An analysis of over-relaxation in a kinetic approximation of systems of conservation laws

The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to apply the equilibrium source term in a more precise way. This is also a key ingredient of the lattice Boltzmann method for achieving second-order accuracy. In this work, we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables.     

The Effect of the Spacer of Bis(biurea) Ligands on the Structure of A2L3‐type (A=anion) Phosphate Complexes

By tuning the length and rigidity of the spacer of bis(biurea) ligands L, three structural motifs of the A₂L₃ complexes (A represents anion, here orthophosphate PO₄^3?), namely helicate, mesocate, and mono‐bridged motif, have been assembled by coordination of the ligand to phosphate anion. Crystal structure analysis indicated that in the three complexes, each of the phosphate ions is coordinated by twelve hydrogen bonds from six surrounding urea groups. The anion coordination properties in solution have also been studied. The results further demonstrate the coordination behavior of phosphate ion, which shows strong tendency for coordination saturation and geometrical preference, thus allowing for the assembly of novel anion coordination‐based structures as in transition‐metal complexes.     

A volatolomic approach using cerumen as biofluid to diagnose bovine intoxication by Stryphnodendron rotundifolium

An innovative volatolomic approach employs the detection of biomarkers present in cerumen (earwax) to identify cattle intoxication by Stryphnodendron rotundifolium Mart., Fabaceae (popularly known as barbatimão). S. rotundifolium is a poisonous plant with the toxic compound undefined and widely distributed throughout the Brazilian territory. Cerumen samples from cattle of two local Brazilian breeds (‘Curraleiro Pé-Duro’ and ‘Pantaneiro’) were collected during an experimental intoxication protocol and analyzed using headspace (HS)/GC–MS followed by multivariate analysis (genetic algorithm for a partial least squares, cluster analysis, and classification and regression trees). A total of 106 volatile organic metabolites were identified in the cerumen samples of bovines. The intoxication by S. rotundifolium influenced the cerumen volatolomic profile of the bovines throughout the intoxication protocol. In this way, it was possible to detect biomarkers for cattle intoxication. Among the biomarkers, 2-octyldecanol and 9-tetradecen-1-ol were able to discriminate all samples between intoxicated and nonintoxicated bovines. The cattle intoxication diagnosis by S. rotundifolium was accomplished by applying the cerumen analysis using HS/GC–MS, in an easy, accurate, and noninvasive way. Thus, the proposed bioanalytical chromatography protocol is a useful tool in veterinary applications to determine this kind of intoxication.     

Synthesis of chiral 2′,3′-pyranone(pyrrolidinone)-fused tryptamines

Chiral pyrano- and pyrrolidino-fused tryptamines were prepared by a diasteroselective trimolecular condensation between indole, Garner's aldehyde and Meldrum's acid, followed by selective functional group transformations.     

Division des distributions et applications à l'étude d'idéaux de fonctions holomorphes

In this Note, we construct residue currents without Hironaka's theorem. As an application, we obtain a representation formula for holomorphic function as in Passare (Math. Scand. 62 (1988) 75–152). To cite this article: E. Mazzilli, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Extension des fonctions holomorphes dans les pseudo-ellipsoïdes

Sans résumé Received 17 April 1996; in final form 9 July 1996     

Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996     

Zero weights and non-zero slacks: Different solutions to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.     

Une note sur les lemmes div–curl

Let $\text{Ω}$ be a strongly Lipschitz domain of $\text{R}{}^{\mathrm{n}}$ (n?2). We give endpoint versions of div–curl lemmata on $\text{Ω}$, for a given function f on $\text{Ω}$ whose gradient belongs to a Hardy space on $\text{Ω}$. To cite this article: P. Auscher et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

tert‐Butyl (6S)‐4‐hydroxy‐6‐isobutyl‐2‐oxo‐1,2,5,6‐tetra­hydropyridine‐1‐carboxyl­ate and tert‐butyl (4R,6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxopiperidine‐1‐carboxyl­ate

X‐ray studies reveal that tert‐butyl (6S)‐6‐iso­butyl‐2,4‐dioxo­piperidine‐1‐carboxyl­ate occurs in the 4‐enol form, viz. tert‐butyl (6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxo‐1,2,5,6‐tetra­hydropyri­dine‐1‐carboxyl­ate, C₁₄H₂₃NO₄, when crystals are grown from a mixture of di­chloro­methane and pentane, and has an axial orientation of the iso­butyl side chain at the 6‐position of the piperidine ring. Reduction of the keto functionality leads predominantly to the corresponding β‐hydroxy­lated δ‐lactam, tert‐butyl (4R,6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxo­piperidine‐1‐car­boxyl­ate, C₁₄H₂₅NO₄, with a cis configuration of the 4‐hydroxy and 6‐iso­butyl groups. The two compounds show similar molecular packing driven by strong O—H⋯O=C hydrogen bonds, leading to infinite chains in the crystal structure.