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WKU Mathematics Faculty Publications

Bold text represents WKU Mathematics faculty, and bold italics text represents former/current WKU Mathematics students.  Some disciplines in mathematics recognize author order as a representation of contribution to the paper, while other simply list authors alphabetically. 


Abdisatarov, B., Ilhom, S., Kholikov, K., Loomis, D., Dobrokhotov, V., Khenner, M., and Er, A.  O., “Morphology and structure of Pb thin films grown on Si(111) by pulsed laser deposition”,  Applied Physics A126, 237 (2020).

Atici, F. M., Dadashova, K., and Jonnalagadda, J., Linear fractional order h-difference equations, Special Issue honoring Professor Johnny Henderson, International Journal of Difference Equations, Volume 15, Number 2, pp. 281-300 (2020).

Atici, F. M., Nguyen, N., Dadashova, K., Pedersen, S., and Koch, G., Pharmacokinetics and Pharmacodynamics Models of Tumor Growth and Anticancer Effects in Discrete Time, Computational Mathematical Biophysics, 8(2020), 114-125.

Atici, F. M. and Zhoroev, T., Controllability and observability of time-invariant linear nabla fractional systems, Fractional Differential Calculus, 10(2020), no. 1, 19-39.

Balko, M., Pór, A., Scheucher, M., Swanepoel, K., Valtr, P.  Almost-equidistant sets, Graphs Comb. 36, No. 3, 729-754 (2020).

Bateiha, S., Autin, M., and Marchionda, H. (2020).  Teaching Style and Attitudes: A Comparison of Two Collegiate Introductory Statistics Classes.  Journal of Statistics Education, 28:2,154-164,DOI: 10.1080/10691898.2020.1765710.

Bhattacharya, T. and Mohammed, A.  On Phragmen-Lindelof type Theorems for k-Hessian equations with lower order terms. Appeared online 02 May 2020, Journal of Geometric Analysis, https://doi.org/10.1007/s12220-020-00415-0.

Bhattacharya, T. and Marazzi, L.  A Phragmen-Lindelof property of viscosity solutions to a class of nonlinear, possibly degenerate, parabolic equations (with L. Marazzi), Rendiconti di Matematica e delle sue Applicazioni, University di Roma (Sapienza) (7) Vol 41 (2020) 59-104.

Durham, S. and Richmond, T.  Connected Subsets of a n x 2 Rectangle. College Mathematics Journal, Vol. 51 no. 1 (2020) 32-42. https://doi.org/10.1080/07468342.2020.1674597.

Fortune, N., Rasmussen, C., Keene, K. A., Bogart, T., & Dunmyre, J. (2020).  Bringing social justice topics to differential equations via a climate change problem: Identity, power, access, and achievement. MathAMATYC Educator, 11(3), 26 – 32, 66 – 67.  https://amatyc.site-ym.com/page/EducatorSpring2020.

Johnson, E., Andrews-Larson, C., Keene, K. A., Melhuish, K., Keller, R., & Fortune, N. (2020). Inquiry and gender inequity in the undergraduate mathematics classroom. Journal for Research in Mathematics Education, 51(4), 504 – 516. https://www.jstor.org/stable/10.5951/jresematheduc-2020-0043.

Khenner, M., “Electromigration-guided composition patterns in thin alloy films: a computational study”, Surface Science698, 121611 (2020).

Lischka, A. E., Gerstenschlager, N., & Seat, J. (2020). A journey toward course assessment as a relational practice in mathematics methods. In C. Edge, A. Standerford, & B. Bergh (Eds.), Textiles and Tapestries: Self-Study for Envisioning New Ways of Knowing. EdTech Books. Retrieved from https://edtechbooks.org/textiles_tapestries_self_study/chapter_25  (Book Chapter)

Özer, A. Ö., Stabilization results for well-posed potential formulations of a current-controlled piezoelectric beam and their approximations, Applied Mathematics and Optimization, (2020).

Price, D. J., Moore, E., Özer, A. Ö., Boundary Control of a 1D Wave Equation by the Filtered Finite Difference Method, Wolfram Demonstrations Project, Published:  June 3, 2020.

Price, D. J., Moore, E., Özer, A. Ö. (2020) "Boundary Stabilization of Euler-Bernoulli and Rayleigh Beam Vibrations," Wolfram Demonstrations Project, Published: September 23, 2020.

Richmond, T.  General Topology: An Introduction, ISBN 978-3-11-068656-2 © 2020, 314 + xii pages.  (Book)

Tassell, J., Gerstenschlager, N. E., Szymanski, T., & Denning, S. (2020). Improving mindfulness, mindset, anxiety, and content knowledge in mathematics for preservice teachers. School Science and Mathematics, 120, 333-344.

Zheng, L. (2020). Introductory Statistics, 1st edition. Kendall Hunt Publishing, Dubuque, IA, 2020 (ISBN: 978-1-7924-2985-9).  (Book)


Atici, F. M., Atici, M., Nguyen, N., Zhoroev, T., and Koch, G., A study on discrete and discrete fractional pharmacokinetics-pharmacodynamics models for tumor growth and anti-cancer effects, Computational Mathematical Biophysics, 7(2019), 10-24.

Atici, F. M. and Nguyen, D. M., Rank conditions for controllability of discrete fractional time-invariant linear systems, Journal of Difference Equations and Applications, 25(2019), Issue 6, Special Issue: Fractional Calculus, Guest Edited by Allan Peterson, 869-881. doi:10.1080/10236198. 2019.1596265.

Autin, M. A. and Gerstenschlager, N. E. (2019).  Battleship and the Negative Hypergeometric Distribution.  Teaching Statistics:  An International Journal for Teachers, 41: 37. https://doi.org/10.1111/test.12160.

Barnette, B., Nichols, W., and Richmond, T.  The Number of Convex sets in a Product of Totally Ordered Sets, Rocky Mountain Journal of Math. 49 (2) (2019) 369-385.  Doi:10.1216/RMJ-2019-49-2-369.

Bettersworth, Z. and Ernst, C. (2019), On the Incoherent Nullification of Knots and Links, J. of Knot Theory and Its Ramifications, Vol. 28, No. 05, doi.org/10.1142/S0218216519500330.

Bhattacharya. T. and Marazzi, L.  A Phragmen-Lindelof property of viscosity solutions to a class of doubly nonlinear parabolic equations: Bounded Case (with L. Marazzi). Rendiconti Del Seminario Matematico Della Universit di Padova. Vol 142 (2019), pages 211-259.

Bhattacharya, T., Emamizadeh, B, and Farjudian, A.  Existence of Continuous Eigenvalues for a Class of Parametric Problems Involving the (p; 2)-Laplacian Operator, Acta Applicandae Mathematicae, vol 165, no 1 (2020) 65-79. Appeared Online Feb 7, 2019, DOI:10.1007/s10440-019-00241-9.

Clark, D. L. (2019). Mathematics educators’ perceptions of passing through the gateway of occupational politicization. In S. Otten, A. G. Candela, Z. de Araujo, C. Haines, & C. Munter, (Eds.), Proceeding of the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (p. 683). St. Louis, MO: University of Missouri.

Dahane, I., Lazaar, S., Richmond, T., and Turki, T.  On Resolvable Primal Spaces, Quaestiones Mathematicae, 42 no. 1 (2019) 15-35. https://doi.org/10.2989/16073606.2018.1437093

Diao, Y., Ernst, C., Por, A., and Ziegler, U. (2019), The Ropelengths of Knots Are Almost Linear in Terms of Their Crossing Numbers, Vol. 28, No. 14, 1850075 doi.org/10.1142/S0218216519500858.

DuCloux, K. K. (2019). Secondary Mathematics Teachers’ Overcoming Difficulties in an Online Real Analysis Course.  In Otten, S., Candela, A. G. de Araujo, Z. Haines, A., & Munter, C. (Eds.). Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 613-614). St. Louis, MO.

DuCloux, K. K. (2019). Facilitating mathematical discourse in online learning environments. In Wachira, P. & Keengwe, J. (Eds.) Handbook of Research on Online Pedagogical Models for Mathematics Teacher Education. (pp. 245-256). IGI Global: Hershey, PA.

DuCloux, K. K., et al (2018).  Catalyzing change in high school mathematics: Initiating critical conversations.  National Council of Teachers of Mathematics.  Reston, VA  (Book)

Dunkum, M., Donnelly, R., George, C., and Schnake, S.  “Counting odd numbers in truncations of Pascal's Triangle,” The Pentagon , 79 (1) (2019), 12-28.

Dunkum, M. and Donnelly, R.  “The Group Action Tri-cycle Theorem,” The American Mathematical Monthly, 126 (2) (2019), 179-179.

Dunkum, M. and Lanphier, D.  “Edge integrity of nearest neighbor graphs and separator theorems", Discrete Mathematics 342 no.9 (2019), 2664-2679.

Dunmyre, J., Fortune, N., Bogart, T., Rasmussen, C., & Keene, K. A. (2019). Climate change in a differential equations course: Using bifurcation diagrams to explore small changes with big effects. Community of Ordinary Differential Equations Educators (CODEE) Journal, 12(1), 1 – 10. https://scholarship.claremont.edu/codee/vol12/iss1/1.

Eaton, C. D., Callender, H. L., Dahlquist, K. D., LaMar, M. D., Ledder, G., Schugart, R. C. “Rule of Five” Framework for Models and Modeling to Unify Mathematicians and Biologists and Improve student Learning, PRIMUS, 29 (8): 799 – 829. doi: 10.1080/10511970.2018.1489318.

George, P. and Nguyen, N. Visualizing music similarity: clustering and mapping 500 classical music composers, Scientometrics, 2019, DOI 10.1007/s11192-019-03166-0.

Gerstenschlager, N. E. & Strayer, J. F. (2019). Number talks for statistics and probability. Mathematics Teaching in the Middle School, 24, 362-368.

Gerstenschlager, N. E. (2019). Re-envisioning the mathematics teaching practices as the statistics teaching practices. Statistics Teacher. Can be retrieved from: http://www.statisticsteacher.org/2019/01/02/statistics-teaching-practices/.

Gerstenschlager, N. E. & Barlow, A. T. (2019). Transitioning from practicing teacher to teacher leader: A case study. Teacher Development, 1, 18-35.

Lanphier, D.  “Determining cuspforms from critical values of convolution L-functions and Rankin-Cohen brackets", International Journal of Number Theory 15 (7) (2019), 1403-1412.

Lazaar, S., Richmond, T., and Sabri, H.  The Autohomeomorphism Group of Connected Homogeneous Functionally Alexandroff Spaces, Communications in Algebra, Vol. 47 no. 9 (2019) 3818-3829.  https://doi.org/10.1080/00927872.2019.1570240.

Nguyen, L., Buşe, C., Diagana, T., and O'Regan, D.  Exponential stability for solutions of continuous and discrete abstract Cauchy problems in Banach spaces. Electron. J. Differential Equations 2019, No. 78, pp 1-16.

Özer, A. Ö., Uniform boundary observability of semi-discrete finite difference approximations of a Rayleigh beam equation with only one boundary observation, Proceedings of the IEEE Conference on Decision and Control (CDC), Nice, France, 2019, 7708-7713 (2019).

Özer, A. Ö. and Khenner, M. (2019) An alternate numerical treatment for nonlinear PDE models of piezoelectric laminates, Proc. SPIE 10967, Active and Passive Smart Structures and Integrated Systems XII, 109671R-20 pages.

Özer, A. Ö. and Morris, K. A. (2019) Modeling and stabilization of current-controlled piezoelectric beams with dynamic electromagnetic field, ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV), (26-8), 1-24.

Rasmussen, C., Dunmyre, J., Fortune, N., & Keene, K. A. (2019). Modeling as a means to develop new ideas: The case of reinventing a bifurcation diagram. PRIMUS, 29(6), 509 – 526. https://doi.org/10.1080/10511970.2018.1472160.

Robinson, M. “Global Behavior in Functional Iteration Problems,” Journal of the Kentucky Academy of Science, Volume 80, No. 1, pp. 47-59 (2019).

Spraker, J.  “Positive Solutions for a fourth order differential inclusion based on the Euler-Bernoulli equation for a cantilever beam”, Differential Equations and Applications Volume 11 No. 4 Nov. 2019, pp 531 – 541. http://dx.doi.org/10.7153/dea-2019-11-26).

Strayer, J. F., Gerstenschlager, N. E., Green, L. B., McDaniel, S., & Rowell, G. H. (2019). Towards a full(er) implementation of active learning. Statistics Education Research Journal, 18(1), 63-82. **Resulted in a Math Ed Podcast (Episode 1907) which can be found at https://www.podomatic.com/podcasts/mathed/episodes/2019-05-07T08_18_52-07_00.

Tassell, J., Novak, E., and Kessler, B.  “Math Comic Books to the Rescue: Can Wonderguy's Escapades Improve Children's Mathematics Attitudes?," Technology, Instruction, Cognition, and Learning 11, 259-286 (2019).

Zheng, L. (2019). Using mutual information as a cocitation similarity measure. Scientometrics . DOI https://doi.org/10.1007/s11192-019-03098-9.

Zheng, L. and Zheng, H. (2019). Authorship attribution via coupon-collector-type indices. Journal of Quantitative Linguistics . DOI: 10.1080/09296174.2019.1577939.

Zhuhadar, L., Daday, J., Marklin, S., Kessler, B., and Helbig, T.  “Using survival analysis to discovering pathways to success in mathematics," Computers in Human Behavior 92, 487-495 (March 2019).


Atici, F. M. and Yaldiz, H., Refinements on the discrete Hermite-Hadamard inequality, Arab. J. Math. (Springer) 7 (2018), no. 3, 175-182.

Bárány, I., Fodor, F., Martínez-Pérez, Á., Montejano, L., Oliveros, D., Pór, A.  a Acknowledgement of priority|-a fractional Helly theorem for boxes, Comput. Geom. 67 (2018), no. 1.

Barlow, A. T., Gerstenschlager, N. E., Strayer, J., Lischka, A., Stephens, D., Hartland, K., & Willingham, J. (2018). Scaffolding for access to productive struggle. Mathematics Teaching in the Middle School, 23, 202-207.

Diao, Y., Ernst, C., Ziegler, U., and Rawdon, E. J. (2018), The Knot Spectrum of Random Knot Spaces, New Directions in Geometric and Applied Knot Theory/Ed. Blatt, Reiter, Schikorra, DeGruyter, pp.205-237, DOI: 10.1515/9783110571493-010.

Diao, Y., Ernst, C., Ziegler, U., and Rawdon, E. J. (2018), Average crossing number and writhe of knotted random polygons in confinement Reactive and Functional Polymers 131(10) doi.org/10.1016/j.reactfunctpolym.2018.07.028.

Diao, Y., Ernst, C., Ziegler, U., and Rawdon, E. J. (2018), Total curvature and total torsion of knotted random polygons in confinement. J. Phys. A: Math. Theor, 51(15) DOI: 10.1088/1751-8121/aab1ed.

Du, L., Khenner, M., and Maroudas, D., “Kinetics of nanorings formation on surfaces of stressed thin films”, Physical Review Materials2, 083403 (2018).

DuCloux, K., Gerstenschlager, N., Marchionda, H., & Tassell, J. (2018). Characterizing prospective mathematics teachers’ productive struggle. In Venenciano, L., and Redmond-Sanogo, A. (Eds.). Proceedings of the 45th Annual Meeting of the Research Council on Mathematics Learning. Baton Rouge, LA.

El-Farrah, M. and Lanphier, D.  “Average orders of subgroups of cyclic groups and values of the Riemann zeta function", The Ramanujan Journal 47 (3) (2018), 547-564.

Ernst, C. and Pham, V. (2018), Loop Numbers of Knots J. of Knot Theory and Its Ramifications, Vol. 27, No. 14, 1850075, doi.org/10.1142/S021821651850075X.

Gerstenschlager, N. E. & Barlow, A. T. (2018). Number talks with fraction multiplication. Dimensions in Mathematics, 38, 6-13.

Hamburger, P., McConnell, R., Pór, A., Spinrad, J., Xu, Z.  Double threshold digraphs, 43rd International Symposium on Mathematical Foundations of Computer Science, LIPIcs. Leibniz Int. Proc. Inform. 117 (2018), 12pp.

Khenner, M. “Modeling solid-state dewetting of a single-crystal binary alloy thin films”, Journal of Applied Physics123, 034302 (2018).

Lanphier, D.  “Duels, truels, gruels, and survival of the unfittest”, in The Mathematics of Various Entertaining Subjects , Volume 2, Princeton University Press, Princeton, New Jersey and the National Museum of Mathematics, New York, New York, 2018.

Lazaar, S., Richmond, T., and Sabri, H.  Homogeneous Functionally Alexandroff Spaces, Bulletin of the Australian Mathematical Society, 97 (2) (2018) 331-339.https://doi.org/10.1017/S0004972717000934.

Lischka, A., Gerstenschlager, N. E., Stephens, C., Strayer, J. F., & Barlow A. T. (2018). Making Room for Inspecting Mistakes. Mathematics Teacher, 111, 432-439. **Resulted in a National Council of Teachers of Mathematics Twitter Chat.

Magazinov, A. and Pór, A.  An Improvement on the Rado Bound for the Centerline Depth , Discrete Comput. Geom. 59  (2018), no. 2, 477-505.

Marchionda, H., DuCloux, K., Gerstenschlager, N., and Tassell, J. (2018). Preservice math teachers’ perceptions of productive struggle. Hodges, T.E., Roy, G. J., & Tyminski, A. M. (Eds.). Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Greenville, SC: University of South Carolina & Clemson University.

Molchanov, S., Zhang, L., and Zheng, L. (2018). Entropic Moments and Domains of Attraction on Countable Alphabets. Mathematical Methods of Statistics , 27 (1): 60-70.

Moody, V. R. & DuCloux, K. K. (2018). Elementary preservice teachers’ perceived confidence and readiness for teaching mathematics. In Venenciano, L., and Redmond-Sanogo, A. (Eds.). Proceedings of the 45th Annual Meeting of the Research Council on Mathematics Learning. Baton Rouge, LA.

Nguyen, L., Buse, C., and O'Regan, D. Global and local versions for a Phóng Vũ theorem for periodic evolution families in Hilbert spaces. Electron. J. Differential Equations 2018, No. 188, pp. 1-12.

Nguyen, L., Buse, C., Khan, A., and Rahmat, G.  Asymptotic Behavior Of Discrete Evolution Families in Banach Spaces. Applicable Analysis, Vol. 97 (2018), no. 2, 160-178.

Özer, A. Ö., Potential formulation and related stabilization results for a charge or currentcontrolled piezoelectric smart composite: electrostatic, quasi-static, and fully-dynamic assumptions, IEEE Transactions on Automatic Control, (64-3) (2018), 989-1002.

Özer, A. Ö., Dynamic and non-dynamic modeling for a piezoelectric smart beam and related preliminary stabilization results, Evolution Equations and Control Theory, 7-4 (2018), 639–668.

Özer, A. Ö., Exponential stabilization of the smart piezoelectric composite beam with only one boundary controller, Proceedings of the International Federation of Automatic Control Conference (51-3) (2018), pp. 80-85.

Özer, A. Ö., Nonlinear modeling and preliminary stabilization results for a class of piezoelectric smart composite beams, Proceedings of the SPIE on Smart Structures & Nondestructive Evaluation, Proceedings Volume 10595, Active and Passive Smart Structures and Integrated Systems XII; 105952C (2018).

Price, D. L., Hennner, V., and Khenner, M., “Morphologies, metastability and coarsening of quantum nanoislands on the surfaces of the annealed  Ag(110) and Pb(111) thin films”, Journal of Applied Physics124, 174302 (2018).

Richmond, T.  Calculus with Curtains, College Mathematics Journal, Vol. 49 no. 5 (2018) 369-370. https://doi.org/10.1080/07468342.2018.1512326.

Spires, H. A., Kerkhoff, S. N., & Fortune, N. (2018). Educational cosmopolitanism and collaborative inquiry: A collective case study with teachers from China and the US. Teaching Education, 30(4), 437 – 454. https://doi.org/10.1080/10476210.2018.1506431.

Zheng, L. (2018). A two-step self-evaluation algorithm on imputation methods for missing categorical data. International Journal of Scientific and Statistical Computing, 7 (1): 1-12.


Atici, F. M., Atici, M., Belcher, M., and Marshall, D., A New Approach for Modeling with Discrete Fractional Equations, Fundamenta Informaticae, 151(2017), 313-324.  doi:10.3233/FI-2017-1494.

Bell, K. and Richmond, T.  Transitions between 4-Intersection Values of Planar Regions Applied General Topology, 18(1) (2017) 183-202.  Doi:10.4995/agt.2017.6717.

Bhattacharya, T. and Marazzi, L.  On the viscosity solutions of eigenvalue problems for a class of nonlinear elliptic operators. Advances in Calculus of Variations, Vol 12 Issue 4 (Oct 2019) pages 393-422. Appeared online, Nov 14, 2017. 30 pages. DOI: https://doi.org/10.1515/acv-2016-0007.

Bhattacharya, T. and Marazzi, L.  On the viscosity solutions to a class of nonlinear degenerate parabolic equations. Revista Matematica Complutense 30(3), 621-656. Appeared Online (April 1, 2017) DOI:10.1007/s13163-017-0229-2. 36 pages.

Clark, D. L. (2017). The crossroads of stakeholders’ views of CCSSM implementation. In E. Galindo & J. Newton, (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (p. 546). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

Diao, Y., Ernst, C. D., Rawdon, E., Ziegler, U. (2017). Relative Frequencies of Alternating and Nonalternating Prime Knots and Composite Knots in Random Knot Spaces.  Experimental Mathematics, 1- 18, DOI: 10.1080/10586458.2017.1320239.

Dunkum, M. and Knowles, T.  “Embracing LEAP in Kentucky,” with T. Knowles, Peer Review 19 (3) Summer 2017.

Iraniparast, N., Nguyen, L., and Khenner, M., “Asymptotic behavior of waves in a nonuniform media”, Applications and Applied Mathematics 12(1), 217 – 229 (2017).

Khenner, M. “Height transitions, shape evolution, and coarsening of equilibrating quantum nanoislands”, Modelling and Simulation in Materials Science and Engineering25, 085003 (2017).

Khenner, M. “Interplay of quantum size effect, anisotropy and surface stress shapes the instability of thin metal films”, Journal of Engineering Mathematics104, 77-92 (2017).

Lazaar, S., Richmond, T., and Turki, T.  Maps Generating the Same Primal Space, Quaestiones Mathematicae 40(1) (2017) 17-28.  doi 10.2989/16073606.2016.1260067.

Mhemdi, A. and Richmond, T.  Complements of Convex Topologies on Products of Finite Totally Ordered Spaces, Positivity, 21(4) (2017) 1369-1382. doi:10.1007/s11117-017-0472-2.

Molchanov, S., Zhang, Z. and Zheng, L. (2017). Central limit theorem of Turing's formula. ACMPT-2017 proceedings , UDC 519.214.

Molchanov, S. and Zheng, L. (2017). Cluster expansion of the resolvent for the Schrödinger operator on non-percolating graphs with applications to Simon-Spencer type theorems and localization. Journal of Spectral Theory , 7 (3): 733-770.

Özer, A. Ö. Modeling and Control results for an active constrained layered (ACL) beam actuated by two voltage sources with/without magnetic effects, IEEE Transactions on Automatic Control, (62-12) (2017), pp. 6445-6450.

Spraker, J.  “Solutions for a Second-Order Delay Differential Inclusion on the Half-Line with Boundary Values”, Differential Equations and Applications,Vol. 9, No.4, pp 543-552 (2017).

Strayer, J. F., Barlow. A. T., Lischka, A. E., Gerstenschlager, N. E., Stephens, D. C., Willingham, J. C., & Hartland, K. S. (2017). Meeting the needs expressed by teachers: Adaptations of the traditional model for demonstration lessons. National Council of Supervisors of Mathematics Journal of Mathematics Education Leadership, 18(1), 18-26.

Zheng, L. and Jiang, J. (2017). A new diversity estimator. The Journal of Statistical Distributions and Applications, 4 (1): 1-13.

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 Last Modified 12/8/20