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 Reviews
Diestelkamp, W. S. (2009). Review of “Design and analysis of experiments - Classical and regression approaches with SAS”. http://www.ams.org/mathscinet/pdf/2440558.pdf.
Contracts
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 - December 2009).
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).
Hovey, P. W. (Co-Principal), Smith, F. R., Boehnlein, T. R.. “Probability of Fracture (PROF) Software Update.” Sponsored by U.S. Air Force Research Laboratory, $185,000. (June 2009 - August 2010).
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, $4,830. (October 1, 2008 - December 31, 2009).
Driskell, S. O.S. (Supporting), Brown, D. J. (Principal). “Dayton Public Schools and Wright State University: Mathematics Inquiry Professional Development Program For Grades 6-12 Teachers.” Sponsored by Ohio Department of Education, K-12 Math Professional Development, $358,798. (June 2008 - June 2009).
Eloe, P. W. (Principal). “Regional Undergraduate Mathematics Conference.” Sponsored by National Science Foundation Grant DMS-0846477, $1,720. (2009).
Keen, V. L. (Principal). “Strengthening Mathematical Understanding through Student Products.” Sponsored by University of Dayton Research Council, $6,000. (January 1, 2009 - December 31, 2009).
Keen, V. L. (Co-Principal). “WeEXCEL.” Sponsored by Ohio Mathematics and Science Partnerships Program, $492,800. (January 1, 2009 - May 31, 2009).
Krakowski, R. J. (Co-Principal). “Mathematics Inquiry Professional Development Program for Grades 6-12 Teachers.” Sponsored by Ohio Department of Education, $177,649. (July 1, 2008 - June 30, 2009).
Krakowski, R. J. (Co-Principal). “WeEXCEL Science and Math Teacher Academies.” Sponsored by Ohio Department of Education, $849,367. (April 2006 - June 2009).
Qumsiyeh, M. (Principal). “University of Dayton Research Council Seed Grant.” Sponsored by University of Dayton, $3,000. (May 1, 2009 - January 1, 2010).
Usman, M. (Principal). “Development of Efficient Meshfree Numerical Schemes to Study Long Time Dynamics of the Korteweg-de Vries Equation.” Sponsored by University of Dayton Research Institute, $6,000. (May 2, 2009 - August 15, 2009).
Invited Lectures
Abueida, A. A. “How many with discrete Mathematics?.” The Seventh Math Day 2009, United Arab Emirates University, Alain, UAE. (April 22, 2009).
Abueida, A. A. “Who is it? with Discrete Mathematics.” The Seventh Math Day, United Arab Emirates University, Alain, UAE. (April 20, 2009).
Busch, A. H. “Arc-traceable tournaments and related digraphs.” Workshop on Paths, Cycles and Related Structures, University of Colorado Denver, Denver, CO. (July 22, 2009).
Busch, A. H., Chen, G., Jacobson, M. S. “Tournament score sequences with partition k-transitive realizations.” 2nd Canadian Discrete and Algorithmic Mathematics Conference, Centre de recherches mathématiques, Montreal, PQ. (May 27, 2009).
Busch, A. H., Jacobson, M. S. “Anti-directed hamiltonian cycles in digraphs.” 2009 SIAM Annual Meeting, Society of Industrial and Applied Mathematics, Denver, CO. (July 10, 2009).
Higgins, A. W. “Demonic Graphs and Undergraduate Research.” Conference on Undergraduate Research in Mathematics, Pennsylvania State University, State College, PA. (November 20, 2009).
Higgins, A. W. “Directing Undergraduate Research - Issues Beyond Solving the Mathematical Problem.” Mathfest, Mathematical Association of America, Portland, OR. (August 8, 2009).
Higgins, A. W. “Pebbling – Demonic Graphs and Troop Deployment.” Colloquium, California State University San Bernardino, San Bernardino, CA. (June 3, 2009).
Higgins, A. W. “Pebbling – Demonic Graphs and Troop Deployment.” Case Lecture, Saint Louis University, St. Louis, MO. (April 24, 2009).
Higgins, A. W. “Demonic Graphs and Undergraduate Research.” Pacific Coast Undergraduate Mathematics Conference, Pacific Coast Undergraduate Mathematics Conference, University of California, Riverside, CA. (March 14, 2009).
Higgins, A. W. “Demonic Graphs and Undergraduate Research.” Graduate Seminar, California State University Channel Islands, Camarillo, CA. (February 4, 2009).
Higgins, A. W., Higgins, W. J., Wyels, C. “Achievable Pebbling Numbers.” Graph Theory Seminar, Saint Louis University, St. Louis, MO. (April 24, 2009).
Islam, M. N. “Almost Linear Equations.” Departmental Colloquium, University of Dayton Mathematics Department, Dayton, OH. (October 1, 2009).
Keen, V. L. “Mathematical Knowledge for Teaching: An Assessment Project.” Teaching Fellows Program, University of Dayton, Dayton, OH. (March 2009).
Liu, R. “Regime-Switching Recombining Tree for Option Pricing.” Department of Mathematics Seminar, Wayne State University, Detroit, MI. (October 8, 2009).
Usman, M. “I don’t like Math because it is abstract, boring, does not make any sense!.” Colloquium, Sinclair Community College, Dayton, OH. (May 15, 2009).
Usman, M. “Some theoretical and computational results about the forced oscillations of the Korteweg-de Vries equation.” Department of Mathematics, Western Illinois University, Macomb, IL. (April 9, 2009).
Journal Articles
Abueida, A. A., Clark, S., Leach, D. (2009). Multidecomposition of the complete graph into graph pairs of order 4 with various leaves. Ars Combinatoria, 93, 403-407.
Abueida, A. A., Roberts, D. (2009). Uniform k-Distant Even Trees are Harmonious. Utilitas Mathematica, 78, 279-285.
Beder, J. H., Diestelkamp, W. S. (2009). Box-Hunter resolution in nonregular fractional factorial designs. Journal of Statistical Theory and Practice, 3(4), 879-889.
Eloe, P. W., Atici, F. (2009). Discrete fractional calculus with the nabla operator. Electronic Journal of Qualitative Theory of Differential Equations, 2009 (Special Edition 1), 1-12.
Eloe, P. W., Atici, F. (2009). Initial value problems in discrete fractional calculus. Proceedings of the American Mathematical Society, 137, 981-989.
Eloe, P. W., Liu, R., Sun, J. (2009). Double barrier options under regime-switching exponential mean-reverting processes. International Journal of Computer Mathematics, 86(6), 964-981.
Eustace, D., Griffin, V. G., Hovey, P. W. (2010). Analyzing the Effects of L.E.D. Traffic Signals on Urban Intersection Safety. ITE Journal 80(4).
Islam, M. N., Raffoul, Y. N. (2009). Bounded solutions and periodic solutions of almost linear Volterra equations. CUBO, A Mathematical Journal, 11(3), 115-124.
Khaliq, A., Liu, R. (2009). New numerical scheme for pricing American option with regime-switching. International Journal of Theoretical and Applied Finance, 12(3), 319-340.
Laubach, L., K. P., Hovey, P. W., Linderman, J. (2009). A Modest Increase in Weekly Step Counts Improved Cardiovascular Function in Healthy Elderly Women. Journal of Exercise Physiology Online, 12(6), 25-32.
Liu, R. (2009). Analytical approximation method of option pricing under geometric mean-reverting process. International Journal of Computer Mathematics, 86(6), 1082-1092.
Liu, R., Raffoul, Y. N. (2009). Boundedness and exponential stability of highly nonlinear stochastic differential equations. Electronic Journal of Differential Equations, 2009(143), 1-10.
Mashburn, J. D. (2009). Linearly ordered topological spaces and weak domain representability. Topology Proceedings, 35, 149-164.
Niess, M. L., Ronau, R. N., Shafer, K., Driskell, S. O.S., Harper, S. R., Johnston, C., Browning, C., Özgün-Koca, S. A., Kersaint, G. (2009). Mathematics teacher TPACK standards and development model. Contemporary Issues in Technology and Teacher Education, 9(1), 4-24
Raffoul, Y. N. (2009). Stability and Periodicity in Dynamic Delay Equations. Computer and Mathematics with Applications, 28(2), 264-272.
Raffoul, Y. N. (2009). The Connection Between Boundedness and Periodicity in Nonlinear Functional Neutral Dynamic Equations on a Time Scale. Nonlinear Dynamics and Systems Theory, 9(1), 89-98.
Raffoul, Y. N. (2009). Inequalities That Lead To Exponential Stability And Instability In Delay. Journal of Inequalities in Pure and Applied Mathematics, 10(3),
Usman, M., Mohyud-Din, S. T., Yildirim, A., Sezer, S. A. Modified Variational Iteration Method for Free-convective Boundary-layer Equation Using Pade´ Approximation. Mathematical Problems in Engineering, 2010, (11).
Usman, M., Poteet, M. (2009). Stability of steady state solutions of the forced Kuramoto-Sivashinsky (KS) equation. Advances in Differential Equations and Control Processes, 4(2), 119-131.
Usman, M., Zhang, B. (2009). Forced oscillations of the Korteweg-de Vries equation on a bounded domain and their stability. Discrete and Continuous Dynamical Systems-Series A, 26(4), 1509-1523.
Other Intellectual Contributions
Diestelkamp, W. S. “Joining the Mathematical Community.” Project NExT Workshop, Mathematical Association of America, Portland, OR. (August 3, 2009).
Driskell, S. O.S., Harper, S. R. “Fostering spatial visualization ability through hands-on and technology-based.” 59th Annual Conference of the Ohio Council of Teachers of Mathematics, Ohio Council of Teachers of Mathematics, Cincinnati, OH. (November 12, 2009).
Higgins, A. W. “Directing Undergraduate Research.” Joint Mathematics Meetings, Mathematical Association of America, American Mathematical Association, Society for Industrial and Applied Mathematics, Washington, DC. (January 2009).
Keen, V. L. “Strengthening Mathematics Knowledge with Streaming Video.” MathFest 2009, Mathematical Association of America, Portland, OR. (August 8, 2009).
Keen, V. L. “Mathematics Tasks with Classroom Connections.” MathFest 2009, Mathematical Association of America, Portland, OR. (August 7, 2009).
Keen, V. L. “Using Video for Enhanced Student Learning of Mathematics: An Action Research Project.” WeEXCEL Spring Conference, WeEXCEL Mathematics and Science Partnership, Wright State University, Dayton, OH. (April 1, 2009).
Keen, V. L., Doenges, B., Escobar, H. “Strengthening Learning and Skill Development through Video-Based Student Presentations.” Faculty Exchange Seminar, Ryan C. Harris Learning Teaching Center, University of Dayton, Dayton, OH. (April 1, 2009).
Usman, M. “Integral Invariants of a Nonlinear Nonholonomic Dynamical System in Poincare Parameters.” SEARCDE 29, National Science Foundation & Mercer University, Macon, GA. (August 17, 2009).
Yengulalp, L. C. “Topology and set theory.” University of Dayton Undergraduate Math Club, University of Dayton, Dayton, OH. (October 6, 2009).
Papers
Eloe, P. W., Atici, F. “Discrete Fractional Calculus with the Nabla Operator.” Sectional Meeting, American Mathematical Society, Waco, TX. (October 17, 2009).
Eloe, P. W., Henderson, J. “Uniqueness implies existence and uniqueness conditions for a class of (k+j)-point boundary value problems for nth order differential equations.” Joint Mathematics Meetings, American Mathematical Society/Mathematical Association of America/Society for Industrial and Applied Mathematics, Washington, DC. (January 8, 2009).
Hovey, P. W., Krilov, B. “Enhanced Monte Carlo Estimation of Extremely Small Probabilities of Failure.” Joint Statistics Meetings, American Statistical Association and Other Statistical Societies, Washington, DC. (August 5, 2009).
Hovey, P. W., Krilov, B. “Bias Correction When Using the Extreme Value Approximation in Monte Carlo Estimation of High Reliability Systems.” Spring Research Conference on Statistics in Science and Industry, American Statistical Association, Institute of Mathematical Statistics, Vancouver, BC, Canada. (May 27, 2009).
Islam, M. N. “Bounded solutions of almost linear Volterra equations.” 29th Southeastern-Atlantic Regional Conference on Differential Equations, Mercer University, Macon, GA. (October 17, 2009).
Li, M., Meeker, W., Hovey, P. W. “Using a Bayesian Model to Jointly Estimate the Flaw Size Distribution and the POD Function.” Review of Progress in Quantitative Nondestructive Evaluation, Center for Nondestructive Evaluation and Department of Aerospace Engineering, Iowa State University, Kingston, RI. (July 26, 2009).
Niess, M. L., Browning, C., Driskell, S. O.S., Johnson, C., Harrington, R. “Mathematics teacher TPACK standards and revising teacher preparation.” Society for Information Technology & Teacher Education 20th International Conference, Society for Information Technology & Teacher Education, Charleston, SC. (March 5, 2009).
Niess, M. L., Driskell, S. O.S., Ronau, R. N., Pugalee, D., Harper, S. R., Shafer, K., Johnson, C., Browning, C., Kosheleva, O. “Using technology standards for mathematics teachers to design learning environments and experiences for methods courses.” 13th Annual Conference of the Association of Mathematics Teacher Educators, Orlando, FL. (February 5, 2009).
Raffoul, Y. N. “Resolvent and Boundedeness in Volterra Equations on Time Scales.” Fall 2009 Central Sectional Meeting of the American Mathematical Society, American Baylor University, Waco, TX. (October 16, 2009).
Raffoul, Y. N. “Population Models Withy Asymptotically Constant or Periodic Solutions.” Joint Mathematics Meeting, American Mathematical Society, Washington, DC. (January 7, 2009).
Yengulalp, L. C., Gavosto, E., Ward, E. “Implementation of web-based skill exams for Precalculus, Calculus I and Calculus II.” Ohio Section Meeting, Mathematical Association of America, Kenyon College, Gambier, OH. (October 31, 2009).
Papers Published in Conference Proceedings
Higgins, A. W. (2009). In Timothy Y. Chow, Daniel C. Isaksen (Ed.), Communicating, Mathematics, Communicating Mathematics - Joe Gallian style (vol. 479, pp. 119-126). Providence, RI: Contemporary Mathematics/American Mathematical Society.
Qumsiyeh, M., Shaughnessy, G. J. (2009). Using the Bootstrap for Analysis of Unreplicated Two-Level Designs with Missing Responses. Alexandria, VA: Joint Statistical Meeting Proceeding.
Qumsiyeh, M., Shaughnessy, G. J. (2009). Using the bootstrap to select active factors in un-replicated factorial experiments. Alexandria, VA: Joint Statistical Meeting 2008 proceedings.
Patents
Driskell, S.O., O’Connell, A., Smith, D., Le, R., Doepker, P. E., Schenk, D., Becker, S., Craven, J., & Tremblay, V. (August 25, 2009). Shape Shifters, Provisional Patent EFS ID: 5950951, United States.
Posters
Qumsiyeh, M., Shaughnessy, G. J. “Using the Bootstrap for Analysis of Unreplicated Two-Level Designs with missing responses.” Joint Statistical Meeting, American Statistical Association. (August 4, 2009).
Workshops
Diestelkamp, W. S. “Advising undergraduate mathematics students.” Project NExT Workshop, Mathematical Association of America, Portland, OR. (August 5, 2009).
Higgins, A. W. “Undergraduate Research -- How to Make it Work.” Project NExT Workshop at Mathfest, Mathematical Association of America, Portland, OR. (August 7, 2009).
Higgins, A. W. “Undergraduate Research -- How to Make it Work.” Project NExT Workshop at Mathfest, Mathematical Association of America, Portland, OR. (August 6 , 2009).
Higgins, A. W. “Undergraduate research: an introduction to our profession.” Southern California Section Meeting of the Mathematical Association of America, Mathematical Association of America Southern California Section NExT, California Lutheran University, Thousand Oaks, CA. (March 21, 2009).
Keen, V. L. “Millions, Billions, and Double Trouble.” Annual Meeting, Ohio Council of Teachers of Mathematics, Cincinnati, OH. (November 13, 2009).
Keen, V. L., LeComte, J. “Streaming Video for Class.” Techno-Fair 2009, Ryan C. Harris Learning Teaching Center, University of Dayton, Dayton, OH. (May 7, 2009).
