Invariant generalized functions on sl(2,R) with values in a sl(2,R)-module

AbstractLet g be a finite-dimensional real Lie algebra. Let ρ:g→End(V) be a representation of g in a finite-dimensional real vector space. Let CV=(End(V)⊗S(g))g be the algebra of End(V)-valued invariant differential operators with constant coefficients on g. Let U be an open subset of g. We consider the problem of determining the space of generalized functions φ on U with values in V which are locally invariant and such that CVφ is finite dimensional.In this article we consider the case g=sl(2,R). Let N be the nilpotent cone of sl(2,R). We prove that when U is SL(2,R)-invariant, then φ is determined by its restriction to U⧹N where φ is analytic (cf. Theorem 6.1). In general this is false when U is not SL(2,R)-invariant and V is not trivial. Moreover, when V is not trivial, φ is not always locally L1. Thus, this case is different and more complicated than the situation considered by Harish-Chandra (Amer. J. Math 86 (1964) 534; Publ. Math. 27 (1965) 5) where g is reductive and V is trivial.To solve this problem we find all the locally invariant generalized functions supported in the nilpotent cone N. We do this locally in a neighborhood of a nilpotent element Z of g (cf. Theorem 4.1) and on an SL(2,R)-invariant open subset U⊂sl(2,R) (cf. Theorem 4.2). Finally, we also give an application of our main theorem to the Superpfaffian (Superpfaffian, prepublication, e-print math.GR/0402067, 2004)

Influence of limestone filler and of the size of the aggregates on DEF

This experimental study aims to determine the effect of limestone filler on concrete expansion due to delayed ettringite formation (DEF). Different mortars made with different sizes and percentages of limestone filler and Portland cement CEM I 52.5N are conserved in water. The expansion of the specimens is measured. Results show that DEF is not inhibited by limestone filler. The kinetics and the amplitude of the swelling depend on the size of the limestone filler. The volume fraction of aggregates changes only the kinetics: the relation between swelling and water uptake depends only on the size of the aggregates.Comment: 16 pages, 9 figures, 4 table

CONTRIBUTION A L'HISTOIRE DES TECHNIQUES ET DE L'ARMEMENT : ESSAIS DE RESTITUTION DU FORGEAGE DE POINTES DE FLECHE A PARTIR DE BARRES DE FER D'EPOQUE ANTIQUE

International audienceCette étude porte sur la recherche des conditions de forgeage optimales ayant conduit à la réalisation de pointes de flèche diverses, identiques à celles dont on dispose pour l'époque antique, parfois en grande abondance, comme cela est le cas pour le site du siège d'Uxellodunum, au Puy d'Issolud (Lot). L'expérimentation a été conduite avec le concours d'un taillandier spécialiste de la restitution d'armes anciennes. L'originalité du travail porte sur le choix du forgeage de barres archéologiques issues des épaves gisant au large des Saintes-Maries-de-la-Mer, en Méditerranée, et des fouilles du Couperé à Saint Bertrand de Comminges, dans les Pyrénées. La caractérisation métallographique préalable de ces barres nous a permis de suivre l'incidence des conditions de forgeage sur la microstructure des pointes de flèche réalisées. Les principaux faciès typologiques et microstructuraux des flèches antiques ont été reproduits, permettant ainsi d'affiner la connaissance technique du protocole de forgeage du fer, au début de notre ère

Icodextrin-induced peritonitis: Study of five cases and comparison with bacterial peritonitis

Icodextrin-induced peritonitis: Study of five cases and comparison with bacterial peritonitis.BackgroundAn epidemic of aseptic peritonitis related to the presence of peptidoglycan contaminant in some batches of icodextrin solution (Extraneal®, Baxter Healthcare Corporation) occurred in Europe in the first six months of 2002.MethodsBy case-control study we examined the clinical and biologic features of 5 patients with icodextrin-induced peritonitis (group AP) and compared them with 7 patients with bacterial peritonitis (group BP) recruited in our clinical center between January and June 2002.ResultsDiagnosis of icodextrin-induced peritonitis was confirmed in all cases by a positive reintroduction test with contaminated batches of icodextrin. No recurrence was observed on re-exposure to icodextrin free of peptidoglycan. Skin tests were positive with contaminated icodextrin in 2 of 5 patients, while they were negative with icodextrin solution free of peptidoglycan (<0.6ng/mL). During peritonitis, serum level of C-reactive protein (CRP) was lower in group AP (42.4 ± 34mg/L) than in group BP (135 ± 59mg/L) (P = 0.01). Leukocyte number in peritoneal dialysis effluent was lower in group AP (284 ± 101/mm3), with a lower neutrophil/monocyte ratio (N/M = 0.67) than in group BP (1410 ± 973/mm3; N/M = 4) (P < 0.05). A low number of peritoneal fluid eosinophilia (11 ± 8%) was detected in group AP.ConclusionIcodextrin-induced peritonitis was associated with a burst of intraperitoneal cytokines. The phenotype of peritoneal neutrophils was different between aseptic and bacterial peritonitis, indicating that inflammatory stimuli that activate neutrophils in both types of peritonitis are clearly distinct. Finally, peritoneal injury measured by weight gain, peritoneal permeability, and CA125 concentration seemed to be less severe during icodextrin-induced peritonitis than during bacterial peritonitis

beta-Cu2V2O7: a spin-1/2 honeycomb lattice system

We report on band structure calculations and a microscopic model of the low-dimensional magnet beta-Cu2V2O7. Magnetic properties of this compound can be described by a spin-1/2 anisotropic honeycomb lattice model with the averaged coupling \bar J1=60-66 K. The low symmetry of the crystal structure leads to two inequivalent couplings J1 and J1', but this weak spatial anisotropy does not affect the essential physics of the honeycomb spin lattice. The structural realization of the honeycomb lattice is highly non-trivial: the leading interactions J1 and J1' run via double bridges of VO4 tetrahedra between spatially separated Cu atoms, while the interactions between structural nearest neighbors are negligible. The non-negligible inter-plane coupling Jperp~15 K gives rise to the long-range magnetic ordering at TN~26 K. Our model simulations improve the fit of the magnetic susceptibility data, compared to the previously assumed spin-chain models. Additionally, the simulated ordering temperature of 27 K is in remarkable agreement with the experiment. Our study evaluates beta-Cu2V2O7 as the best available experimental realization of the spin-1/2 Heisenberg model on the honeycomb lattice. We also provide an instructive comparison of different band structure codes and computational approaches to the evaluation of exchange couplings in magnetic insulators.Comment: 11 pages, 10 figures, 2 tables: revised version, extended description of simulation result

Activité Anti-Hyperglycémiante Et Élucidation Structurale Des Composés Isolés Des Feuilles De Spondias Purpurea L. (Anacardiaceae)

Spondias purpurea L. (Anacardiaceae) is a Senegalese traditional pharmacopoeia plant, which leaves are used in the treatment of various diseases. The leaves’ ethanolic extract exhibited antihyperglycemic activity on models of temporary hyperglycemia. The tests were performed on normoglycemic rats with a glucose tolerance test. The phytochemical investigation of the leaves resulted in the isolation of four flavonoids (quercetin 9, kaempferol 10, quercetin-3- ß-glucopyranoside 6, kaempferol3-ß-galactopyranoside 8), five phenolic compounds (2,4-dihydroxybenzoic acid 2, 4-hydroxybenzoic acid 5, protocatechic 4-ß-glucoside acid 1, hydroxycynnamic acid 7, 5-caffeoylquinic acid 3) and one tannin (Strictinin 4). The known isolated compounds were characterized by NMR and massspectrometry. The present study constitutes the first phytochemical examination of the leaves and the anti-hyperglycemic activity of the ethanolic extract of Spondias Purpurea L