Elementary constructive theory of Henselian local rings

We give an elementary theory of Henselian local rings and construct the Henselisation of a local ring. All our theorems have an algorithmic content. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Etude de la détonation de mélanges pauvres H2NO2/N2O4

Calculations of the detonation reaction zone of gaseous H₂NO₂/N₂O₄ mixtures in the range of equivalence ratio Φ between 0.25 and 0.7 show that for 0.25Φ0.4 the chemical energy is released in two distinct and successive exothermic steps characterised by different chemical characteristic times. As for rich mixtures, the first exothermic step is mainly due to the reaction NO₂ + H → NO + OH, but the second one is different since it results from the exothermic decomposition of NO into N₂ and O₂. For Φ=0.3 the measured detonation velocity in a tube of 52 mm internal diameter is very much smaller than the calculated value and the mean size of the cellular structure is very much larger than the value extrapolated from data obtained with mixtures of higher but close equivalence ratio. All these results show that the detonation, though self-sustained and steady, is ‘non-ideal’, i.e. it is supported only by a part of the available chemical energy, that provided mainly by the first exothermic step. To cite this article: D. Desbordes et al., C. R. Mecanique 332 (2004).     

Boundedness of a class of bi-parameter square functions in the upper half-space

We consider a class of bi-parameter kernels and related square functions in the upper half-space, and give an efficient proof of a boundedness criterion for them. The proof uses modern probabilistic averaging methods and is based on controlling double Whitney averages over good cubes.     

Kato’s Euler system and rational points on elliptic curves I: A p-adic Beilinson formula

This article is the first in a series devoted to Kato’s Euler system arising from p-adic families of Beilinson elements in the K-theory of modular curves. It proves a p-adic Beilinson formula relating the syntomic regulator (in the sense of Coleman-de Shalit and Besser) of certain distinguished elements in the K-theory of modular curves to the special values at integer points ≥ 2 of the Mazur-Swinnerton-Dyer p-adic L-function attached to cusp forms of weight 2. When combined with the explicit relation between syntomic regulators and p-adic étale cohomology, this leads to an alternate proof of the main results of [Br2] and [Ge] which is independent of Kato’s explicit reciprocity law.     

Cyclic and ruled Lagrangian surfaces in Euclidean four space

We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a Legendrian curve in the 3-sphere or a Legendrian curve in the anti-de Sitter 3-space. We describe ruled Lagrangian surfaces and characterize the cyclic and ruled Lagrangian surfaces which are solutions to the self-similar equation of the Mean Curvature Flow. Finally, we give a partial result in the case of Hamiltonian stationary cyclic surfaces.     

Flavonoids: hemisynthesis, reactivity, characterization and free radical scavenging activity

Phenolic compounds form one of the main classes of secondary metabolites. They display a large range of structures and they are responsible for the major organoleptic characteristics of plant-derived-foods and beverages, particularly color and taste properties and they also contribute to the nutritional qualities of fruits and vegetables. Phenolic compounds are also highly unstable compounds which undergo numerous enzymatic and chemical reactions during postharvest food storage and processing thus adding to the complexity of plant polyphenol composition. Among these compounds flavonoids constitute one of the most ubiquitous groups of all plant phenolics. Owing to their importance in food organoleptic properties and in human health, a better understanding of their structures, their reactivity and chemical properties in addition to the mechanisms generating them appears essential to predict and control food quality. The purpose of this work is an overview of our findings concerning the hemisynthesis, the reactivity and the enzymatic oxidation of some flavonoids and shed light on the mechanisms involved in some of these processes and the structures of the resulting products. The free radical scavenging activity of some of the synthesized compounds is also presented and a structure-activity relationship is discussed. The first part of this review concerns the synthesis and structural characterization of modified monomeric flavanols. The use of these compounds as precursor for the preparation of natural and modified dimeric procyanidin derivatives was then explored through different coupling reactions. The full characterization of the synthesized compounds was achieved by concerted use of NMR and ESI-MS techniques. The free radical scavenging activity of some of the synthesized compounds was investigated. The second part of this review concerns the enzymatic oxidation of several flavonols by Trametes versicolor laccase. Most of the major oxidation products have been isolated as pure compounds and their structures unambiguously established through spectroscopic methods. Correlation between the structure of the oxidation product and the substitution pattern of the starting materials allows mechanistic features of this transformation to be elucidated.     

Synthesis of PEDOT Nanoparticles and Vesicles by Dispersion Polymerization in Alcoholic Media

Summary: The synthesis of PEDOT nanoparticles and vesicles by dispersion polymerization in a methanol/water mixture (3/2, v/v) is reported, using either ammonium persulfate or iron(III) p‐toluenesulfonate as oxidants and α‐EDOT‐PEO as a reactive stabilizer. The influence of the oxidant as well as the α‐EDOT‐PEO molar mass and concentration on the core‐shell particle morphology and conductivity properties have been investigated. PEDOT particles with conductivities up to 1.5 × 10⁻² S · cm⁻¹ have been obtained in high yield.

TEM image of PEDOT vesicles prepared using PEO‐based stabilizers of 25 000 g · mol⁻¹ in water/methanol mixture (2:3 v/v) at room temperature using ammonium persulfate as an oxidant.