1H, (19)F, and (31)P PGSE NMR diffusion studies on chiral organic salts: ion pairing and the dependence of a diffusion value on diastereomeric structure

1H, (19)F and (31)P pulsed field gradient spin-echo (PGSE) diffusion studies on chiral organic salts that contain hexacoordinate phosphate anions, namely tris(tetrachlorobenzenediolato)phosphate(V) (TRISPHAT) and bis(tetrachlorobenzenediolato)mono([1,1']binaphthalenyl-2,2'diolato)-phosphate(V) (BINPHAT), are reported. The first example of the dependence of a diffusion value on diastereomeric structure is presented. Marked solvent and concentration effects on the diffusion constants (D) of these salts are noted and the question of ion pairing is discussed.     

Ruthenium-catalyzed enyne cycloisomerizations. Effect of allylic silyl ether on regioselectivity

The ruthenium-catalyzed cycloisomerization of 1,6- and 1,7-enynes substituted in the terminal allylic position with a tert-butyldimethylsilyl ether group emerges as an effective reaction to form unprecedented five- or six-membered rings possessing a geometrically defined enol silane. Straightforward synthetic access to a variety of achiral 1,6- and 1,7-enynes, as well as chiral ones, is presented. Ruthenium catalysts effect efficiently such single-step cycloisomerization at room temperature in acetone under neutral conditions. The cycloisomerization functions with (E) or (Z) 1,2-disubstituted alkenes. Parameters influencing the enol silane geometry are discussed. The level of selectivity depends on the alkyne substitution, the geometry of the double bond, and the nature of the catalyst. Furthermore, examples of stereoinduction are shown and lead to highly substituted carbo- and heterocycles with excellent diastereocontrol.     

Testing Gravity on Astrophysical Scales

We summarize a series of observational tests of the law of gravity on large astrophysical scales. These tests account for testing both the Poisson equation (inverse square law) using weak lensing and the Einstein equivalence principle through the test of the constancy of the constants of Nature. We emphasize the need to test general relativity on cosmological scales in light of the cosmological constant problem and of recent observational claims concerning the variation of fine structure constant.     

Beta zeolite supported on silicon carbide for Friedel-Crafts fixed-bed reactions

Beta zeolite supported on silicon carbide, with high thermal conductivity and high mechanical strength, was successfully used as an active and stable catalyst for Friedel-Crafts reactions in a fixed bed configuration.     

Interchange of infimum and integral

We prove a new interchange theorem of infimum and integral. Its distinguishing feature is, on the one hand, to establish a general framework to deal with interchange problems for nonconvex integrands and nondecomposable sets, and, on the other hand, to link the theorems of Rockafellar and Hiai-Umegaki with the one of Bouchitté-Valadier. We give an application to relaxation of nonconvex geometric integrals of Calculus of Variations.Received: 20 March 2002, Accepted: 12 March 2003, Published online: 16 May 2003     

The acceleration of the universe and the physics behind it

Using a general classification of dark enegy models in four classes, we discuss the complementarity of cosmological observations to tackle down the physics beyond the acceleration of our universe. We discuss the tests distinguishing the four classes and then focus on the dynamics of the perturbations in the Newtonian regime. We also exhibit explicitely models that have identical predictions for a subset of observations.     

Gradient estimates for a degenerate parabolic equation with gradient absorption and applications

Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and the nonlinear absorption. In particular, the limit as t→∞ of the L¹-norm of integrable solutions is identified, together with the rate of expansion of the support for compactly supported initial data. The persistence of dead cores is also shown. The proof of these results strongly relies on gradient estimates which are first established.     

Tests of general relativity on astrophysical scales

While tested to a high level of accuracy in the Solar system, general relativity is under the spotlight of both theoreticians and observers on larger scales, mainly because of the need to introduce dark matter and dark energy in the cosmological model. This text reviews the main tests of general relativity focusing on the large scale structure and more particularly weak lensing. The complementarity with other tests (including those on Solar system scales and the equivalence principle) is discussed.     

An oracle based method to compute a coupled equilibrium in a model of international climate policy

This paper proposes a computational game-theoretic model for the international negotiations that should take place at the end of the period covered by the Kyoto protocol. These negotiations could lead to a self-enforcing agreement on a burden sharing scheme given the necessary global emissions limit that will be imposed when the real extent of climate change is known. The model assumes a non-cooperative behavior of the parties except for the fact that they will be collectively committed to reach a target on total cumulative emissions by the year 2050. The concept of normalized equilibrium, introduced by J.B. Rosen for concave games with coupled constraints, is used to characterize a family of dynamic equilibrium solutions in an m-player game where the agents are (groups of) countries and the payoffs are the welfare gains obtained from a Computable General Equilibrium (CGE) model. The model deals with the uncertainty about climate sensitivity by computing an S-adapted equilibrium. These equilibria are computed using an oracle-based method permitting an implicit definition of the payoffs to the different players, obtained through simulations performed with the global CGE model GEMINI-E3. Partly supported by GICC (French Ministry of Ecology), TOCSIN (EU-044287) and the Swiss-NSF NCCR-Climate program of the Swiss NSF. For helpful comments and discussions, we thank A. Bernard, P. Thalmann, and the anonymous referee.     

Structure-Activity Relationship in Ambergris-Type Woody Odorants possessing a hydronaphthalene skeleton

A series of methyl hydronaphthyl alcohols, formates, acetates, and ketones were prepared and their odour properties evaluated. Minor structural changes, even opposite to the osmophoric group, were found to have major effects on the odour. ¹³C? NMR shift assignments of the hydronaphthyl derivatives are presented.