A Model Predictive Control Algorithm Applied To Non-Linear Processes

Model predictive control (MPC) is an optimization-based approach that has been successfully applied to a wide variety of control problems. In most of nonlinear strategies, the controllers are based on linear models with fixed parameters so that the vast body of linear control theory can be applied. Other solutions include the use of a nonlinear analytical model, combinations of linear empirical models, etc. This paper presents an MPC algorithm which uses on-line simulation and rule-based control. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Generalization of the Hutchinson Measure

The Hutchinson measure is the invariant measure associated with an iterated function system with probabilities. Generalized iterated function systems (GIFS) are generalizations of iterated function systems which are obtained by considering contractions from X × X to X, rather than contractions from a metric space X to itself. Along the lines of this generalization we consider GIFS with probabilities. In this paper we prove the existence of an analogue of Hutchinson measure associated with a GIFS with probabilities and present some of its properties. The work was supported by CNCSIS grant 8A;1067/2006.     

Dimension Reduction and Optimality of the Uniform State in a Phase-Field-Crystal Model Involving a Higher-Order Functional

We study a phase-field-crystal model described by a free energy functional involving second-order derivatives of the order parameter in a periodic setting and under a fixed mass constraint. We prove a $$\Gamma $$-convergence result in an asymptotic thin-film regime leading to a reduced two-dimensional model. For the reduced model, we prove necessary and sufficient conditions for the global minimality of the uniform state. We also prove similar results for the Ohta–Kawasaki model.     

Unprecedented Relaxivity Gap in pH-Responsive FeIII-Based MRI Probes

Two mononuclear ferric complexes are reported that respond to a pH change with a 27- and 71-fold jump, respectively, in their capacity to accelerate the longitudinal relaxation rate of water-hydrogen nuclei, and this starting from a negligible base value of only 0.06. This unprecedented performance bodes well for tackling the sensitivity issues hampering the development of Molecular MRI. The two chelates also excel in the fully reversible and fatigue-less nature of this phenomenon. The structural reasons for this performance reside in the macrocyclic nature of the hexa-dentate ligand, as well as the presence of a single pendant arm displaying a five-membered lactam or carbamate which show (perturbed) pK_a values of 3.5 in the context of this N6 N5O1 coordination motif.     

Positive radial solutions for Dirichlet problems via a Harnack-type inequality

We deal with the existence and localization of positive radial solutions for Dirichlet problems involving $\varphi$-Laplacian operators in a ball. In particular, $p$-Laplacian and Minkowski-curvature equations are considered. Our approach relies on fixed point index techniques, which work thanks to a Harnack-type inequality in terms of a seminorm. As a consequence of the localization result, it is also derived the existence of several (even infinitely many) positive solutions.