## Showcasing our scholarship.

The intellectual power and creative vitality of the College of Arts and Sciences reside in our faculty. While students lie at the center of the College’s attention, the work of the College’s faculty makes possible the distinctive education in the liberal arts and sciences that our graduates attain. All of the College’s achievements and aspirations spring in some way from faculty members’ creativity, talent, and dedication in scholarship, teaching, and professional service. Recent faculty research and scholarship projects are listed below.

### Contracts, Grants and Sponsored Research

###### Contracts

Hovey, P. W. (Supporting). "Quick Reaction Evaluation of Materials and Processes." Sponsored by US Air Force Research Laboratories, $10,000. (December 15, 2013 - May 1, 2014). Hovey, P. W. (Co-Principal), Smith, F. R. (Principal), Boehnlein, T. R. (Co-Principal). "A-10 Fleet Management Analysis Tool." Sponsored by US Air Force through Northrup Grumman,$350,000. (November 22, 2013 - March 31, 2015).

###### Grants

Brown, J. M. (Co-Principal), Reznikoff, S. (Principal), Nagy, G. (Co-Principal), "Great Plains Operator Theory Symposium." Sponsored by National Science Foundation, $50,000. (March 1, 2014 - September 1, 2014). Brown, J. M. (Co-Principal), Rumsey, C. (Principal), Bennett, A. (Supporting), Allen, D. (Supporting), Martine, S. (Supporting). "MILeS." Sponsored by Kansas Department of Education,$300,000. (March 1, 2013 - July 1, 2014).

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). 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).

Kublik, C. (Principal). "A new boundary integral algorithm for implicit interfaces." Sponsored by University of Dayton, $6,250. (May 12, 2014 - August 20, 2014). Ren, D. (Principal). "Grant-in-aid." Sponsored by University of Dayton,$1,450. (June 2014 - August 2014).

Ren, D. (Principal). "Research Council Seed Grant." Sponsored by University of Dayton, $5,000. (June 2014 - August 2014). ### Presentations ###### Invited Lectures or Addresses Brown, J. M. "Progress on the Classification of etale groupoid C*-algebras." Colloquium, Wright State University, Dayton OH. (October 31, 2014). Brown, J. M. "The Center of a Leavitt Path Algebra." Colloquium, University of Colorado Colorado Springs, Colorado Springs, CO. (October 8, 2014). Brown, J. M. "Simplicity of groupoid C*-algebras." Colloquium, University of Dayton, Dayton, OH (September 4, 2014). Liu, R. "Optimal Stopping and American Option in Switching Diffusion Models with State Dependent Switching Rates." Department of Mathematics Colloquium, Wayne State University, Detroit, MI. (June 24, 2014). Liu, R. "Optimal Investment and Consumption with Proportional Transaction Costs in Regime-Switching Model." Special Session on Mathematical Finance, American Mathematical Society (AMS) Western Spring Sectional Meeting, University of New Mexico, Albuquerque, NM. (April 5, 2014). Raffoul, Y. N. "Qualitative Analysis of Solutions of Nonlinear Delay Dynamic Equations." SEARCDE-2014, SEARCDE, Univ. of Memphis, TN. (October 11, 2014). Raffoul, Y. N. "Boundedness And Exponential Stability In Highly Nonlinear Stochastic Differential Equations." AMS,Western Spring Sectional Meeting, AMS, University of New Mexico, Albuquerque, NM. (April 5, 2014). Raffoul, Y. N. "Qualitative Analysis of Functional Stochastic Differential Equations." Colloquium, Notre Dame University, Beirut Lebanon. (March 21, 2014). Raffoul, Y. N. "Exponential Stability And Instability In Finite Delay Nonlinear Volterra Integro-Ddifferential And Difference Equations." Colloquium, Balamand University, Balamand University, Lebanon. (March 20, 2014). Raffoul, Y. N. "Qualitative Analysis of Functional Differential equations Using Fixed Point Theory." Colloquium, American University of Beirut. (March 5, 2014). Raffoul, Y. N. "Comparison between fixed point theory and Lyapunov functionals." Colloquium, Notre Dame University, Beirut, Lebanon. (March 3, 2014). Raffoul, Y. N. "Fixed Point Or Lyapunov Functional?” Colloquium, Canakkale Onsekiz Mart University, Canakkale, Turkey. (March 2, 2014). Ren, D. "Shortfall Aversion." SIAM Conference on Financial Mathematics & Engineering, SIAM, Chicago, IL. (November 14, 2014). Ren, D. "Shortfall Aversion." AMS Sectional Meeting, University of New Mexico, Albuquerque, NM. (April 4, 2014). Usman, M. "Sinc Collocation Methods to Study Problems of Korteweg-de Vries and Kuramoto-Sivashinsky type Equations." The 34th Southeastern-Atlantic Regional Conference on Differential Equations (SEARCDE 2014), NSF and University of Memphis, Memphis, TN. (October 12, 2014). ###### Panels and Other Brown, J. M. "Groupoids and the Baire Category Theorem", University of Dayton, Dayton, OH. (September 1, 2014). Driskell, S. O.S., Bush, S. B., Rakes, C. R., Niess, M. L., Pugalee, D. L. "Professional development shifts in mathematics education technology." Association of Mathematics Teacher Educators 18th Annual Conference, Association of Mathematics Teacher Educators, Irvine, CA. (February 7, 2014). Rakes, C. R., Ronau, R. N., Pugalee, D. L., Bush, S. B., Niess, M. L., Driskell, S. O.S. "A survey of mathematics education technology dissertation scope and quality: 1968-2009." American Educational Research Association 2014 Annual Meeting, American Educational Research Association. Philadelphia, PA. (April 5, 2014). ###### Papers Busch, A. H. "Strongly chordal k-trees." Midwest Graph Theory Conference XLV, Indiana University Purdue University Fort Wayne, Fort Wayne, IN. (October 4, 2014). Eloe, P. W., Neugebauer, J. "Application of mu {0} positive operators to boundary value problems for fractional differential equations." National Meeting, American Mathematical Society, Baltimore, MD. (January 18, 2014). Eloe, P. W., Ouyang, Z. "Multi-term linear fractional nabla difference equations with constant coefficients." Sectional Meeting, American Mathematical Society, Greensboro, NC. (November 8, 2014). Islam, M. N. "Asymptotically stable and L^1 solutions of Caputo fractional differential equations." 34th Southeastern-Atlantic Regional Conference on Differential Equations, University of Memphis, Memphis, TN. (October 11, 2014). Yengulalp, L. C. "From subcompact to domain representable." Spring Topology and Dynamics Conference, University of Richmond, Richmond, VA. (March 15, 2014). ###### Posters Eustace, D., Hovey, P. W., Almutari, O. "Using Decision Tree Modeling to Analyze Factors Contributing to Injury and Fatality of Run-Off-Road Crashes in Ohio." Transportation Research Board 93rd Annual, US Department of Transportation, Washington DC. (January 12, 2014). ###### Workshops Usman, M. "Option Pricing using Finite Difference Methods." Delivered a joint workshop on Equity Pricing: Black Scholes and Beyond, with mathematicians from Kent State University and Tata Institute India, Ministry of Education, Government of Pakistan, Lahore University of Management Sciences (LUMS), Pakistan. (May 16, 2014). ### Published Intellectual Contributions ###### Journal Articles Abueida, A. A., Blinco, A., Clark, S., Daven, M., Eggleton, R. (2014). On Heterogeneous Decompositions of Uniform Complete Multigraphs into Spanning Trees. AKCE International Journal of Graphs and Combinatorics, 11(2), 199-220. Abueida, A. A., Lian, C. (2014). Decompositions of Complete Graphs into Cycles and Stars on the same number of edges. Discussiones Mathematicae Graph Theory, 34(1), 113-125. Abueida, A. A., Perkins, C. (2014). Decompositions of complete graphs with holes of the same size into the graph-pair of order 4. JCMCC, 91, 291-298. Brown, J. M., Clark, L. (2014). A groupoid forumulation of the Baire Category Theorem. Fundamenta Mathematicae, 226(2), 123-130. Brown, J. M., Clark, L., Farthing, C., Sims, A. (2014). Simplicity for algebras associated to etale groupoids. Semigroup Forum, 88(2), 433–452. Brown, J. M., Goehle, G. (2014). The Brauer semigroup for groupoid dynamical systems. Transactions of the American Mathematical Society, 366(4), 1943-1972. Brown, J. M., Nagy, G., Reznikoff, S. (2014). Generalized Cuntz-Kreiger Uniqueness for k-graphs. Journal of Functional Analysis, 266(4), 2590–2609. Brown, J. M., an Huef, A. (2014). Centers of algebras associated to higher-rank graphs. Revista Matematica Iberoamericana, 30(4), 1387–1396. Brown, J. M., an Huef, A. (2014). Decomposing the C*-algebras of groupoid extensions. Proceedings of the American Mathematical Society, 142(4), 1261-1274. Busch, A. H., Ferrara, M., Hartke, S., Jacobson, M. S. (2014). A Degree Sequence Variant of Graph Ramsey Numbers. Graphs and Combinatorics, 30(4), 847-859. www.springerlink.com/content/1435-5914/ Eloe, P. W., Neugebauer, J. (2014). Conjugate points for fractional differential equations. Fractional Calculus and Applied Analysis, 17(3), 855--871. Eloe, P. W., Neugebauer, J. (2014). Existence and comparison of smallest eigenvalues for a fractional boundary value problem. Electronic Journal of Differential Equations, 2014(43), 1--10. Islam, M. N. (2015). Bounded, asymptotically stable, and L^1 solutions of Caputo fractional differential equations. Opuscula Mathematica, 35, 181-190. http://www.opuscula.agh.edu.pl/ Islam, M. N., Adivar, M. (2014). Asymptotically stable solutions of a nonlinear Volterra integral equation. Communications in Applied Analysis/ Dynamic Publishers, INC., 18(1 & 2), 155-162. Islam, M. N., Raffoul, Y. N. (2014). Periodic and asymptotically periodic solutions in coupled nonlinear systems of Volterra integrodifferential equations. Dynamic systems and applications/ Dynamic Publishers INC, 23(2 & 3), 235-244. Islam, M. N., Raffoul, Y. N. (2014). Periodic and asymptotically periodic solutions in coupled nonlinear systems of Volterra integrodifferential equations. Dynamic systems and applications/ Dynamic Publishers INC, 23(2 & 3), 235-244. Khan, Y., Usman, M. (2014). Modified Homotopy Perturbation Transform Method: A Paradigm for Nonlinear Boundary Layer Problems. International Journal of Nonlinear Sciences and Numerical Simulation, 15(1), 19--25. Lee, H. S., Kersaint, G., Harper, S. R., Driskell, S. O.S., Jones, D., Leatham, K. R., Angotti, R. L., Adu-Gamfi, K. (2014). Teachers’ use of transnumeration in solving statistical tasks with dynamic statistical software. Statistics Education Research Journal, 13(1), 25-52. iase-web.org/Publications.php?p=SERJ_issues Liu, R. (2014). Optimal Investment and Consumption with Proportional Transaction Costs in Regime-Switching Model. Journal of Optimization Theory and Applications, 163(2), 614-641. Liu, R. (2014). A Finite-Horizon Optimal Investment and Consumption Problem Using Regime-Switching Models. International Journal of Theoretical and Applied Finance, 17(4), 18 pages. Patterson, M. A., Qumsiyeh, M., Hansen, K. M., Subramanyam, G., H. Y., D. W. (2014). Construction of a Twin-Pier Platform for Biological Sensing. Proceedings/IEEEE NAECON Aerospace and Electronic Conference (2014), Pages 5-9. Raffoul, Y. N. (2014). 89 Qualitative Analysis of Solutions of Functional Difference Equations Using Fixed Point Theory. Communications of the Korean Mathematical Society, 29(1), 195-204. http://pdf.medrang.co.kr/kms01/CKMS/29/CKMS-29-1-195-204.pdf Raffoul, Y. N., (2014). Stability In Nonlinear Delay Volterra Integro-differential Systems. Journal of Nonlinear Sciences and Applications, 7(2014), 422-428. www.tjnsa.com Raffoul, Y. N., Adivar, M., Koyuncuoğlu, H. C., (2014). Existence of periodic solutions in shifts$\delta {\pm}\$ for neutral nonlinear dynamic systems on time scales. Advances in Applied Mathematics, 242(1), 328-339. arxiv.org/abs/1402.2540

Raffoul, Y. N., Alsahafi, S., Sanbo, A., (2014). Qualitative Analysis of Solutions in Volterra Nonlinear Systems of Difference Equations. International Journal of Mathematical Analysis, 8(31), 1505-1515. www.m-hikari.com/ijma/ijma-2014/ijma-29-32-2014/raffoulIJMA29-32-2014.pdf

Raffoul, Y. N., Islam, M. N., (2014). Periodic and Asymptotically Periodic Solutions in Coupled Nonlinear Systems of Volterra Integro-differential Equations. Dynamic Systems and Application, 23, 235-244. http://www.dynamicpublishers.org/journals/index.php/DSA

Raffoul, Y. N., Kublik, C., (2014). Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations. Acta Mathematica Vietnamica. link.springer.com/article/10.1007%2Fs40306-014-0098-4

Raffoul, Y. N., Yankson, E., (2014). Existence Of Bounded Solutions For Almost Linear Volterra Difference Equations Using Fixed Point Theory and Lyapunov Functionals. Nonlinear Studies, 21(4), 663-674. http://nonlinearstudies.com/index.php/nonlinear/search/authors/view?firstName=Youssef&middleName=Naim&lastName=Raffoul&affiliation=University%20of%20Dayton&country=US

Ronau, R. N., Rakes, C. R., Bush, S. B., Driskell, S. O.S., Niess, M. L., Pugalee, D. K. (2014). A survey of mathematics education technology dissertation scope and quality: 1968-2009. American Educational Research Journal: Teaching, Learning and Human Development, 51(5), 974-1006.

Trubee, N. W., Vanderburgh, P. M., Diestelkamp, W. S., Jackson, K. (2014). Effects of Heat Stress and Sex on Pacing in Marathon Runners. Journal of Strength & Conditioning Research, 28(6), 1673-1678.

Usman, M., Imran, M. (2014). A Generalization of the Poincare-Cartan Integral Invariants for Nonlinear Nonholonomic Dynamical Systems. Dynamics of Continuous, Discrete & Impulsive Systems, Series A: Mathematical Analysis, 21(1), 111--134. online.watsci.org/abstract_pdf/2014v21/v21n1a-pdf/6.pdf

###### Papers Published in Conference Proceedings

Eustace, D., Almuitairi, O., Hovey, P. W., Shoup, G. (2014), Using Decision Tree Modeling to Analyze Factors Contributing to Injury and Fatality of Run-off-Road Crashes in Ohio. (, vol. 93, pp. 19 pages). Washington, D.C.: 93th TRB Annual Meeting Proceedings.

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### Department of Mathematics

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300 College Park
Dayton, Ohio 45469 - 2316

937-229-2511