Well-posedness of the shooting algorithm for control-affine problems with a scalar state constraint

We deal with a control-affine problem with scalar control subject to bounds, a scalar state constraint and endpoint constraints of equality type. For the numerical solution of this problem, we propose a shooting algorithm and provide a sufficient condition for its local convergence. We exhibit an example that illustrates the theory.Comment: arXiv admin note: substantial text overlap with arXiv:1411.171

Effects of sodium polystyrene sulfonate on gingival plaque: Microbiological investigation and clinical follow-up

A new antiplaque agent was tested on nine subjects. The antiplaque agent, a 5% aqueous solution (p/v) of sodium polystyrene sulfonate, applied on the tooth surfaces by daily topical application for two weeks, caused a statistically significant 30% reduction of plaque index (PI), with corresponding reduction of total bacteria and qualitative modifications of plaque formation with reduction of Gram-negative bacteria.A new antiplaque agent was tested on nine subjects. The antiplaque agent, a 5% aqueous solution (p/v) of sodium polystyrene sulfonate, applied on the tooth surfaces by daily topical application for two weeks, caused a statistically significant 30% reduction of plaque index (PI), with corresponding reduction of total bacteria and qualitative modifications of plaque formation with reduction of Gram-negative bacteria

Second order analysis of control-affine problems with scalar state constraint

In this article we establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition

Optimality conditions (In Pontryagin form)

International audienc