On avoiding odd partial Latin squares and r-multi Latin squares

We show that for any positive integer k?4, if R is a (2k-1)×(2k-1) partial Latin square, then R is avoidable given that R contains an empty row, thus extending a theorem of Chetwynd and Rhodes. We also present the idea of avoidability in the setting of partial r-multi Latin squares, and give some partial fillings which are avoidable. In particular, we show that if R contains at most nr/2 symbols and if there is an n×n Latin square L such that δn of the symbols in L cover the filled cells in R where 0<δ<1, then R is avoidable provided r is large enough.     

On the Design of Fluorescent Ratiometric Nanosensors

Advances in nanoparticle technology have recently offered new tools to the bioanalytical field of research. In particular, new nanoparticle‐based sensors have appeared able to give quantitative information about different species (ions, metabolites, biomolecules) in biosamples through ratiometric measurements. This article describes the methodologies developed so far in the design of such nanosensors. In particular, the different approaches to immobilize fluorescent chemosensor dyes to nanoparticles are presented. Concept designs of ratiometric nanosensors in terms of composition and architecture are also described and illustrated with examples taken from the literature.     

1H-NMR Metabolomics as a Tool for Winemaking Monitoring

The chemical composition of wine is known to be influenced by multiple factors including some viticulture practices and winemaking processes. ¹H-NMR metabolomics has been successfully applied to the study of wine authenticity. In the present study, ¹H-NMR metabolomics in combination with multivariate analysis was applied to investigate the effects of grape maturity and enzyme and fining treatments on Cabernet Sauvignon wines. A total of forty wine metabolites were quantified. Three different stages of maturity were studied (under-maturity, maturity and over-maturity). Enzyme treatments were carried out using two pectolytic enzymes (E1 and E2). Finally, two proteinaceous fining treatments were compared (vegetable protein, fining F1; pea protein and PVPP, fining F2). The results show a clear difference between the three stages of maturity, with an impact on different classes of metabolites including amino acids, organic acids, sugars, phenolic compounds, alcohols and esters. A clear separation between enzymes E1 and E2 was observed. Both fining agents had a significant effect on metabolite concentrations. The results demonstrate that ¹H-NMR metabolomics provides a fast and robust approach to study the effect of winemaking processes on wine metabolites. These results support the interest to pursue the development of ¹H-NMR metabolomics to investigate the effects of winemaking on wine quality.     

Partial regularity for harmonic maps and related problems

Via gauge theory, we give a new proof of partial regularity for harmonic maps in dimensions m ≥ 3 into arbitrary targets. This proof avoids the use of adapted frames and permits us to consider targets of “minimal” C²‐regularity. The proof we present extends to a large class of elliptic systems. © 2007 Wiley Periodicals, Inc.     

Conservation laws for conformally invariant variational problems

We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations,..., etc.) in divergence form. These divergence-free quantities generalize to target manifolds without symmetries the well known conservation laws for weakly harmonic maps into homogeneous spaces. From this form we can recover, without the use of moving frame, all the classical regularity results known for 2-dimensional conformally invariant non-linear elliptic PDE (see [Hel]). It enables us also to establish new results. In particular we solve a conjecture by E. Heinz asserting that the solutions to the prescribed bounded mean curvature equation in arbitrary manifolds are continuous and we solve a conjecture by S. Hildebrandt [Hil1] claiming that critical points of continuously differentiable elliptic conformally invariant Lagrangian in two dimensions are continuous.     

Self-healing slip pulses along a gel/glass interface

We present experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity: steady sliding at high velocity (>V(c) approximately 100--125 microm/s), characterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a "healing instability" occurring when the local sliding velocity reaches the macroscopic transition velocity V(c). At driving velocities close below V(c), the system exhibits complex spatiotemporal behavior.