Publications
Generating Functions for the q-Bernstein Bases (with R. Goldman and Y. Simsek), SIAM Journal on Discrete Mathematics, 28(3)(2014), 1009–1025.
Asymptotics of Generalized Derangements (with M. E. H. Ismail), Advances in Computational Mathematics, 39(1)(2013), 101–127.
Quantum B-Splines (with R. Goldman), BIT Numerical Mathematics, 53(1)(2013), 193–223.
Connection Relations and Characterizations of Orthogonal Polynomials (with M. E. H. Ismail), Advances in Applied Mathematics, 49(2)(2012), 134–164.
Formulas and Algorithms for Quantum Differentiation of Quantum Bernstein Bases and Quantum B´ezier Curves Based on Quantum Blossoming (with R. Goldman), Graphical Models, 74(6)(2012), 326–334.
q-Blossoming: A New Approach to Algorithms and Identities for q-Bernstein Bases and q-B´ezier Curves (with R. Goldman and V. Zafiris), Journal of Approximation Theory, 164(1)(2012), 77–104.
h-Blossoming: A New Approach to Algorithms and Identities for h-Bernstein Bases and h-B´ezier Curves (with R. Goldman and V. Zafiris), CAGD (Computer Aided Geometric Design), 28(2011), 549–565.
On a Family of Positive Linear Integral Operators (with M. E. H. Ismail), in Notions of Positivity and the Geometry of Polynomials (eds. P. Branden, M. Passare, and M. Putinar), Trends in Mathematics Series, Springer Basel, 2011, ISBN: 978-3-0348-0141-6, 259–274.
Nonlinear Equations for the Recurrence Coefficients of Discrete Orthogonal Polynomials (with M. E. H. Ismail), Journal of Mathematical Analysis and Applications, 376(1) (2011), 259–274.
Research Interest
My research interests are in the fields of approximation theory, special functions, orthogonal polynomials, combinatorics, and computer aided geometric design. I have published 25 research papers in highly ranked and refereed mathematics journals, 2 papers in conference proceedings, and two book chapters since 1998. I have visited City University of Hong Kong 5 times during 2010-2013 as a senior research fellow. I have collaborated and I am collaborating with a number of researchers including 2 leading mathematicians-Professors Mourad Ismail-Univ. of Central Florida and Ron Goldman-Rice University. I have refereed for over 10 math journals. I have used my research to design topics for undergraduate student projects and studies.
Awards
I have twice been a finalist for the UHD Scholarship/Creativity Award-2005 and 2011, and once a recipient of the UHD Faculty Development Leave Award-Fall 2011-spent at City University of Hong Kong. I have received a number of UHD ORCA and FDL grants. My 5 visits at the City University of Hong Kong were funded by research grants from Hong Kong Research Council.
