Optimal control for infinite dimensional stochastic differential equations with infinite Markov jumps and multiplicative noise

In this paper we solve an infinite-horizon linear quadratic control problem for a class of differential equations with countably infinite Markov jumps and multiplicative noise. The global solvability of the associated differential Riccati-type equations is studied under detectability hypotheses. A nonstochastic, operatorial approach is used. Some properties of the linear stochastic systems, such as stability, stabilizability and detectability, are also discussed on the basis of a new solution representation result. A generalized Ito's formula which applies to infinite dimensional stochastic differential equations with countably infinite Markov jumps is also provided.     

Kinetics of tartrazine photodegradation by UV/H2O2 in aqueous solution

In the present work, kinetics of tartrazine decay by UV irradiation and H₂O₂ photolysis, and the removal of total organic carbon (TOC) under specific experimental conditions was explored. Irradiation experiments were carried out using a photoreactor of original design with a low-pressure Hg vapour lamp. The photodegradation rate of tartrazine was optimised with respect to the H₂O₂ concentration and temperature for the constant dye concentration of 1.035 × 10^?5 M. Tartrazine degradation and the removal of TOC followed the pseudo-first-order kinetics. The much higher k _obs value for tartrazine degradation (7.91 × 10^?4 s^?1) as compared with the TOC removal (2.3 × 10^?4 s^?1) confirmed the presence of reaction intermediates in the solution.