Role Of Convexity Research Articles

Generalized convexity in mathematical programming

The role of convexity in the development of mathematical programming is reviewed. Many recent generalizations of convexity and their applications to optimization theory are discussed.

The role of perturbations, shunts, cusps and convexity reversals in elucidating enzyme kinetic mechanisms and hysteresis pathways

Irregular perturbations and convexity reversals in enzyme kinetic reactions are mathematically modeled by inhibition, catalytic, and rearrangement reactions. The convexity reversal model is especially interesting since it offers a simple alternative to the conformational argument of allosterism and the subunit coupling notion inherent to the Hill equation. Another unusual pattern, a cusp-like intersection on a fermentation hysteresis trajectory, is tentatively attributed to enzyme denaturation countering enzyme production. The role of convexity in reaction schemes where intermediate concentrations are not measured is also discussed. It is proposed that negative convexity in an early reaction rate transient is a clue to the presence of a shunting pathway in the chemical mechanism.