Research & 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.
Book Chapters
Niess, M. L., Ronau, R. N., Driskell, S. O., Kosheleva, O., Pugalee, D. (2008). "Technological Pedagogical Content Knowledge: Preparation of mathematics teachers for 21st century teaching and learning." In Fran Arbaugh and P. Mark Taylor (Ed.), AMTE Monograph series: Inquiry into mathematics teacher education (vol. V, pp. 143-156). San Diego, CA: AMTE.
Ronau, R. N., Niess, M. L., Browning, C., Pugalee, D., Driskell, S. O., Harrington, R. (2008). "Framing the research on digital technologies and student learning in mathematics." In Bell, L., Schrum, L., Thompson, A. D. (Ed.), Framing research on technology and student learning in the content areas: Implications for educators (pp. 13-31). Charlotte, NC: Information Age Publishing.
Contracts
Diestelkamp, W. S. (Supporting), Krane, C. M. (Co-Principal), Pinnell, M. F. (Co-Principal). "Assessing the causes of variability in seal quality and tissue changes resulting from the use of the Ethicon Harmonic R surgical system." Sponsored by Ethicon Endo-Surgery, $116,000. (May 2007 - August 2008).
Diestelkamp, W. S. (Supporting), Krane, C. M. (Co-Principal), Pinnell, M. F. (Co-Principal). "Assessing the feasibility of intraluminal ultrasonic tissue welder." Sponsored by Ethicon Endo-Surgery, $115,596. (October 2008).
Hovey, P. W. (Principal). "Statistical Support of the Air Force Materials Laboratory Nondestructive Evaluation Research Branch in the Area of Interpreting Inspection Results for Use in Planning Maintenance of Aging Aircraft." Sponsored by National Institute of Aviation Research, $75,000. (October 2007 - October 2009).
Grants
Abueida, A. A. (Principal), Eloe, P. W. (Co-Principal). "Problem Solving and Critical Thinking with Discrete Mathematics, K-7." Sponsored by Ohio Board of Regents, $311,935. (January 2008 - August 2009).
Busch, A. H. (Principal). "Graphs which contain k disjoint matchings." Sponsored by University of Dayton Research Institute Seed Grant, $4,830. (October 1, 2008 - December 31, 2009).
Busch, A. H. (Principal). "Tournaments with Large Transitive Subtournaments." Sponsored by University of Dayton Research Institute Seed Grant, $5,920. (October 1, 2007 - December 31, 2008).
Driskell, S. (Supporting), Brown, D. (Principal). "Dayton Public Schools and Wright State University: Mathematics Inquiry Professional Development Program For Grades 6-12 Teachers." Sponsored by Dayton Public Schools and Wright State University, $358,798. (June 2008 - June 2010).
Driskell, S. (Co-Principal), Keen, V. L. (Co-Principal). "Programmatic Assessment of Mathematical Content Knowledge for Teaching." Sponsored by West Ohio Center of Excellence for Science and Mathematics Education Mini-Grant 2008, $9,000. (May 2008).
Keen, V. L. (Principal). "Extending van Hiele Levels of Geometric Reasoning to Transformational Geometry." Sponsored by Research Council Seed Grant, $6,000. (January 1, 2008 - December 31, 2008).
Keen, V. L. (Principal). "Tools for the Enhancement of Mathematics Learning." Sponsored by Learning Teaching Center - funding of tool in unfunded Innovation Grant Proposal, $500. (January 2008 - December 2008).
Krakowski, R. J. (Co-Principal). "Science & Math Academies for Teachers through EXCEL." Sponsored by Ohio Department of Education, $492,800. (July 2008).
Krakowski, R. J. (Co-Principal). "Life Science, Physical Science, and Mathematics Professional Development Project for Grades 6-11." Sponsored by Ohio Board of Regents, $202,655. (April 2007 - September 2008).
Krakowski, R. J. (Co-Principal). "WeEXCEL Science and Math Teacher Academies." Sponsored by Ohio Department of Education, $849,367. (April 2006 - June 2008).
Liu, R. (Principal). "Optimal Stopping Problem in Financial Mathematics." $6,000. (May 15, 2008 - August 15, 2008).
Raffoul, Y. N. "Dynamical Systems and Periodic Solutions in Stochastic Differential Equations." Sponsored by The Scientific and Technological Research Council of Turkey, $5,000. (July 2008 - August 2008).
Raffoul, Y. N. "Stochastic Differential Equations." Sponsored by SEE, University of Dayton, $4,500. (May 2008 - August 2008).
Usman, M. (Principal). "Research Council Seed Grant." Sponsored by University of Dayton, $6,000. (May 2, 2008 - August 15, 2008).
Invited Lectures
Abueida, A. A. "Cycle Extension on Two Classes of Graphs." Mathematics Seminar, Department of Mathematics, University of Queensland, Brisbane, Australia. (August 2008).
Abueida, A. A. "Inverse Spread of a Matrix." 9th Research Conference, United Arab Emirates University, Alain, UAE. (March 2008).
Abueida, A. A., Daven, M. "Multidecompositions of graph products." 1st Istanbul Design Theory and Combinatorics Conference, Koc University, Istanbul, Turkey. (June 2008).
Diestelkamp, W. S. "On the difficulty of faking data." Fall Meeting, Ohio Section of the Mathematical Association of America, Columbus, OH. (October 24, 2008).
Diestelkamp, W. S. "Box-Hunter resolution in arbitrary fractional factorial designs." Mathematics Colloquium, Department of Mathematics, Wright State University, Dayton, OH. (May 23, 2008).
Diestelkamp, W. S. "How to lie with statistics." Mathematics Colloquium, Department of Mathematics, Sinclair Community College, Dayton, OH. (May 9, 2008).
Higgins, A. W. "Demonic Graphs and Undergraduate Research." Claremont Colleges Mathematical Colloquium, Claremont Center for the Mathematical Sciences, Claremont, CA. (December 10, 2008).
Higgins, A. W. "Pebbling -- pure and applied." Colloquium, Brigham Young University, Provo, UT. (November 20, 2008).
Higgins, A. W. "Remarks recognizing high achievement inmathematics." Recognition dinner for undergraduates excelling in mathematics, Department of Mathematics, Brigham Young University, Provo, UT. (November 20, 2008).
Higgins, A. W. "Pebbling on Graphs." Summer Mathematics Program, Carleton College, Northfield, MN. (June 26, 2008).
Islam, M. N. "Qualitative Properties of Volterra Equations." World Congress of Nonlinear Analysts - 2008, Florida Institute of Technology, Melbourne, FL. (August 1, 2008).
Liu, R. "New Numerical Scheme for Pricing American Option with Regime-Switching." Department of Mathematical Sciences Seminar, Middle Tennessee State University, Murfreesboro, TN. (October 31, 2008).
Liu, R. "Introduction to Option and Financial Mathematics." The 12th Annual High School Mathematics Contest, University of Dayton, Dayton, OH. (March 1, 2008).
Raffoul, Y. N. "Fixed Point Theory OR Lyapunov Functionals." Workshop on Dyanamical Systems, Izmir University of Economics, Izmir, Turkey. (August 7, 2008).
Raffoul, Y. N. "Boundedness and Exponential Stability In Highly Nonlinear Stochastic Differential Equations." Workshop on Dynalmical Systems, Izmir University of Economics, Izmir, Turkey. (August 3, 2008).
Saintignon, P. L. "Fun with Mathematics." New Student Orientation, University of Dayton, Dayton, OH. (August 18, 2008).
Usman, M. "Initial and Boundary Value Problems of Nonlinear Dispersive Wave Equation." Applied and Computational Mathematics Seminar, Mathematics Department, Ohio University, Athens, OH. (March 10, 2008).
Journal Articles
Abueida, A. A. (2008). "Multidesigns of the complete graph with a hole into the graph-pair of order 4." Bulletin of the Institute of Combinatorics and its Applications, 53, 17-20.
Eloe, P. W., Liu, R., Yatsuki, M., Yin, G., Zhang, Q. (2008). "Optimal selling rules in a regime-switching exponential Gaussian diffusion model." SIAM Journal on Applied Mathematics, 69(3), 810-829.
Islam, M. N., Neugebauer, J. (2008). "Qualitative properties of nonlinear Volterra integral equations." Electronic J. of Qualitative Theory of Differential Equations, 1(12), 1-16.
Mashburn, J. D. (2008). "An order model for infinite classical states." Foundations of Physics, 38(1), 47-75.
Raffoul, Y. N. "A second order boundary value problem with impulsive effects on an unbounded domain." Nonlinear Analysis, 69(9), 2924-2929.
Raffoul, Y. N. (2008). "Existence Results for Periodic solutions of integro-dynamic equations on time scales, Annali di Matematica Pura ed Applicata." Annali di Matematica Pura ed Applicata, 10.
Raffoul, Y. N. (2008). "Impulsive dynamic equations on a time scale." Electronic Journal of Differential Equations, 2008(67), 9.
Raffoul, Y. N. (2008). "On the discrete-time multi-species competition-predation system with several delays." Appl. Math. Let., 2008(1), 15-22.
Raffoul, Y. N. (2008). "Periodicity in nonlinear systems with infinite delay." Adv. Dyn. Syst. Appl, 3(1), 185-194.
Other Intellectual Contributions
Diestelkamp, W. S. "How to lie with statistics – a workshop on deceptive methods in statistics." (April 9, 2008).
Diestelkamp, W. S. "Statistical consulting for a local high school." Joint Mathematics Meetings, Mathematical Association of America, American Mathematical Association, Association for Symbolic Logic, Association for Women in Mathematics, National Association of Mathematicians, Society for Industrial and Applied Mathematics, San Diego, CA. (January 2008).
Keen, V. L. "Mathematical Knowledge for Teaching: An Assessment Project." International Congress on Mathematics Education, The International Commission on Mathematical Instruction, Monterrey, MX. (July 9, 2008).
Krakowski, R. J. "Use of Geometer's Sketchpad and Guided Inquiry to Foster Conceptual Understanding of Precalculus Topics." Joint Mathematics Meetings, Mathematical Association of America, San Diego, CA. (January 2008).
Usman, M. 28th South Eastern-Atlantic Regional Conference on Differential Equations, NSF, University of Arkansas at Little Rock, Little Rock, AR. (October 11, 2008).
Papers
Busch, A. H. "Recognizing Interval Bigraphs." Joint Mathematics Meetings 2008, American Mathematical Society & Mathematical Association of America, San Diego, CA. (January 2008).
Busch, A. H., Brown, D. E., Isaak, G. "Recognition Algorithms for Some Generalizations of Interval Graphs." Math Fest 2008, Mathematical Association of America, University of Wisconsin, Madison, WI. (July 31, 2008).
Busch, A. H., Jacobson, M., Chen, G. "All tournament score sequences are pan-partition transitive." Midwest Graph Theory Conference XLVI, West Virginia University, Morgantown, WV. (April 2008).
Busch, A. H., Jacobson, M., Chen, G. "All tournament score sequences are pan-partition transitive." Discrete Mathematics Seminar, Wright State University, Dayton, OH. (March 2008).
Driskell, S. O.S., Harper, S. R., Edwards, M. T. "Using Fathom with prospective teachers." 12th Annual Conference, Association of Mathematics Teacher Educators, Tulsa, OK. (January 2008).
Eloe, P. W. "Uniqueness implies uniqueness and existence conditions." SEARCDE/NSF, Little Rock, AR. (October 10, 2008).
Eloe, P. W., Liu, R. "Upper and lower solution methods in finance." Joint Mathematics Meetings, AMS/MAA/SIAM, San Diego, CA. (January 8, 2008).
Harper, S. R., Driskell, S. O.S. "Helping middle school students develop spatial visualization skills." Eastern Regional Conference, National Council of Teachers of Mathematics, Cleveland, OH. (October 2008).
Harper, S. R., Driskell, S. O.S., Nickell, J. "Exploring probabilities by simulating card games using Fathom." 86th Annual Meeting, National Council of Teachers of Mathematics, Salt Lake City, UT. (April 2008).
Hovey, P. W. "Using the Information in Field Service Inspections to Assess the Damage State of the Aircraft and the Detection Capability of the Inspection System." Review of Progress in Quantitative Nondestructive Evaluation, QNDE Programs, Chicago, IL. (July 20, 2008).
Hovey, P. W. "Enhanced Monte Carlo Estimation of High Reliability Systems." Spring Research Conference on Statistics in Industry and Technology, American Statistical Association, Atlanta, GA. (May 19, 2008).
Hovey, P. W., Meeker, W. Q., Li, M. "Joint Estimation of the Flaw Size Distribution and Pod Function." Review of Progress in Quantitative Nondestructive Evaluation, QNDE Programs, Chicago, IL. (July 20, 2008).
Islam, M. N. "Almost Linear Volterra Equations." Southeastern Atlantic Regional Conference on Differential Equations, University of Arkansas at Little Rock, Little Rock, AR. (October 11, 2008).
Keen, V. L. "What are they thinking?" National Council of Teachers of Mathematics, Cleveland, OH. (October 17, 2008).
Keen, V. L. "YOU are the Link: Connecting Mathematics and Children’s Books." Professional Development Day, Dayton Association for Young Children, Dayton, OH. (September 27, 2008).
Keen, V. L. "Selecting Children’s Books that Support Learning to Meaningfully Count." Ohio Early Care and Education Conference, Ohio Association for the Education of Young Children, Columbus, OH. (April 5, 2008).
Liu, R. "Regime-Switching Recombining Tree for Option Pricing." American Mathematical Society Fall Central Meeting, Western Michigan University, Kalamazoo, MI. (October 18, 2008).
Liu, R. "Implicit Penalty Method for Pricing American Option with Regime-Switching." CBMS/NSF Regional Research Conference in Mathematical Sciences: Malliavin Calculus and its Applications, Kent State University, Kent, OH. (August 12, 2008).
Nickell, J., Harper, S. R., Driskell, S. O.S. "Using technology-based projects to foster geometric thinking in the middle grades." 86th Annual Meeting, National Council of Teachers of Mathematics, Salt Lake City, UT. (April 2008).
Niess, M. L., Harper, S. R., Browning, C., Ronau, R. N., Shafer, K., Pugalee, D., Driskell, S. O.S. "Preparing teachers with mathematics Technological Pedagogical Content Knowledge." 12th Annual Conference, Association of Mathematics Teacher Educators, Tulsa, OK. (January 2008).
Raffoul, Y. N. "Exponential Analysis of Solutions of Differential Equations with Unbounded Terms." 1044th Sectional Meeting, American Mathematical Society, University of Alabama, Huntsville, AL. (October 23, 2008).
Raffoul, Y. N. "Exponential Analysis of Solutions of Functional Differential Equations with Unbounded Terms." SEARCDE-28, University of Arkansas at Little Rock, Little Rock, AR. (October 11, 2008).
Raffoul, Y. N. "Basic and Recent Results in Differential Equations." World Congress on Nonlinear Analysis, Federation of Nonlinear Analysis, Orlando, FL. (July 3, 2008).
Raffoul, Y. N. "Existence of Periodic and Positive Periodic Solutions in Totally Nonlinear Delay Differential Equations." World Congress on Nonlinear Analysis, Federation of Nonlinear Analysis, Orlando, FL. (July 3, 2008).
Usman, M. "Some interesting examples and applications that I use in the classroom to increase the interest in Numerical Analysis." Ohio NExT Workshop, MAA, Capital University, Columbus, OH. (October 24, 2008).
Usman, M. "Some Interesting Applications of Numerical Analysis in Science and Engineering." MathFest 2008, MAA, Madison, WI. (August 1, 2008).
Usman, M. "A Generalization of Poincare Cartan Integral Invariant for a Nonlinear Nonholonomic Dynamical System." International Conference; Dynamical Systems, Differential Equations and Applications, American Institute of Mathematical Sciences, University of Texas at Arlington, Arlington, TX. (May 20, 2008).
Usman, M., Eloe, P. W. "Bifurcations in Steady State Solution of Damped Forced KdV Equation." 28th SouthEastern-Atlantic Regional Conference on Differential Equations, NSF, University of Arkansas at Little Rock, Little Rock, AR. (October 10, 2008).
Posters
Hovey, P. W., Donahue, R. "Comparisons of the Uses of Logistic and Probit Regression in the Aerospace and Biomedical Fields." Joint Statistical Meetings, American Statistical Association, Denver, CO. (August 3, 2008).
Shaughnessy, G. J., Qumsiyeh, M. "Using the Bootstrap to Select Active Factors in Unreplicated Factorial Experiments." Joint Statistical Meeting, American Statistical Association, Denver, CO. (August 2008).
Workshops
Higgins, A. W. "Undergraduate Research -- how to make it work." Project NExT Workshop at Mathfest, Mathematical Association of America, Madison, WI. (August 2008).
Higgins, A. W. "Directing Undergraduate Research." Joint Mathematics Meetings, Mathematical Association of America, American Math Society, San Diego, CA. (January 2008).
