The Picard group of the loop space of the Riemann sphere

The loop space of the Riemann sphere consisting of all C^k or Sobolev W^{k,p} maps from the circle S^1 to the sphere is an infinite dimensional complex manifold. We compute the Picard group of holomorphic line bundles on this loop space as an infinite dimensional complex Lie group with Lie algebra the first Dolbeault group. The group of Mobius transformations G and its loop group LG act on this loop space. We prove that an element of the Picard group is LG-fixed if it is G-fixed; thus completely answer the question by Millson and Zombro about G-equivariant projective embedding of the loop space of the Riemann sphere.Comment: International Journal of Mathematic

Direct observation of Fe spin reorientation in single crystalline YbFe6Ge6

We have grown single crystals of YbFe6Ge6 and LuFe6Ge6 and characterized their anisotropic behaviour through low field magnetic susceptibility, field-dependent magnetization, resistivity and heat capacity measurements. The Yb+3 valency is confirmed by LIII XANES measurements. YbFe6Ge6 crystals exhibit a field-dependent, sudden reorientation of the Fe spins at about 63 K, a unique effect in the RFe6Ge6 family (R = rare earths) where the Fe ions order anti-ferromagnetically with Neel temperatures above 450 K and the R ions' magnetism appears to behave independently. The possible origins of this unusual behaviour of the ordered Fe moments in this compound are discussed.Comment: 12 pages, 8 figures, accepted in J. Phys.: Cond. Matte

Fractionnement et caractérisation de la matière organique des lixiviats de décharges d'ordures ménagères

Les lixiviats de décharge constituent une source de nuisance qui vient s'ajouter aux nombreux problèmes de contamination du milieu environnant s'ils ne sont pas traités avant leur rejet. La matière organique, principale composante de ces effluents, doit retenir une grande attention dans la mesure où il est difficile d'éviter la propagation et la diffusion de cette pollution dans les sols et vers les nappes phréatiques. Cette étude vise à fractionner et à caractériser la matière organique présente dans des lixiviats de décharges d'ordures ménagères afin de prévoir et d'orienter le choix des traitements les plus adaptés compte tenu de leur biodégradabilité.La méthode de fractionnement utilisée comprend une adsorption spécifique sur résines macroporeuses Amberlite XAD (combinaison de XAD-7 et XAD-4) pour séparer les composés hydrophobes et hydrophiles qui sont ensuite extraits à la soude (composés acides) et au dichlorométhane (composés neutres). Le fractionnement de la matière organique par filtration sur résines XAD-7 et XAD-4, après une première étape de précipitation en milieu acide (pH=1), a permis de répartir l'ensemble des composés organiques du lixiviat dans six fractions de spécificités différentes fonction de la taille et/ou du caractère hydrophile ou hydrophobe des molécules. Les résultats montrent que ce protocole expérimental permet d'extraire au moins 98 % de la matière organique totale (pourcentage relatif aux teneurs de la demande chimique en oxygène ou DCO), dont la plus grande proportion est constituée des substances humiques (76 % à 90 % en DCO). Diverses méthodes analytiques ont été proposées en vue de caractériser les fractions isolées telles que l'analyse élémentaire, la spectrophotométrie infrarouge, la résonanoe magnétique nucléaire C13 (RMN Cl3) et la chromatographie CG/FID et CG/SM.Landfill leachates represent an obvious source of pollution for the environment and many studies have attempted to analyze organic pollutants found in leachates. A number of methods have been described in the literature for the isolation and concentration of dissolved organic matter from landfill leachate samples. Membrane ultrafiltration, gel permeation and high performance liquid chromatography are commonly used because these techniques can be easily adapted to separate soluble organic substances from large volumes of leachate. The objective of this study was to fractionate and characterize dissolved organic matter found in leachates collected from sanitary landfills.The discharges are defined with regard to the geological context from which they are situated and the nature of the waste. The discharges are classified in three categories, based upon the value of the permeability coefficient K, the substratum and its continuity.- class 1; impermeable site (K 10-[sup]6 ms-¹). The studied leachates come from landfill of class 2:- Crézin (Haute-Vienne) of compacted type: it was used for household rubbish and assimilated ordinary wastes. - Foussais-Payre (Vendée): leachate coming from the fermentation area of a composting plant and from the compost refuse. Fractionation of dissolved organic matter was applied on three leachates samples. The first sample was the raw leachate collected from the Crézin landfill and the two others came from Foussais-Payre (a raw sample and a sample treated in an aerated lagoon for 52 days). Because of the wide variety of organic compounds that can be found in such leachates, we classified and isolated the different groups of organic constituents using an XAD resin adsorption procedure. The experimental method consisted of acidifying samples to pH 1 to isolate the first fraction (fig. 1) and then treating the remaining supernatant with XAD-7 and XAD-4 resins. The adsorption on XAD resins allowed the isolation of the other organic fractions (figs. 2 to 6). Various analytical techniques were applied to characterize the isolated fractions such as elementary analysis infrared spectroscopy, ¹3C nuclear magnetic resonance (¹3C CP/MAS NMR), gas chromatography (GC/FID), and gas chromatography coupled to mass spectrometry (GC/MS). Results showed that more then 90% of the total organic carbon (TOC) in leachates can he recovered by the isolation procedure. Most of the isolated compounds corresponded to humic substances (76% to 90% of the chemical oxygen demand). Hydrophobic and hydrophilic neutral compounds were found only in small concentrations

Adsorption du pentachlorophenol sur divers matériaux : Influence de co-adsorbats organiques (Substances humiques et lindane)

Nous avons réalisé, pour de faibles concentrations, l'étude de l'adsoprtion d'un pesticide le pentachlorophénol, sur plusieurs matériaux adsorbants : le charbon actif, la kaolinite et la bentone. Les résultats montrent que l'adsorption du pentachlorophénol sur la kaolinite reste négligeable tandis que la bentone SD-3 (argile traitée) permet d'obtenir des résultats intéressants avec toutefois une capacité maximale d'adsorption 10 à 100 fois plus faible que celle du charbon actif. Le charbon actif reste le meilleur matériau adsorbant pour le pentachlorophénol. La solubilité de ce composé étant très variable en fonction du pH du milieu on constate que l'adsorption du pentachlorophénol-pentachlorophénate (5 mg.l-1) diminue pour des valeurs de pH supérieures au pKa du couple acide-base que nous avons déterminé expérimentalement, égal à 5,9 ± 0,1. L'adsorption du pentachlorophénol n'est pas affectée par la présence d'acides humiques (obtenus à partir de substances commerciales) utilisés comme coadsorbats (10 mg.l-1) alors que les acides fulviques (20 mg.l-1) extraits de sols semblent provoquer une promotion de l'adsorption. On observe d'autre part que le pentachlorophénol n'affecte pas l'adsorption des acides humiques mais augmente légèrement celle des acides fulviques. Ces remarques suggèrent la possible formation d'un complexe acides fulviques-pentachlorophénol. Lorsqu'on utilise le lindane, pesticide hydrophobe comme coadsorbat (165 mg.l-1), on observe encore d'une façon systématique pour tous les nombreux essais une légère promotion de l'adsorption.Adsorption studies for the removal of the pesticide pentachlorophenol found in a number of water supplies (BELAMIE and GIROUD, 1986) were carried out using various materials including kaolinite, bentone SD-3 and powdered activated carbon (WEBER and GOULD, 1966; WEBER and JODELHAH, 1985). It was found that adsorption on kaolinite was negligible, whereas bentone SD-3 presented and adsorption efficiency from 10 to 100-fold less than equivalent quantities of powdered activated carbon (LOTSE et al., 1968; SHAROM et al., 1980). The effect of the pH on the removal of pentachlorophenol by activated carbon was studied. The removal efficiency of pentachlorophenol by activated carbon is better in acidic media. A clear dependence of adsorption on the pH appeared to be the result of a marked variation of the pesticide solubility as a function of the pH (fig. 3). Adsorption of pentachlorophenol/phenate (5mg.l-1) diminishes markedly at pH values above the pKa of this weak acid (that we found equal to 5,9 ± 0,1) when the pentachlorophenol exists almost entirely in ionic form in aqueous solution, and is enhanced at low pH when the percentage of molecular species (whose concentration can be determined from pKa value) becomes significant (WARD and GETZEN, 1970). These remarks and the adsorptive capacities (163 mg.g-1= 0,6 mmol.g-1 at pH = 5,2 and 79 mg.g-1 0,3 mmol.g-1 at pH =12,7), suggest a П-П interaction between pentachlorophenol and activated carbon which seems to be confirmed by the results with bentone SD-3 (tables 1 to 4), and the values of the electrokinetic potential of these materials. This study emphasizes the effect of organic coadsorbates (e.g., dissolved humic substances and the pesticide lindane) on the adsorption capacity of activated carbon for pentachlorophenol. Two different natural organic matters were studied as coadsorbates : purified humic acids from a commercial source (at 10 mg.l-1) and fulvic acids extracted from a top soil horizon (et 20 mg.l-1) (SCHNITZER and SKINNER, 1963; THURMAN and MALCOLM, 1981). Pentachlorophenol adsorption was not affected by humic acids, whereas an increase of adsorption seemed to be observed in the presence of fulvic acids (fig. 6). Pentachlorophenol does not affect the adsorption of humic acids, but improves slightly the removal of fulvic acids. This suggests an association between the two kinds of organic compounds (WERSNAW et al., 1969; KHAN, 1972; OGNER and SCHNITZER, 1970), the resulting « complex », fulvic acids/pentachlorophenol, being more adsorbed than the compounds themselves. The coadsorbate lindane (0,65 mg.l-1) which is easily adsorbed by activated carton (GOMELLA and BELLE, 1975...) seemed also to Improve slightly the removal efficiency of pentachlorophenol by activated carton (fig. 7)

Banach Analytic Sets and a Non-Linear Version of the Levi Extension Theorem

We prove a certain non-linear version of the Levi extension theorem for meromorphic functions. This means that the meromorphic function in question is supposed to be extendable along a sequence of complex curves, which are arbitrary, not necessarily straight lines. Moreover, these curves are not supposed to belong to any finite dimensional analytic family. The conclusion of our theorem is that nevertheless the function in question meromorphically extends along an (infinite dimensional) analytic family of complex curves and its domain of existence is a pinched domain filled in by this analytic family.Comment: 19 pages, This is the final version with significant corrections and improvements. To appear in Arkiv f\"or matemati

les peupleuments de Fourmis et les peuplements d'Acridiens du Mont Ventoux. II. Les peuplements de Fourmis

The composition of the ant communities and the relative frequency of each species are described, as well as their ecological and altitudinal amplitudes. The richness and/or the composition of the communities differs from one vegetation zone to another. All the communities show a very hierarchical structure. The Shannon' eaver index of evenness is roughly equal in all communities. The communities are very varied, but three species are predominant over the mountain : Lasiw; niger, Tetramorium caespitum and Formica lemani. Of the environmental features, temperature is the most important, producing a marked altitudinal zonation of species and communities. The effects of aridity are important among certain species, leading to vertical discontinuities in their ranges. The vegetation caver affects species dependant on particular plants ; these species have been considerably affected by reafforestation, especially on the lower parts of the southern slopes, leading to a notable increase in L. niger. At the summit, the main limiting factor is temperature on the northern slope ; and the dessicating effects of the winds on the southern slopes

Identification of the First Oomycete Mating-type Locus Sequence in the Grapevine Downy Mildew Pathogen, Plasmopara viticola

Mating types are self-incompatibility systems that promote outcrossing in plants, fungi, and oomycetes. Mating-type genes have been widely studied in plants and fungi but have yet to be identified in oomycetes, eukaryotic organisms closely related to brown algae that cause many destructive animal and plant diseases. We identified the mating-type locus of Plasmopara viticola, the oomycete responsible for grapevine downy mildew, one of the most damaging grapevine diseases worldwide. Using a genome-wide association approach, we identified a 570-kb repeat-rich non-recombining region controlling mating types, with two highly divergent alleles. We showed that one mating type was homozygous, whereas the other was heterozygous at this locus. The mating-type locus encompassed 40 genes, including one encoding a putative hormone receptor. Functional studies will, however, be required to validate the function of these genes and find the actual determinants of mating type. Our findings have fundamental implications for our understanding of the evolution of mating types, as they reveal a unique determinism involving an asymmetry of heterozygosity, as in sex chromosomes and unlike other mating-type systems. This identification of the mating-type locus in such an economically important crop pathogen also has applied implications, as outcrossing facilitates rapid evolution and resistance to harsh environmental conditions