Une nouvelle méthode de raffinement de maillage spatio-temporel pour l'équation des ondes

In the present Note we introduce an extension of the conservative space–time mesh refinement method presented by Fouquet et al. We also propose a post-treatment of the solution that reduces the spurious phenomena due to the non-conformity between the time meshes. A reinterpretation of the equations in terms of new unknowns leads to a new scheme with second order consistent coupling equations. Numerical experiments in 2D and a plane wave analysis for the 1D model show that the method is second order accurate for an arbitrary refinement. To cite this article: J. Rodríguez, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Oxygenolysis of flavonoid compounds: DFT description of the mechanism for quercetin.

Flavonoids are naturally occurring phenol derivatives present in substantial amounts in a large variety of plants, fruits and vegetables daily eaten by humans. Most of these compounds exhibit several interesting biological activities, such as antiradical and antioxidant actions. Indeed, by complexation with specific enzymes, flavonoids are notably liable to metabolize molecular dioxygen. On the basis of experimental results describing oxygenolysis of the flavonoid quercetin, activated by the enzyme quercetin 2,3-dioxygenase (2,3-QD),ur attention has focused on the role of metal center in the activation of the substrate quercetin. Thus, in the present study, by means of DFT calculations at the B3LYP/ 6-31(+)G* level on model molecular systems, we describe different mechanisms for dioxygen metabolization by quercetin. Stationary points are described, and energetic and structural analyses along the reaction paths are reported. Our calculations show that the copper cation must act as an oxidant towards the substrate and that the reaction proceeds through a 1,3-cycloaddition.     

UV index experimental values during the years 2000 and 2001 from the Spanish broadband UV-B radiometric network

An analysis is made of experimental ultraviolet erythemal solar radiation data measured during the years 2000 and 2001 by the Spanish UV-B radiation evaluation and prediction network. This network consists of 16 Robertson-Berger type pyranometers for evaluating solar erythemal radiation and five Brewer spectroradiometers for evaluating the stratospheric ozone. On the basis of these data the Ultraviolet Index (UVI) was evaluated for the measuring stations that are located either in coastal regions or in the more densely populated regions inland on the Iberian Peninsula. It has been checked that in most cases the maximum irradiance values corresponded to solar noon, although there were exceptions that could be explained by cloudiness. The maximum experimental values of the UVI were around 9 during the summer, though frequently passing this value at the inland measurement stations. The annual accumulated dose of irradiation on a horizontal plane has also been studied, as well as the evolution through the year in units of energy, standard erythemal doses and minimum erythemal doses, according to different phototypes.     

Biosynthesis of Streptolidine Involved Two Unexpected Intermediates Produced by a Dihydroxylase and a Cyclase through Unusual Mechanisms

Streptothricin‐F (STT‐F), one of the early‐discovered antibiotics, consists of three components, a β‐lysine homopolymer, an aminosugar D ‐gulosamine, and an unusual bicyclic streptolidine. The biosynthesis of streptolidine is a long‐lasting but unresolved puzzle. Herein, a combination of genetic/biochemical/structural approaches was used to unravel this problem. The STT gene cluster was first sequenced from a Streptomyces variant BCRC 12163, wherein two gene products OrfP and OrfR were characterized in vitro to be a dihydroxylase and a cyclase, respectively. Thirteen high‐resolution crystal structures for both enzymes in different reaction intermediate states were snapshotted to help elucidate their catalytic mechanisms. OrfP catalyzes an Fe^II‐dependent double hydroxylation reaction converting L ‐Arg into (3R,4R)‐(OH)₂‐L ‐Arg via (3S)‐OH‐L ‐Arg, while OrfR catalyzes an unusual PLP‐dependent elimination/addition reaction cyclizing (3R,4R)‐(OH)₂‐L ‐Arg to the six‐membered (4R)‐OH‐capreomycidine. The biosynthetic mystery finally comes to light as the latter product was incorporation into STT‐F by a feeding experiment.     

Electromechanical phase transition in hexacyanometallate nanostructure (Prussian Blue)

This paper demonstrates the importance of the structural changeover in controlling the physical-chemical properties of hexacyanometalate-like materials (Prussian Blue). A meticulous in situ study of compositional variations using electroacoustic impedance techniques associated to electrogravimetric techniques in hexacyanoferrates containing K+ alkali metals reveals the existence of a nanostructural changeover coupled to a change of the magnetic properties of these electromagnetic materials. In the same way, the electroacoustic impedance techniques can be useful both in the understanding and in the in situ monitoring of the structural changeovers and the magnetic behavior of all kinds of materials.     

Complete classification of the direction loci for three-wave collinear quadratic parametric interactions in biaxial acentric crystals

One new topological classification of the phase-matching direction loci for sum/difference frequency generation in biaxial acentric crystals is presented. Based on nine fundamental axial wave constant mismatches, 12 locus indices are used to distinguish permissible direction loci. Totally 66 kinds of combined loci belonging to 30 main classes are found and categorized by a set of ternary-digit class symbols or equivalently by sequence numbers. They are well illustrated in a classification diagram, indicative of 170 possible transitions among the loci. By an analysis of the dispersion of refractive indices, the historic “optically well-behaved crystals” are redefined and improved with simplified classification diagrams and corresponding schematic stereographic projections.     

Mechanistic Insights into the Substrate‐Controlled Stereochemistry of Glycals in One‐Pot Rhodium‐Catalyzed Aziridination and Aziridine Ring Opening

We carried out a principle study on the reaction mechanism of rhodium‐catalyzed intramolecular aziridination and aziridine ring opening at a sugar template. A sulfamate ester group was introduced at different positions of glycal to act as a nitrene source and, moreover, to allow the study of the relative reactivity of the nitrene transfer from different sites of the glycal molecule. The structural optimization of each intermediate along the reaction pathway was extensively done by using BPW91 functional. The crucial step in the reaction is the Rh‐catalyzed nitrene transfer to the double bond of the glycal. We found that the reaction could proceed in a stepwise manner, whereby the N atom initially induced a single‐bond formation with C1 on the triplet surface or in a single step through intersystem crossing (ISC) of the triplet excited state of the rhodium–nitrene transition state to the singlet ground state of the aziridine complexes. The relative reactivity for the conversion of the nitrene species to the aziridine obtained from the computed potential energy surface (PES) agrees well with the reaction time gained from experimental observation. The aziridine ring opening is a spontaneous process because the energy barrier for the formation of the transition state is very small and disappears in the solution calculations. The regio‐ and stereoselectivity of the reaction product is controlled by the electronic property of the anomeric carbon as well as the facial preference for the nitrene insertion, and the nucleophilic addition.     

On evolutoids of planar convex curves

There are many interesting curves which we can associate with a given convex curve, however, in this work we are especially interested in studying the relations between the given curve and its evolutoids: that is, the curve obtained as the envelope of lines making a fixed angle with the normal line at every point of the curve. The first result is an inequality between the area enclosed by the given curve and the area enclosed by its evolutoid. Also, we proved that a convex curve is of constant width (centrally symmetric) if and only if its evolutoid for a fixed angle is of constant width (centrally symmetric).