Faculty Research

Ellina Grigorieva, Ph.D.

Research Specialty: Optimal Control Theory and Differential Games

My current research interest is in modeling and control of complex dynamical systems and in mathematics education. Most of my papers emphasize the utility of analytical methods and have been published in the application of optimal control and game theory to industry, economics, medicine, biology and ecology. Within this field of application, I developed analytical methods of solving nonlinear optimal control problems that have the benefit of tractability and interpretability over the conventional numerical methods: a warranty is provided that the type of optimal solution can be found for any given set of the model parameters. Using my methods, a complex Two Point Boundary Value Problem (TPBVP) for the Maximum principle that arises in many optimization problems can be reduced to a considerably simpler problem of finite dimensional optimization, and relevant guidance for the practical design of control policy becomes transparent.

I am presently actively engaged in the following specific research projects:

Biology and Medicine

• Mathematical Epidemiology
• Optimal Control of HIV or AIDS Treatment
• Autoimmune Disorders (Psoriasis and Allergy)

Business and Economics

• Modeling and Optimal Control in Business and Economics
• Hierarchical Differential Games with two or more players

Math Education

• Methods of Solving Complex Math Problems
• Rediscovery of Mathematical Intelligence

Junalyn Navarra-Madsen, Ph.D.

Research Specialty: Knot Theory

Knot theory is a field of topology that that studies mathematical knots. The Division of Mathematics is currently engaged in an ongoing project modeling protein-DNA interactions. The enzymatic mechanisms are modeled using knot theoretical concepts. To learn more about her current research projects, contact Dr. Navarra-Madsen at JNavarramadsen@twu.edu.

Other research interests: mathematical analysis, stochastic modeling, topology, biomathematics, industrial mathematics.