Research Interests 

Ergodic theory, dynamical systems, and interdisciplinary applications.   


Selected Publications in Refereed Journals: 

·         Quantization for infinite affine transformations, to appear in Fractal and Fractional, 2022 (Jointly with M.K. Roychowdury)

·         Canonical sequences of optimal quantization for condensation measures, to appear in Qualitative Theory and Dynamical Systems, 2022 (Jointly with M.K. Roychowdury)

·         Individual ergodic theorems for infinite measure, Colloquium Mathematicum, 167 (2), 219-238, 2022 (Jointly with V. Chilin and S.N. Litvinov)

·         Quantization for uniform distributions of Cantor dusts on 2, Topology Proceedings, 56, 195-218, 2020 (Jointly with M.K. Roychowdury)

·         Quantization for uniform distributions on stretched Sierpiński triangles, Monatshefte für Mathematik,190, 79-100, 2019 (Jointly with M.K. Roychowdury)

·         Good modulating sequences for ergodic Hilbert transformTurkish J. Math., 39, 124-138, 2015 (Jointly with A. Akhmedov)

·         Steady-state skill level of workers in learining and forgetting environments: A dynamical system analysisEuropean J. Oper. Res.232, 9-21, 2014 (Jointly with S. Teyarachakul and H. Tarakci)

·         Individual ergodic theorem with operator-valued Besicovitch weightsPositivity17, 27-46, 2013 (Jointly with S.N.Litvinov)


Books Published:

Fundamentals of Functional Analysis, Linus Learning, Inc. 2017; ISBN-13: 978-1-60797-751-3



Refereed Encyclopedia Entries:

·         Modern ergodic theory: from a physics hypothesis to a mathematical theory with transformative interdisciplinary impact, in Handbook of the Mathematics of the Arts and Sciences, Chapter 31-1, 1969-1992, 2021, Springer Nature, ISBN-13: 978-3-319-57072-3 (online), 978-3-319-57071-6 (print)

·         Mathematics in Asia West, Encyclopedia of Mathematics and Society, 74-76, Salem Press, 2012, ISBN-13: 978-1587658440 (Jointly with S.J. Greenwald and J.E. Thomley)

·         Curves, Encyclopedia of Mathematics and Society, 280-282, Salem Press, 2012, ISBN-13: 978-1587658440 (Jointly with S.J. Greenwald and J.E. Thomley)

·         Mathematics Genealogy Project, Encyclopedia of Mathematics and Society, 628-629, Salem Press, 2012, ISBN-13: 978-1587658440

·         Polyhedra, Encyclopedia of Mathematics and Society, 782-784, Salem Press, 2012, ISBN-13: 978-1587658440 (Jointly with S.J. Greenwald and J.E. Thomley)

·         Surfaces, Encyclopedia of Mathematics and Society, 964-966, Salem Press, 2012, ISBN-13: 978-1587658440 (Jointly with S.J. Greenwald and J.E. Thomley)


Selected Articles on Assessment in Mathematics:

  • Developing a Departmental Assessment Program: NDSU Mathematics, MAA-Supporting Assessment in Undergraduate Mathematics, New Case Studies, 93-101, 2006 (Jointly with W.O. Martin)
  • Quantitative Literacy as an Integral Component of Mathematics Curriculum, Case at NDSU, MAA Notes #70, Current Practices in Quantitative Literacy, 155-163, 2007 (Jointly with W.O. Martin)


Selected Interdisciplinary Articles:

·         Networking Antarctic Research Discoveries to a U.S. Science Classroom, Science Scope, 32 (2) 30-33, 2008 (Jointly with A. Podoll, B. Olson, L.M. Montplaisir, D.P. Schwert, K. McVicar, and W.O. Martin)

  • Selectivity and affinity of matrix metalloprotease inhibitorsModelling Str. & Reactivity in Bio. Syst., Roy. Soc. Of Chem., Cambridge, UK, 193-205, 2006 (by V. Lukachova, A. Khandelwal, Y. Zhang, D. Comez, D.M. Kroll and S. Balaz)
  • A combination of docking QM/MM methods, and MD simulation for binding affinity estimation of metalloprotein ligandsJ. Med. Chem., 48, 5437-5447, 2005 (by A. Khandelwal, V. Lukacova, D. Comez, D.M. Kroll, S. Raha, and S. Balaz)
  • comparision of the binding sites of matrix metalloproteins and tumor necrosis factor-α converting enzyme: implications for selectivityJ. Med. Chem., 48, 2361-2370, 2005 (by V. Lukacova, Y. Zhang, D.M. Kroll, S. Raha, D. Comez, and S. Balaz)
  • Processing multimode binding situations in simulation-based prediction of ligand-macromolecule affinitiesThe J. of Pyhs. Chem. A Letters109, 6387-6391, 2005 (by A. Khandelwal, V. Lukacova, D.M. Kroll, S. Raha,D. Comez, and S. Balaz)
  • Simulation-based predictions of binding affinities of matrix metalloproteinase inhibitorsQasar and Comb. Sci., 23, 754-766, 2004 (by A. Khandelwal, V. Lukacova, D.M. Kroll, D. Comez, S. Raha, and S. Balaz)