Représentations -adiques et normes universelles I. Le cas cristallin

Let be a crystalline -adic representation of the absolute Galois group of an finite unramified extension of , and let be a lattice of stable by . We prove the following result: Let be the maximal sub-representation of with Hodge-Tate weights strictly positive and . Then, the projective limit of is equal up to torsion to the projective limit of . So its rank over the Iwasawa algebra is .

     

Modélisation de structures électromagnétiques périodiques – matériaux bianisotropes avec mémoire

In this Note we propose a rigorous justification of the limit constitutive law of a periodic bi-anisotropic electromagnetic structure with memory. This study is based on the periodic unfolding method, introduced by D. Cioranescu, A. Damlamian and G. Griso, and is applied on the time domain and on the frequency domain. To cite this article: A. Bossavit et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the plane. We provide a general construction that for any arc-connected compact set $X$ X in $\mathbb{R }^2$ R 2 that is not an axis-aligned rectangle and for any positive integer $k$ k produces a family $\mathcal{F }$ F of sets, each obtained by an independent horizontal and vertical scaling and translation of $X$ X , such that no three sets in $\mathcal{F }$ F pairwise intersect and $\chi (\mathcal{F })>k$ χ ( F ) > k . This provides a negative answer to a question of Gyárfás and Lehel for L-shapes. With extra conditions we also show how to construct a triangle-free family of homothetic (uniformly scaled) copies of a set with arbitrarily large chromatic number. This applies to many common shapes, like circles, square boundaries or equilateral L-shapes. Additionally, we reveal a surprising connection between coloring geometric objects in the plane and on-line coloring of intervals on the line.     

Descente infinie et hauteurp-adique sur les courbes elliptiques à multiplication complexe

Sans résumé     

Application of chemiluminescence for the detection of peroxy compounds in high-performance liquid chromatography

The possibility of applying post-column reaction and chemiluminescence to determine organic peroxy compounds by RP-HPLC was investigated. Conditions of qualitative and quantitative analyses have been established. The applicability of the method has been demonstrated for a series of compounds representative of the most important groups of peroxy-type compounds, that is, hydroperoxides, dialkyl peroxides, diacyl peroxides, peroxyesters, and peroxyacids.     

Formation of pentagonal tunnels bordered with P2O7 groups in diphosphate tungsten bronzes (P2O4)2(WO3)2m: A HREM investigation

During the investigation of the phosphate bronzes (PO₂)₄(WO₃)_2m [MPTB_P] and K_x(P₂O₄)₂WO₃)_2m [DPTB_H] crystals of a new type were observed. HREM images of these crystals showed twinned ReO₃-type slabs the junction of which was parallel to the (102)_ReO3 plane. The proposed model identified the twin boundary as built from P₂O₇ groups involving the formation of pentagonal tunnels. The structure of this new type of extended defects is quite original: it corresponds to a new structural type named “diphosphate tungsten bronzes with pentagonal tunnels” [DPTB_P], for which no regular member could be synthesized. Image calculations were performed to confirm the junction model. Apart from the disordered stacking of the ReO₃-type slabs, very few defects were observed and shear planes were only obtained in reduced samples. This new structural type takes its place in the large family of phosphate tungsten bronzes where all members (DPTB_H, MPTB_H, MPTB_P) are very closely related.     

[Mo12S12O12(OH)12(H2O)6]: A Cyclic Molecular Cluster Based on the [Mo2S2O2]2+ Building Block

The pH-dependent self-condensation of the [Mo ₂ S ₂ O ₂ ] ²⁺ complex fragment gives the wheellike Mo₁₂ cluster depicted on the right (ball-and-stick model; large balls: S, medium balls: O, small balls: Mo). Applying this synthetic strategy to other starting materials could provide access to other polyoxothiometalates with well-defined cavities.     

Synthesis and Pesticidal Properties of Thio and Seleno Analogs of Some Common Urea Herbicides

Thio and seleno analogs of fenuron, isoproturon, chlorotoluron, metoxuron, monuron, and diuron were synthesized from the corresponding aryl amines. Their reaction with thiophosgene leads to isothiocyanates. Aryl amines were also converted (via isocyanides) to isoselenocyanates. The reaction of both isothio- and isoselenocyanates with dimethylamine affords the corresponding thio and seleno analogs of the above-mentioned urea herbicides. Herbicidal activity of the synthesized compounds was slightly lower than the activity of the parent urea herbicides. The thio and seleno analogs as well as the parent ureas showed good fungicidal activity at a concentration of 200 ppm against selected fungi.     

Insights into the biosynthesis of hormaomycin, an exceptionally complex bacterial signaling metabolite

Hormaomycin produced by Streptomyces griseoflavus is a structurally highly modified depsipeptide that contains several unique building blocks with cyclopropyl, nitro, and chlorine moieties. Within the genus Streptomyces, it acts as a bacterial hormone that induces morphological differentiation and the production of bioactive secondary metabolites. In addition, hormaomycin is an extremely potent narrow-spectrum antibiotic. In this study, we shed light on hormaomycin biosynthesis by a combination of feeding studies, isolation of the biosynthetic nonribosomal peptide synthetase (NRPS) gene cluster, and in vivo and in vitro functional analysis of enzymes. In addition, several nonnatural hormaomycin congeners were generated by feeding-induced metabolic rerouting. The NRPS contains numerous highly repetitive regions that suggest an evolutionary scenario for this unusual bacterial hormone, providing new opportunities for evolution-inspired metabolic engineering of novel nonribosomal peptides.