Abstract: This paper is concerned with a system of
Hamilton-Jacobi-Bellman equations coupled with an autonomous
dynamical system. The mathematical system arises in the differential
game formulation of political economy models as an infinite-horizon
continuous-time differential game with discounted instantaneous
payoff rates and continuously and discretely varying state variables.
The existence of a weak solution of the PDE system is proven and
a computational scheme of approximate solution is developed for a
class of such systems. A model of democratization is mathematically
analyzed as an illustration of application.
Abstract: This paper demonstrates a model of an e-Learning
system based on nowadays learning theory and distant education
practice. The relationships in the model are designed to be simple
and functional and do not necessarily represent any particular e-
Learning environments. It is meant to be a generic e-Learning
system model with implications for any distant education course
instructional design. It allows online instructors to move away from
the discrepancy between the courses and body of knowledge. The
interrelationships of four primary sectors that are at the e-Learning
system are presented in this paper. This integrated model includes
[1] pedagogy, [2] technology, [3] teaching, and [4] learning. There
are interactions within each of these sectors depicted by system loop
map.