Association of America, American Mathematical Association, Society for Industrial and Applied Mathematics, Boston, MA. (January 6, 2012).

**Higgins, A. W.**, Gallian, J. “Getting Students Involved in Undergraduate Research.” Joint Mathematics Meetings, Mathematical Association of America, American Mathematical Association, Society for Industrial and Applied Mathematics, Boston, MA. (January 4, 2012).

## Papers

Busch, A. H., Dragan, F., Krishnamurthy, C., Sritharan, R. “Induced and distance-k matchings and some related min-max relations.” 16th SIAM Conference on Discrete Mathematics, Society for Industrial and Applied Mathematics, Halifax, Canada. (June 18, 2012).

**Raffoul, Y. N.** “Recent Results in Functional Differential Equations.” International Conference on The Theory, Methods and Applications of Nonlinear Equations, International Society of Nonlinear Analysis, Texas A&M, Kingsville. (December 19, 2012).

**Raffoul, Y. N.** “Necessary and Sufficient Conditions For Uniform Boundedness In Functional Dierence Equations.” 2012 Fall Eastern Sectional Meeting, American Mathematical Society, Rochester Institute of Technology, Rochester, NY. (September 22, 2012).

**Raffoul, Y. N.** “Exponential Sytability and Instability in Finite Delay Nonlinear Volterra Integro-differential Equations.” The 8th International Conference on Differential Equations and Dynamical Systems, Unversity of Waterloo, Unversity of Waterloo. (August 3, 2012).

**Raffoul, Y. N.** “On the permanence of discrete-time multi-species competition predation system with several delays.” 2012 Spring Eastern Sectional Meeting, American Mathematical Society, George Washington University, Washington DC. (March 17, 2012).

**Raffoul, Y. N.** “Periodicity In General Delay Nonlinear Difference Equations Using Fixed Point Theory.” Joint Mathematics Meeting, American Mathematical Society, Boston. (January 4, 2012).

**Yengulalp, L. C.**, Fleissner, W. “When Cp(X) is Domain Representable.” Spring Topology and Dynamics Conference, Mexico City, Mexico. (March 23, 2012).

## Posters

**Diestelkamp, W. S.**, Mutyam, V., Frisbie, J., Krane, C., Goldstein, D. “Functional role of the aquaglyceroporin, HC-3 in mediating hypotonic-induced cell shape changes in erythrocytes from H. chrysoscelis.” Meeting of the Ohio Physiological Society, Ohio Physiological Society, Dayton, OH. (October 27, 2012).

**Diestelkamp, W. S.**, Mutyam, V., Frisbie, J., Krane, C., Goldstein, D. “Aquaglyceroporin expression and erythrocyte osmoregulation in cultures from freeze tolerant anuran, Cope’s gray treefrog, Hyla chrysoscelis.” FASEB Experimental Biology Meeting, San Diego, CA. (April 21, 2012).

Eads, C. N., Fannin, H. B., **Mashburn, J. D.**, Masthay, M. B. “Microcanonical and Canonical Temperatures in Two-Level Parmagnetic Spin Lattices.” 43rd CERMACS, American Chemical Society, Dearborn, MI. (June 7, 2012).

**Qumsiyeh, M.** “Using the Bootstrap for Estimating the Sample Size in Statistical Experiments.” Joint Statistical Meeting, American Statistical Association, San Diego, California. (July 31, 2012).

**Usman, M.** “A Numerical Study of a Model for In Vitro Inhibition of Cancer Cell Mutation.” Model-based analysis and control of cellular processes, NSF, Purdue University. (October 9, 2012).

## Presentation

Mergia, W., Eustace, D., **Qumsiyeh, M.** “Exploring Factors Contributing to Injury Severity at Freeway Merging and Diverging Locations in Ohio.” 91st TRB Annual Meeting, Transportation Research Board (TRB), Washington, D.C.. (January 24, 2012).