Size minimization and approximating problems

We consider Plateau type variational problems related to the size minimization of rectifiable currents. We realize the limit of a size minimizing sequence as a stationary varifold and a minimal set. Other examples of functionals to be minimized include the integral over the underlying carrying set of a power q of the multiplicity function, with .Because minimizing sequences may have unbounded mass we make use of a more general object called a rectifiable scan for describing the limit. This concept is motivated by the possibility of recovering a flat chain from a sufficiently large collection of its slices. In case the given boundary is smooth and compact, the limiting scan has finite mass and corresponds to a rectifiable current.Received: 11 February 2002, Accepted: 16 June 2002, Published online: 17 December 2002Mathematics Subject Classification (2000): 49Q15, 28A75Thierry De Pauw: The research of the first author was supported by a Marie Curie fellowship of the European Community program Human Potential under contract HMPF-CT-2001-01235Robert Hardt: The research of the second author was partially supported by NSF grant DMS-0072486     

Magnetic anisotropy in icosahedral cobalt clusters

Magnetic anisotropy has been measured in multiply twinned, icosahedral cobalt clusters. It is found that the low-temperature magnetization of deposited cluster layers is well defined with the Stoner–Wohlfarth model by averaging over clusters with a range of anisotropy energy. Anisotropy energy calculation based on Néel's pair model shows that the icosahedral structure and the layer-by-layer growth of the clusters induce oscillations of the magnetic anisotropy as a function of the filling of the outer surface of the particle. The magnetization measurement at room temperature indicates a weakly correlated cluster glass, as deduced from the approach to saturation that is well described with 2D random anisotropy model.     

Sensitivity indices for multivariate outputs

We define and study a generalization of Sobol sensitivity indices for the case of a vector output.     

2,2′-Bipyridine-3,3′-dicarboxylic carbohydrate esters and amides. Synthesis and preliminary evaluation as ligands in Cu(II)-catalysed enantioselective electrophilic fluorination

A series of 10 new carbohydrate-substituted bipyridines were prepared from 2,2′-bipyridine-3,3′-dicarboxylic acid, itself easily available from ortho-phenanthroline. As a preliminary exploration of their use as chiral ligands, Cu(II)-catalysed asymmetric electrophilic fluorination of model β-ketoesters using these simple and easily accessible chiral bipyridines was studied. Only modest enantioselectivity was observed in this reaction, although the ee was in a similar range as those provided by known and more elaborate ligands.     

Detection of Frozen–Thawed Duck Fatty Liver by MALDI-TOF Mass Spectrometry: A Chemometrics Study

The marketing of poultry livers is only authorized as fresh, frozen, or deep-frozen. The higher consumer demand for these products for a short period of time may lead to the marketing of frozen–thawed poultry livers: this constitutes fraud. The aim of this study was to design a method for distinguishing frozen–thawed livers from fresh livers. For this, the spectral fingerprint of liver proteins was acquired using Matrix-Assisted Laser Dissociation Ionization-Time-Of-Flight mass spectrometry. The spectra were analyzed using the chemometrics approach. First, principal component analysis studied the expected variability of commercial conditions before and after freezing–thawing. Then, the discriminant power of spectral fingerprint of liver proteins was assessed using supervised model generation. The combined approach of mass spectrometry and chemometrics successfully described the evolution of protein profile during storage time, before and after freezing-thawing, and successfully discriminated the fresh and frozen–thawed livers. These results are promising in terms of fraud detection, providing an opportunity for implementation of a reference method for agencies to fight fraud.     

Local exact Lagrangian controllability of the Burgers viscous equation

We study and give the definition of the exact Lagrangian controllability of the viscous Burgers equation and prove a local result. We give similar results for the heat equation in dimension 1.     

Synthèse et étude de modèles de NADH à noyaux accolés en série pyrrolo[2,3-b] et [3,2-b]pyridines

Pyrrolo[2,3-b] and [3,2-b]pyridines derivatives, precursors for annealated NADH models have been prepared. Several methods for building a pyridinic annealates ring have been used starting from 2- or 3-aminopyrrole. The corresponding dihydropyridine structure leads to highly reactive NADH models compounds and are very much more stable than common models.