Asymptotique de la norme $L^2$ d'un cycle géodésique dans les revêtements de congruence d'une variété hyperbolique arithmétique

Let M be an arithmetic hyperbolic manifold and be a codimension 1 geodesic cycle. In this paper, we study the asymptotic growth of the -norm of the lifts of F in the congruence tower above M. We obtain an explicit value for the growth rate of this norm. In particular, we provide a new proof of a celebrated result of Millson [Mi] on the homology of the arithmetic hyperbolic manifolds. The method is quite general and gives a new way of getting non zero homology classes in certain locally symmetric spaces. Received: 20 April 2001; in final form: 26 September 2001 / Published online: 28 February 2002     

A combinatorial outlook on symmetric functions

We establish a combinatorial interpretation for various operations on symmetric functions, such as plethysm, scalar product, and derivation. Thus we obtain proofs of formulas involving symmetric functions in term of combinatorial constructions on permutations.     

Models of linear logic

We engage a study of nonmodal linear logic which takes times ⊗ and the linear conditional ⊸ to be the basic connectives instead of times and linear negation ()^⊥ as in Girard's approach. This difference enables us to obtain a very large subsystem of linear logic (called positive linear logic) without an involutionary negation (if the law of double negation is removed from linear logic in Girard's formulation, the resulting subsystem is extremely limited). Our approach enables us to obtain several natural models for various subsystems of linear logic, including a generic model for the so-called minimal linear logic. In particular, it is seen that these models arise spontaneously in the transition from set theory to multiset theory. We also construct a model of full (nonmodal) linear logic that is generic relative to any model of positive linear logic. However, the problem of constructing a generic model for positive linear logic remains open. Bibliography: 2 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 220, 1995, pp. 23–35. Original     

Forme harmonique duale à un cycle quasi-fuchsienDual harmonic form to a quasi-Fuchsian cycle

Following the ideas of [2,3], we describe an explicit construction of the dual harmonic form to a quasi-Fuchsian surface in a hyperbolic 3-manifold. To cite this article: N. Bergeron, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 395–400.     

Preliminary estimate of the cost of ethanol production for ssf technology

The Solar Energy Research Institute (SERI) recently completed a detailed engineering and economic analysis of the simultaneous saccharification and fermentation (SSF) based wood-to-ethanol process. The reference-case design was based on a plant capacity of 1920 dry t/d and a wood cost of $42/dry t. For this case, the preliminary estimate of the production cost of the ethanol product is about $1.22/gal. The combined effects of optimizing SSF enzyme loading, increasing plant capacity to 10,000 dry t/d, and reducing wood cost to $34/dry t are to reduce the preliminary estimate of the production cost to about $0.95/gal. Other technological improvements may further reduce the production cost. Certain technical assumptions, inherent in the analysis, are being investigated further.

     

Interfacial microgels formed by oppositely charged polyelectrolytes and surfactants. Part 2. Influence of surfactant chain length and surfactant/polymer ratio

The adsorption and complexation of polystyrene sulfonate (a highly charged anionic polyelectrolyte) and a series of cationic surfactants, alkyltrimethylammonium bromide, CnTAB, n = 8-16, at the air-water interface has been studied by combining surface tension and ellipsometry measurements. We find that increasing the chain length of the surfactant from 8 to 10 carbons leads to a sharp increase in adsorption of PSS/CnTAB complexes. When the surfactant tail length is further increased to 12 and 14 carbons, surface adsorption becomes less favored than macroscopic phase separation, resulting in a partial surface depletion. Furthermore, we find that when surface tensions are plotted against surfactant/monomer molar concentration ratio, all data collapse to a single curve. This result shows that the surfactant-polymer molar ratio, s/p, is a key parameter for tuning the surface activity of the complexes formed.     

Synthesis of Heterobactins A and B and Nocardia Heterobactin

The synthesis of the Rhodococcus erythropolis siderophores heterobactins A and B, and the structurally related Nocardia heterobactin, is described. Two approaches for the assembly of these asymmetric ligand donor chelators are explored. In the first approach, a scheme predicated on the biosynthesis of the Paracoccus denitrificans siderophore, parabactin, is employed. In this approach, the central donor synthon is added last. In the second scheme, the central donor and the terminal 2,3-dihydroxybenzoyl fragment are first fixed to the ligand’s d-ornithine backbone. This is followed by condensation with the cyclic ornithine hydroxamate glycine segment. The schemes offer a flexible approach to other heterobactins. Job’s plots suggest that heterobactin A and Nocardia heterobactin form 1:1 ligand/metal complexes, while heterobactin B forms a 3:2 ligand/metal complex.     

A Pieri-type formula for isotropic flag manifolds

We give the formula for multiplying a Schubert class on an odd orthogonal or symplectic flag manifold by a special Schubert class pulled back from the Grassmannian of maximal isotropic subspaces. This is also the formula for multiplying a type (respectively, type ) Schubert polynomial by the Schur -polynomial (respectively, the Schur -polynomial ). Geometric constructions and intermediate results allow us to ultimately deduce this formula from formulas for the classical flag manifold. These intermediate results are concerned with the Bruhat order of the infinite Coxeter group , identities of the structure constants for the Schubert basis of cohomology, and intersections of Schubert varieties. We show that most of these identities follow from the Pieri-type formula, and our analysis leads to a new partial order on the Coxeter group and formulas for many of these structure constants.

     

Ermittelung metallischer Gifte

Ohne Zusammenfassung