Solutions of the Allen-Cahn equation which are invariant under screw-motion

Let ${\phi(x)}$ be a rational function of degree >?1 defined over a number field K and let ${\Phi_{n}(x,t) = \phi^{(n)}(x)-t \in K(x,t)}$ where ${\phi^{(n)}(x)}$ is the nth iterate of ${\phi(x)}$ . We give a formula for the discriminant of the numerator of Φ _n (x, t) and show that, if ${\phi(x)}$ is postcritically finite, for each specialization t ₀ of t to K, there exists a finite set ${S_{t_0}}$ of primes of K such that for all n, the primes dividing the discriminant are contained in ${S_{t_0}}$ .     

Nonlinear Schrödinger equations: concentration on weighted geodesics in the semi-classical limit

We consider the problem

${?}^2\mathrm{\Delta }u?V(x)u+u^p=0,u>0,u\in H^1({\mathbb{R}}^2),$

where $p>1$, $?>0$ is a small parameter and V is a uniformly positive, smooth potential. Let Γ be a closed curve, nondegenerate geodesic relative to the weighted arclength ${\int }_{\Gamma }{V}^{\sigma }$, where $\sigma =\frac{p+1}{p?1}?\frac{1}{2}$. We prove the existence of a solution $u_{\mathrm{\epsilon }}$ concentrating along the whole of Γ, exponentially small in ? at any positive distance from it, provided that ? is small and away from certain critical numbers. This proves a conjecture raised in [A. Ambrosetti, A. Malchiodi, W.-M. Ni, Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I, Commun. Math. Phys. 235 (2003) 427–466] in the two-dimensional case. To cite this article: M. del Pino et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

A re-statement of the Hohenberg–Kohn theorem and its extension to finite subspaces

Bearing in mind the insight into the Hohenberg–Kohn theorem for Coulomb systems provided recently by Kryachko (Int J Quantum Chem 103:818, 2005), we present a re-statement of this theorem through an elaboration on Lieb’s proof as well as an extension of this theorem to finite subspaces. Contribution to the Serafin Fraga Memorial Issue.     

Determination of ageing time of spirits in oak barrels using a headspace–mass spectrometry (HS-MS) electronic nose system and multivariate calibration

The aromatic composition of sugar cane spirits and, in general, of alcoholic beverages, is mainly influenced by the ageing process in wood barrels. There are several factors that affect the quality of the final aged product, but the time of the storage in the barrel is perhaps the most important one. Ageing time must therefore be controlled in order to detect counterfeits; however, this parameter is very difficult to control and, at present, there is no analytical method available to determine it. We propose a quantitative method for determining the ageing time of sugar cane spirits in oak barrels by using an electronic nose based on coupling directly a headspace sampler to a mass spectrometer (HS-MS), and multivariate calibration. The method developed is simple and provides, in 5 min, the ageing time of spirits with an accuracy of about 1 month.     

Focused microwave-assisted micellar extraction combined with solid-phase microextraction--gas chromatography/mass spectrometry to determine chlorophenols in wood samples

This work describes the utilization of the focused microwave-assisted micellar extraction in combination with the solid-phase microextraction (SPME) to determine chlorophenols in wood samples. The influence of the nature of the surfactant in the extraction process, the optimization of the variables of the focused-microwave system, and the effect of the ageing time of the samples in the extraction efficiency of the method, have been assessed in this study. The overall method using the non-ionic surfactant POLE as extracting medium allows us to determine chlorophenols in wood samples achieving an average extraction efficiency of 104.1%, limits of detection ranging from 2 to 120 ng g⁻¹, and intermediate precision values ranging between 3.5 and 13.2%. The proposed method is also characterized by short analysis times (around 5 min for the microwaves extraction step) and by avoiding the use of organic solvents.     

Thermodynamic and structural properties of confined discrete-potential fluids

The thermodynamic and structural behaviors of confined discrete-potential fluids are analyzed by computer simulations, studying in a systematic way the effects observed by varying the density, temperature, and parameters of the potentials that characterize the molecule-molecule interactions. The Gibbs ensemble simulation technique for confined fluids [A. Z. Panagiotopoulos, Mol. Phys. 62, 701 (1987)] is applied to a fluid confined between two parallel hard walls. Two different systems have been considered, both formed by spherical particles that differ by the interparticle pair potential: a square well plus square shoulder or a square shoulder plus square well interaction. These model interactions can describe in an effective way pair potentials of real molecular and colloidal systems. Results are compared with the simpler reference systems of square-shoulder and square-well fluids, both under confinement. From the adsorption characterization through the use of density profiles, it is possible to obtain specific values of the interparticle potential parameters that result in a positive to negative adsorption transition.     

Assignment of acetyl groups to O-2 and/or O-3 of pectic oligogalacturonides using negative electrospray ionization ion trap mass spectrometry

Partially acetylated and methylated oligogalacturonides produced by enzymatic hydrolysis of sugar beet pectin were analysed by negative electrospray ionization ion trap mass spectrometry (ESI-ITMS). The (18)O labelling of the oligomer reducing end allowed the precise assignment of the fragments resulting from glycosidic bond and cross-ring cleavages. The collisional-induced dissociation of the C(i) and Z(j) fragment ions through sequential MS(n) experiments always displayed (0, 2)A-type cross-ring cleavage ions which were related to C(2)H(4)O(2) losses. These (0, 2)A ions appeared to be highly diagnostic ions allowing the precise location of the acetyl groups to the O-2 and/or O-3 of the acetylated galacturonic acid residues.