The turnpike property in finite-dimensional nonlinear optimal control

Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces, the first and the last of which being transient short-time arcs, and the middle piece being a long-time arc staying exponentially close to the optimal steady-state solution of an associated static optimal control problem. We provide in this paper a general version of a turnpike theorem, valuable for nonlinear dynamics without any specific assumption, and for very general terminal conditions. Not only the optimal trajectory is shown to remain exponentially close to a steady-state, but also the corresponding adjoint vector of the Pontryagin maximum principle. The exponential closedness is quantified with the use of appropriate normal forms of Riccati equations. We show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method, or a shooting method. In particular, we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector, not at the initial time, but at the middle of the trajectory.     

First passage percolation and escape strategies

Consider first passage percolation on with passage times given by i.i.d. random variables with common distribution F. Let be the time from u to v for a path π and the minimal time among all paths from u to v. We ask whether or not there exist points and a semi‐infinite path such that for all n. Necessary and sufficient conditions on F are given for this to occur. When the support of F is unbounded, we also obtain results on the number of edges with large passage time used by geodesics. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 414–423, 2015     

Molecular Recognition of Nucleotides in Water by Scorpiand‐Type Receptors Based on Nucleobase Discrimination

The detection of nucleotides is of crucial importance because they are the basic building blocks of nucleic acids. Scorpiand‐based polyamine receptors functionalized with pyridine or anthracene units are able to form stable complexes with nucleotides in water, based on coulombic, π–π stacking, and hydrogen‐bonding interactions. This behavior has been rationalized by means of an exploration with NMR spectroscopy and DFT calculations. Binding constants were determined by potentiometry. Fluorescence spectroscopy studies have revealed the potential of these receptors as sensors to effectively and selectively distinguish guanosine‐5′‐triphosphate (GTP) from adenosine‐5′‐triphosphate (ATP).     

Phosphatidylcholine‐Coated Iron Oxide Nanomicelles for In Vivo Prolonged Circulation Time with an Antibiofouling Protein Corona

We report the synthesis of micellar phosphatidylcholine‐coated superparamagnetic iron oxide nanoparticles as a new long circulation contrast agents for magnetic resonance imaging. Oleic acid‐coated Fe₃O₄ nanoparticles were first prepared through thermal degradation and then encapsulated into small clusters with a phosphatidylcholine coating to obtain hydrophilic nanomicelles. A thorough characterization confirmed the chemical nature of the coating and the excellent colloidal stability of these nanomicelles in aqueous media. Magnetization and relaxivity properties proved their suitability as magnetic resonance imaging (MRI) contrast agent and in vitro cell viability data showed low toxicity. Vascular lifetime and elimination kinetics in the liver were assessed by blood relaxometry and by in vivo MRI in rats and compared with “control” particles prepared with a polyethylene glycol derivative. These micellar particles had a lifetime in blood of more than 10 h, much longer than the control nanoparticles (≈2 h), which is remarkable considering that the coating molecule is a small biocompatible zwitterionic phospholipid. The protein corona was characterized after incubation with rat serum at different times by high‐throughput proteomics, showing a higher proportion of bound apolipoproteins and other dysopsonins for the phosphatidylcholine particles. The antibiofouling properties of this corona and its resistance to the adsorption of proteins corroborate the observed enhanced stability and prolonged systemic circulation.     

Two C3‐Symmetric Dy3III Complexes with Triple Di‐μ‐methoxo‐μ‐phenoxo Bridges,Magnetic Ground State,and Single‐Molecule Magnetic Behavior

Two series of isostructural C₃‐symmetric Ln₃ complexes Ln₃ ? [BPh₄] and Ln₃ ? 0.33[Ln(NO₃)₆] (in which Ln^III=Gd and Dy) have been prepared from an amino‐bis(phenol) ligand. X‐ray studies reveal that Ln^III ions are connected by one μ₂‐phenoxo and two μ₃‐methoxo bridges, thus leading to a hexagonal bipyramidal Ln₃O₅ bridging core in which Ln^III ions exhibit a biaugmented trigonal‐prismatic geometry. Magnetic susceptibility studies and ab initio complete active space self‐consistent field (CASSCF) calculations indicate that the magnetic coupling between the Dy^III ions, which possess a high axial anisotropy in the ground state, is very weakly antiferromagnetic and mainly dipolar in nature. To reduce the electronic repulsion from the coordinating oxygen atom with the shortest Dy?O distance, the local magnetic moments are oriented almost perpendicular to the Dy₃ plane, thus leading to a paramagnetic ground state. CASSCF plus restricted active space state interaction (RASSI) calculations also show that the ground and first excited state of the Dy^III ions are separated by approximately 150 and 177 cm^?1, for Dy₃ ? [BPh₄] and Dy₃ ? 0.33[Dy(NO₃)₆], respectively. As expected for these large energy gaps, Dy₃ ? [BPh₄] and Dy₃ ? 0.33[Dy(NO₃)₆] exhibit, under zero direct‐current (dc) field, thermally activated slow relaxation of the magnetization, which overlap with a quantum tunneling relaxation process. Under an applied H_dc field of 1000 Oe, Dy₃ ? [BPh₄] exhibits two thermally activated processes with U_eff values of 34.7 and 19.5 cm^?1, whereas Dy₃ ? 0.33[Dy(NO₃)₆] shows only one activated process with U_eff=19.5 cm^?1.     

Shallow Water equations for Non-Newtonian fluids

The purpose of this paper is to provide a consistent thin layer theory for some Non-Newtonian fluids that are incompressible and flowing down an inclined plane under the effect of gravity. We shall provide a better understanding of the derivation of Shallow Water models in the case of power-law fluids and Bingham fluids. The method is based on asymptotic expansions of solutions of the Cauchy Momentum equations in the Shallow Water scaling and in the neighbourhood of steady solutions so that we can close the average equations on the fluid height h and the total discharge rate q. Such a method has been first introduced in the case of Newtonian fluids where the computations are proved to be rigorous (Vila, in preparation [20]; Bresch and Noble, 2007 [9]) whereas the more complex case of arbitrary topography has been treated formally (Boutounet et al., 2008 [5]). The well posedness of the free surface Cauchy Momentum equations for these Non-Newtonian fluids is still an open problem: the computations carried out here are only formal.     

Radical anions containing the dioxidated 1,2,5‐thiadiazole heterocycle. Part II

Radical anions from several 3,4‐aryl‐disubstituted derivatives of 1,2,5‐thiadiazole 1,1‐dioxide were accumulated through chemical reduction of the substrates in aprotic solvents. The radical anions were characterized by electron spin resonance and cyclic voltammetry. DFT theoretical calculations were also performed for the 3,4‐diphenyl derivative. The course of the reductions was followed using cyclic voltammetry. Uncommon reductants, such as amides, were found to be effective under certain conditions. Copyright © 2010 John Wiley & Sons, Ltd.