(with V. Jovanovic) The Ritz method with Lagrange multipliers. International Journal of Numerical Analysis and Modeling (2014), to appear.
Positive semigroups and abstract Lyapunov equations. Positivity (2014), DOI 10.1007/s11117-014-0279-3
(with V. Jovanovic) D'Alembert sums for vibrating bar with viscous ends. Journal of Engineering Mathematics, 85 (2014), 99-114
(with V. Hrynkiv) Invasion Waves in the Presence of a Mutualist. Mathematical Methods in Applied Sciences (2013) DOI: 10.1002/mma.2964
A short proof of the Arendt-Chernoff-Kato theorem. Archiv der Mathematik, 101 (2013), 143–147
(with Y. Cui) Generating ARMA Count Series from Renewal Processes. Discussions Mathematics - Probability and Statistics, 32 (2012), 5-16
(with V. Jovanovic) Synchronization of Huygens' Clocks and the Poincar\`e Method. Journal of Sound and Vibration, 331 (2012), 2887-2900
(with V. Jovanovic) Explicit solution for vibrating bar with viscous boundaries and internal damper. Journal of Engineering Mathematics, 76 (2012), no.1, 101-121
Gauge theory of Faddeev-Skyrme functionals. Communications in Contemporary Mathematics 12 (2010), no.5, 871-908
Homotopy classification of maps into homogeneous spaces. Journal of Homotopy and Related Structures 4 (2009), no. 1, 331-346
I have been teaching mathematics courses at the university level for over 15 years, including service courses, graduate courses, computer sessions, and large freshman classes, as well as mentoring Research Experience for Undergraduates (REU) students. Each group and each student is a challenge, and I always try to find ways of teaching that work best for them and for the subject. Most of this time I have taught in the US, first as a GTA at Kansas State University, then as a Boas assistant professor at Northwestern University and currently as an assistant professor at UHD.
After coming to Houston I developed several new research collaborations, some with the CMS faculty. Collaborations in analytical mechanics, applied statistics and mathematical biology resulted in published and submitted papers to peer-reviewed journals in 2010-2012. These cover such topics as applications of positive evolution equations to mathematical biology and synchronization of nonlinear oscillators applicable to various areas where collective behavior is observed.
I also published a paper that applied geometry to physics and submitted one on the stability of operator equations that occur in optimal control problems. Currently, I am working on developing new approximation techniques for non-traditional problems in mathematical physics and continue my work on operator equations. Some of my newest work is in mathematical biology, I am currently working with Mike Tobin from the Natural Sciences department on developing a model of water transport in trees. Aside from purely scientific interest, we plan to use this model as a basis for senior and REU projects for students. Another new project is in the spectral graph theory, it is a study of asymptotic spectral invariants of a band, block-circulant, and block-Toeplitz graphs. These graphs appear in organic chemistry and require a mix of linear algebra and probability theory for their study aside from the graph theory itself. Awards
200 2 Hostinsky Outstanding Graduate Teaching Assistant in Academics
- 2015 NSF Improving Undergraduate STEM Education Grant (IUSE) (co-PI, under review)
- 2014 UHD Teaching Circles Initiative, (PI, funded)
- 2014 NSF Research Experience for Undergraduates (REU) (co-PI, under review)
- 2013 UHD Organized Research Grant (PI, funded)