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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

Liu, R. (2011). "Recombining Tree for Regime-Switching Model: Algorithm and Weak Convergence." In Tsoi, A., Nualart, D., Yin, G. (Ed.), Stochastic Analysis, Stochastic Systems, and Applications to Finance (pp. 211-232). World Sci. Publishing.

Book Reviews

Diestelkamp, W. S. (2011). "Review of Design of experiments: An introduction based on linear models” by Max Morris. Providence, RI.

Contracts

Hovey, P. W. (Principal). “Visiting Professor at the UA Air Force Academy.” Sponsored by US Air Force, $122,707. (July 6, 2010 - May 25, 2011).

Keen, V. L. (Principal). “Math in the Early Childhood Classroom (and Beyond) Part II.” Sponsored by Miami Valley Child Development Centers, $1,000. (March 25, 2011).

Pinnell, M. F. (Co-Principal), Krane, C. M. (Co-Principal), Diestelkamp, W. S. (Supporting), Allen, D. L. (Supporting). “R-18988: Tissue Welding Assessment.” Sponsored by Ethicon Endosurgery, $53,889. (April 1, 2011 - August 15, 2012).

Grants

Bigelow, K. E. (Principal), Diestelkamp, W. S. (Supporting), Krane, C. M. (Supporting), Pinnell, M. F.(Supporting).”Multi-disciplinary STEM Grant Preparation Support in Bioengineering.” Sponsored by National Science Foundation Advance-LEADER Consortium Mini-Grant, $5,000. (December 2010 - December 2011).

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).

Eloe, P. W. (Principal). “Regional Undergraduate Mathematics Conference.” Sponsored by National Science Foundation Grant DMS-0846477, $1,750. (June 1, 2011 - December 30, 2011).

Keen, V. L. (Principal). “Evidence of Mathematics Learning through Storybooks.” Sponsored by University of Dayton Research Council, $5,000. (January 1, 2011 - September 30, 2011).

Krakowski, R. J. (Co-Principal). “Mathematics, Life and Physical Science Professional Development Program for 4-12 Grade Teachers.” Sponsored by Ohio Board of Regents -Improving Teacher Quality Grant, $185,378. (April 1, 2010 - May 31, 2011).

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 - National Science Foundation Advance Program, $5,000. (January 1, 2010 - June 30, 2012).

Qumsiyeh, M. (Principal). “Seed Grant.” Sponsored by University of Dayton, $4,800. (May 1, 2011 - October 1, 2011).

Usman, M. (Principal). “A Computational Study of Bioheat Propagation in Living Tissue.” Sponsored by University of Dayton Research Institute, $5,000. (May 16, 2011 - August 15, 2011).

Yengulalp, L. C. (Principal). “AWM Travel Grant.” Sponsored by Association for Women in Mathematics, $700. (March 2011).

Journal Articles

Abueida, A. A., Lefevre, J., Waterhouse, M. (2011). "Equitable edge colored Steiner Triple Systems." Australasian Journal of Combinatorics, 50, 153-61.

Diestelkamp, W. S., Krane, C. M., Pinnell, M. F. (2011). "Design of a factorial experiment with randomization restrictions to assess medical device performance on vascular tissue." BMC Medical Research Methodology, 11(75), 1-6.

Eloe, P. W., Atici, F. (2011). "Linear systems of fractional nabla difference equations." Rocky Mountain Journal of Mathematics, 41, 353-370.

Eloe, P. W., Atici, F. (2011). "Two-point boundary value problems for finite fractional difference equations." Journal of Difference Equations and Applications, 17, 445-456.

Eloe, P. W., Henderson, J. (2011). "Optimal Intervals for Uniqueness of Solutions for Nonlocal Boundary Value Problems." Communications on Applied Nonlinear Analysis, 18, 89-97.

Eloe, P. W., Henderson, J. (2011). "Uniqueness implies existence and uniqueness conditions for a class of (k+j) - point boundary value problems for nth order differential equations." Mathematische Nachrichten, 284, 229-239.

Eloe, P. W., Khan, R., Asif, N. (2011). "Existence of positive solutions to a singular system of boundary value problems." Dynamics of Continuous and Impulsive Systems, Series A: Mathematical Analysis, 18, 353-361.

Eloe, P. W., Khan, R., Ur Rehman, M. (2011). "Positive solutions of nonlocal boundary value problem for higher order fractional differential system." Dynamic Systems and Applications, 20, 169-182.

Eloe, P. W., Liu, R. (2011). "Upper and Lower Solutions for Regime-Switching Diffusions with Applications in Financial Mathematics." SIAM Journal on Applied Mathematics, 71(4), 1354-1373.

Eloe, P. W., Usman, M. (2011). "Fully Nonlinear Boundary Value Problems with Impulses." Electronic Journal of Qualitative Theory of Differential Equations(21), 1-11.

Eustace, D., Indupuru, V. K., Hovey, P. W. (2011). "Identification of Risk Factors Associated with Motorcycle Related Fatalities in Ohio.” Paper under review by the ASCE Journal of Transportation Engineering. ASCE Journal of Trans-portation Engineering, 137(7), 437-480.

Islam, M. N. (2011). "Three fixed point theorems; periodic solutions of Volterra type integral equation with infinite heredity." Canadian Mathematical Bulletin.

Islam, M. N. (2011). "Periodic solutions of Volterra type integral equations with finite delay." Communications in Applied Analysis, 15(1), 57-68.

Keen, V. L., Rose, A. (2011). "The Pen Pal Partnership Project: Connecting Theory to Practice." Journal of Urban Mathematics Education, 4(2), pp. 15-25.

Khan, R. A., Usman, M. (2011). "Eventual Periodicity of Forced Oscillations of the Korteweg-de Vries Type Equation." Applied Mathematical Modelling, 36(2), 736-742.

Liu, R., Zhang, Q. (2011). "Valuation of guaranteed equity-linked life insurance under regime-switching model." Dynamic Systems and Applications, 20, 101-128.

Mohyud-Din, S. T., Yildirim, A., Usman, M. (2011). "Homotopy Analysis Method for Fractional Partial Differential Equations." International Journal of the Physical Sciences, 6(1), 136-145.

Qumsiyeh, M., Kirchner, K. (2011). "Estimation Methods for Missing Data in Un-Replicated 2^k Factorial and 2^(k-p) Fractional Factorial Designs." Journal of Statistics: Advances in Theory and Applications, 4(2), 91–106.

Raffoul, Y. N. (2011). "Large Contraction and Existence of Periodic Solutions in Infinite Delay Volterra Integro-differential Equations," Journal of Mathematical Sciences: Advances and Applications, 11(2), 69-77.

Raffoul, Y. N. (2011). "Classification of Positive Solutions of Nonlinear Systems of Volterra Integral Equations." Ann. Funct. Anal., 2(2), 34-41.

Raffoul, Y. N. (2011). "Exponential Stability and Instability in Multiple Delay Differential Equations." International Journal of Mathematics Sciences and Applications, 1(2), 120-134.

Raffoul, Y. N. (2011). "Inequalities And Exponential Decay In Time Varying Delay Differential Equations." Mathematical and Computer Modelling, 54(2011), 794-802.

Raffoul, Y. N. (2011). "Positive Periodic Solutions In Neutral Dynamic Equations on a Time Scales." Nonlinear Studies, 18(1), 75-85.

Rivas, I., Usman, M., Zhang, B.-Y. (2011). "Global Well-Posedness and Asymptotic Behavior of a Class of Initial-Boundary-Value Problems of the KdV Equation on a Finite Domain." Mathematical Control and Related Fields, 1(1), 61-81.

Usman, M., Singh, A. (2011). "A New Under-graduate Curriculum on Mathematical Biology at University of Dayton." Journal of STEM Education, 12(5 & 6), 58-66.

Usman, M., Yildirim, A., Mohyud-Din, S. T. (2011). "A Reliable Algorithm for Physical Problems." International Journal of Physical Sciences, 6(1), 146-153.

Other

Blust, R. P., Diestelkamp, W. S., Donnelly, P. G., Hughes, S. M. Hassell, L. R., E. S. “Making UD’s Faculty Maternity Leave Policy Work for Everyone.” Faculty Exchange Series on Faculty Maternity Leave, University of Dayton Faculty Development Committee, LTC. (October 19, 2011).

Driskell, S. O.S., Browning, C., Harrington, R. A., Johnston, C., Niess, M. L. “Preparing teachers to integrate technology in teaching mathematics: What the research tells us.” Association of Mathematics Teacher Educators 15th Annual Conference, Association of Mathematics Teacher Educators, Irvine, CA. (January 28, 2011).

Driskell, S. O.S., Harper, S. R. “Geometry and PreCalculus Investigations using GeoGebra.” 61st Annual Ohio Council of Teachers of Mathematics Conference, Ohio Council of Teachers of Mathematics, Toledo, OH. (October 13, 2011).

Harper, S. R., Shay, N., Driskell, S. O.S. “Interactive geometry in more dimensions using Google SketchUp.” National Council of Teachers of Mathematics 2011 Annual Meeting, National Council of Teachers of Mathematics, Indianapolis, IN. (April 14, 2011).

Higgins, A. W. “Undergraduate Research - How to Make it Work.” Project NExT Workshop at Mathfest, Mathematical Association of America, Lexington, KY. (August 5, 2011).

Higgins, A. W. “Undergraduate Research - How to Make it Work.” Project NExT Workshop at Mathfest, Mathematical Association of America, Lexington, KY. (August 4, 2011).

Higgins, A. W. “Getting Students Involved in Undergraduate Research.” Joint Mathematics Meetings, Mathematical Association of America, American Mathematical Association, Society for Industrial and Applied Mathematics, New Orleans, LA. (January 8, 2011).

Keen, V. L. “Connecting Mathematics Learning with Teaching.” Joint Mathematics Meetings, Mathematical Association of America and the American Mathematical Society, New Orleans, LA. (January 6, 2011).

Lee, H. S., Driskell, S. O.S., Harper, S. R., Jones, D. L., Kersaint, G. “Creating a framework to examine mathematics teachers’ exploratory data analysis.” National Council of Teachers of Mathematics 2011 Research Presession, National Council of Teachers of Mathematics, Indianapolis, IN. (April 12, 2011).

Ronau, R. N., Rakes, C. R., Niess, M. L., Pugalee, D. K., Driskell, S. O.S., Bush, S. “Research in mathematics instructional technology: Current Trends and Future Demands.” Association of Mathematics Teacher Educators 15th Annual Conference, Association of Mathematics Teacher Educators, Irvine, CA. (January 28, 2011).

Usman, M. “A Study of Bifurcations in Steady State Solutions of a Forced Kuramoto-Sivashinsky Equation.” The Seventh IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, University of Georgia and NSF, Athens, GA. (April 6, 2011).

Yengulalp, L. C. (Principal). “Summer Research Fellowship.” Sponsored by University of Dayton Research Council, $4,800. (June 10, 2011 - August 25, 2011).

Papers

Abueida, A. A. “The spectrum of non-polychromatic equitable edge colored Steiner Triple Systems.” Canadian Discrete and Algorithmic Mathematics Conference, Fields Institute, University of Victoria, CMS. SMC, Victoria, Canada. (May 31, 2011).

Busch, A. H., Dragan, F., Krishnamurthy, C., Sritharan, R. “Induced/distance-k matchings and min-max relations.” Fifth Workshop on Graph classes, Optimiation, and Width Parameters, KAIST, South Korea, Daejeon, South Korea. (October 29, 2011).

Busch, A. H., Dragan, F., Sritharan, R., Krishnamurthy, C. “Largest induced matching: computation and min-max relations.” Canadian Discrete and Algorithmic Mathematics Conference, University of Victoria, Canada, Victoria, Canada. (June 3, 2011).

Driskell, S. O.S., Ronau, R. N., Rakes, C. R., Bush, S., Niess, M. L., Pugalee, D. K. “Research in mathematics educational technology: Current trends and future demands.” 33rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, North American Chapter of the International Group for the Psychology of Mathematics Education, Reno, NV. (October 21, 2011).

Eloe, P. W., Altwaty, A., Altwaty, A. “Boundary Value Problems for Impulsive Differential.” Differential Equations Meeting, Nonlinear Dynamics and Systems, Atlanta, GA. (May 24, 2011).

Eloe, P. W., Henderson, J., Altwaty, A. “Concavity and Avery Type Fixed Point Theorems.” Sectional Meeting, American Mathematical Society, Winston-Salem, NC. (September 21, 2011).

Islam, M. N. “Three fixed point theorems and periodic solutions of integral equations.” Mathematics Colloquium, Department of Mathematics, UD, Dayton, Ohio. (September 22, 2011).

Lee, H. S., Driskell, S. O.S., Harper, S. R., Leatham, K. R., Kersaint, G., Angotti, R. L. “Prospective teachers’ use of representations in solving statistical tasks with dynamic statistical software.” 33rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, North American Chapter of the International Group for the Psychology of Mathematics Education, Reno, NV. (October 21, 2011).

Raffoul, Y. N. “Necessary and sufficient conditions for uniform stability in volterra systems of integro-dynamic equations on time scale.” 2011 Fall Central Section Meeting, American Mathematical Society, American Mathematical Society, University of Nebraska-Lincoln, Lincoln, NE. (October 16, 2011).

Raffoul, Y. N. “Classification Of Positive solutions Of Nonlinear Systems Of Volterra Integro-Dynamic Equations On Time Scales.” The 31st Southeastern-Atlantic Regional Conference on Differential equations, Georgia Southern University. (October 1, 2011).

Raffoul, Y. N. “Positive periodic solutions in neutral dynamic equations on time scale.” 2011 Spring Southeastern meeting, American Mathematical Society, American Mathematical Society, Georgia Southern University. (March 12, 2011).

Yengulalp, L. C. “Non-normality points in beta X..” Spring Topology and Dynamical Systems Conference, University of Texas - Tyler. (March 18, 2011).

Papers Published in Conference Proceedings

Driskell, S. O.S., Ronau, R. N., Rakes, C. R., Bush, S., Niess, M. L., Pugalee, D. K. (2011). "Research in mathematics educational technology: Current trends and future demands." Reno, NV: North American Chapter of the International Group for the Psychology of Mathematics Education.

Lee, H. S., Driskell, S. O.S., Harper, S. R., Leatham, K. R., Kersaint, G., Agnotti, R. L. (2011). "Prospective teachers’ use of representations in solving statistical tasks with dynamic statistical software." Reno, NV: North American Chapter of the International Group for the Psychology of Mathematics Education.

Posters

Hovey, P. W., Eustace, D., Griffin, V., Chowdhury, M. “Empirical Bayes Estimation of Roadway Improvements.” Joint Statistics Meetings, American Statistical Association, Miami Beach, FL. (August 3, 2011).

Qumsiyeh, M., Shaughnessy, G. J. “Comparison of Resamling Methods to Generalized Linear Model snd Transformations.” Joint Statistical Meeting, American Statistical Association, Miami Beach, Florida. (August 1, 2011).

Presentations (Invited Lectures or Addresses)

Busch, A. H., Ferrara, M. J., Hartke, S. G., Jacobson, M. S. “Ramsey-type Numbers for Degree Sequences.” 2011 Joint Mathematics Meetings, American Math. Soc. and Math. Assoc. of America, New Orleans, LA. (January 9, 2011).

Higgins, A. W. “Demonic Graphs and Undergraduate Research.” Carleton Summer Mathematics Program, Carleton College, Northfield, MN. (June 21, 2011).

Higgins, A. W. “Demonic Graphs and Undergraduate Research.” Annual meeting of the Metropolitan New York Section of the Mathematical Association of America, Metropolitan New York Section of the Mathematical Association of America, Stony Brook, NY. (May 1, 2011).

Higgins, A. W. “Is pebbling useful, or is it just for fun?” Pi Mu Epsilon Ohio Zeta Chapter Initiation, Pi Mu Epsilon Ohio Zeta Chapter, Dayton, OH. (April 27, 2011).

Islam, M. N. “Bounded solutions of almost linear Volterra equations.” The 31st Southeastern Atlantic regional Conference on Differential Equations, Georgia Southern University, Statesboro, Georgia. (October 1, 2011).

Islam, M. N. “Bounded solutions of nonlinear Volterra integrodifferential equations.” The Sixth International Conference on Dynamic Systems and Applications, Morehouse College -Division of Science and Mathematics, Atlanta, Georgia. (May 27, 2011).

Keen, V. L., Ertle, K., Bucher, J. L. “Strengthening Mathematical Knowledge through Video Creation.” Annual Meeting, National Council of Teachers of Mathematics, Indianapolis, IN. (April 15, 2011).

Keen, V. L., Smethurst, K., Kleiner, S. “Student-created Geometry Books for Kids: A Transforming Partnership.” Annual Meeting, National Council of Teachers of Mathematics, Indianapolis, IN. (April 15, 2011).

Liu, R. “Option Pricing in Regime-Switching Models (part 2).” Department of Mathematical Sciences Graduate Seminar, Stevens Institute of Technology, Hoboken, NJ. (October 31, 2011).

Liu, R. “Option Pricing in Regime-Switching Models (part 1).” Department of Mathematical Sciences Graduate Seminar, Stevens Institute of Technology, Hoboken, NJ. (October 24, 2011).

Liu, R. “Regime-Switching Recombining Tree for Option Pricing.” Department of Mathematical Sciences Seminar, Stevens Institute of Technology, Hoboken, NJ. (April 25, 2011).

Usman, M. “Development of Interdisciplinary Mathematical Biology Course at the University of Dayton.” Ohio NExT Workshop, MAA and University of Findlay, University of Findlay, OH. (October 21, 2011).

Yengulalp, L. C. “Non-normality points in beta X..” AMS section meeting, AMS, Georgia Southern University. (March 12, 2011).

Technical Reports

Smith, F. R., Boehnlein, T. R., Hovey, P. W., Miedlar, P. C., Berens, A. P. (2011). PRoF v3.1 PRobability Of Failure Aging Aircraft Risk Analysis Update.

Smith, F. R., Boehnlein, T. R., Hovey, P. W., Miedlar, P. C., Berens, A. P. (2011). PRoF v3.1 PRobability Of Failure COM Manual.

Smith, F. R., Boehnlein, T. R., Hovey, P. W., Miedlar, P. C., Berens, A. P. (2011). PRoF v3.1 PRobability Of Failure User’s Manual.

Workshops

Diestelkamp, W. S. “Advising undergraduate mathematics students.” Project NExT Workshop, Mathematical Association of America, Lexington, KY. (August 2, 2011).

Eloe, P. W. “Blending Knowledge, Skills and Experience in a Professional Science Master’s Program.” NPSMA’s Best Practices Workshop, NPSMA, Buffalo, NY. (October 14, 2011).

Keen, V. L. “Transforming Instruction and Assessment Using Student-created Video.” Turning Dreams into Reality: Transformations and Paradigm Shifts in Mathematics Education, The Mathematics Education into the 21st Century Project, Grahamstown, South Africa. (September 12, 2011).

University of Dayton, Ohio

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