Convexes Hyperboliques et Quasiisométries

For any m ≥ 3, we construct properly convex open sets Ω in the real projective space whose Hilbert metric is Gromov hyperbolic but is not quasiisometric to the hyperbolic space . We show that such examples cannot exist for m = 2. Some of our examples are divisible, i.e. there exists a discrete group Г of projective transformations preserving Ω with a compact quotient Г\Ω. The open set Ω is strictly convex but the group Г is not isomorphic to any cocompact lattice in the isometry group of .     

A characterization of quasiconvex vector-valued functions

The aim of this paper is to characterize in terms of scalar quasiconvexity the vector-valued functions which are -quasiconvex with respect to a closed convex cone in a Banach space. Our main result extends a well-known characterization of -quasiconvexity by means of extreme directions of the polar cone of , obtained by Dinh The Luc in the particular case when is a polyhedral cone generated by exactly linearly independent vectors in the Euclidean space .

     

Castelnuovo-Mumford regularity and extended degree

Our main result shows that the Castelnuovo-Mumford regularity of the tangent cone of a local ring is effectively bounded by the dimension and any extended degree of . From this it follows that there are only a finite number of Hilbert-Samuel functions of local rings with given dimension and extended degree.

     

No fluorescence decay from low-lying electronic states excited into single vibronic levels with synchrotron radiation

Fluorescence decay of NO has been studied by single photon counting using the synchrotron radiation from the Orsay Electron Storage Ring (ACO) as a source of excitation. Emissions from A²Σ⁺(υ = 0,1,2,3), B²Π(υ = 5), C²Π(υ = 0, 1) and D²Σ⁺(υ = 0, 1, 2, 3) levels have been observed in function of NO gas pressure in the 0.02–4 torr range. Collision-free lifetimes and self-quenching rate constants have been derived from these measurements for all these levels and compared to previous data. Particular attention has been paid to the C²Π(υ = 0) level decay properties. By narrow-band (≈ 45 cm^?1) excitation inside the rotational envelope of this level we show that the decay is non-exponential with a short-living component (≈ 3 ns) a long-living one (≈ 20 ns). We develop a number of arguments in order to prove the short-living levels (J > 5 or 7) are weakly predissociated.     

STRUCTURES OF THE BERGAMOTTIN PHOTOPRODUCTS

The extensive use of bergamot oil in perfumery and cosmetics led us to study the photoreactivity of 5-geranoxypsoralen (bergamottin), the major chromophore in this oil. Structure determination of the bergamottin photoproducts was achieved using extensive NMR techniques including two-dimensional NMR: ¹H-¹³C correlation by long-range coupling, ¹H-¹H correlation spectroscopy (COSY) and ¹H-¹H COSY phase sensitive (COSYPH). Bergaptol is formed according to the well-known fragmentation of allyl-aryl ethers. The other photoproducts arise from an intramolecular [2 + 2] photocycloaddition and appeared as an equimolecular mixture of diastereomeric cyclobutyl derivatives. The relative configurations were determined by nuclear Overhauser effect analysis. These structures were further corroborated by X-ray crystal analysis. The facile formation of an intramolecular cyclobutyl derivative in bergamottin might prevent the intermolecular cyclobutane adduct formation with pyrimidine DNA bases responsible, in part, for phototoxicity of psoralens.     

Convexes divisibles IV : Structure du bord en dimension 3

Divisible convex sets IV: Boundary structure in dimension 3 Let Ω be an indecomposable properly convex open subset of the real projective 3-space which is divisible i.e. for which there exists a torsion free discrete group Γ of projective transformations preserving Ω such that the quotient M := Γ\Ω is compact. We study the structure of M and of ∂Ω, when Ω is not strictly convex: The union of the properly embedded triangles in Ω projects in M onto an union of finitely many disjoint tori and Klein bottles which induces an atoroidal decomposition of M. Every non extremal point of ∂Ω is on an edge of a unique properly embedded triangle in Ω and the set of vertices of these triangles is dense in the boundary of Ω (see Figs. 1 to 4). Moreover, we construct examples of such divisible convex open sets Ω.      

Nanoindentation mapping of a wood-adhesive bond

A mapping experiment of a wood phenol–resorcinol–formaldehyde adhesive bond was performed by means of grid nanoindentation. The variability of the modulus of elasticity and the hardness was evaluated for an area of 17 μm by 90 μm. Overall, the modulus of elasticity of the adhesive was clearly lower than the modulus of wood cell walls, whereas the hardness of the adhesive was slightly higher compared to cell walls. A very slight trend of decreasing modulus of elasticity was found with increasing distance from the immediate bond line. However, the trend was superimposed by a high variability of the modulus of elasticity in dependence on the position in the wood cell wall. The unexpectedly high variation of the modulus between 12 and 24 GPa may be explained by the interaction between the helical orientation of the cellulose microfibrils in the S2 layer of the wood cell wall and the geometry of the three-sided Berkovich type indenter pyramid used. Corresponding to the very slight decrease in modulus with increasing distance from the bond line, a similar but clearer trend was found for hardness. Both trends of changing mechanical properties of wood cell walls with varying distance from the bond line are attributed to effects of adhesive penetration into the wood cell wall. PACS 81.70.-q     

Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming

We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the augmented system gives a primal-dual Newton step and also a step in the barrier parameter. Based on local information and a line search, the decrease of the barrier parameter is automatically adjusted. We analyze local convergence properties, report numerical experiments on a standard collection of nonlinear problems and compare our results to a state-of-the-art interior-point implementation. In many instances, the adaptive algorithm reduces the number of iterations and of function evaluations. Its design guarantees a better fit between the magnitudes of the primal-dual residual and of the barrier parameter along the iterations.     

Quasiparticle line shape of Sr2RuO4 and its relation to anisotropic transport

The bulk-representative low-energy spectrum of Sr2RuO4 can be directly measured by angle-resolved photoemission. We find that the quasiparticle spectral line shape of Sr2RuO4 is sensitive to both temperature and momentum. Along the (0,0)-(pi,0) direction, both gamma and beta bands develop a sharp quasiparticle peak near k(F) at low temperatures, but as the temperature increases the spectra quickly lose coherent weight and become broad backgrounds above approximately 130 K, which is the metal-nonmetal crossover temperature, T(M), in the c-axis resistivity. However, spectra along the (0,0)-(pi,pi) direction evolve smoothly across T(M). A simple transport model can describe both in-plane and c-axis resistivity in terms of the quasiparticle line shape. Comparisons are also made to the cuprates, with implications for two dimensionality, magnetic fluctuations, and superconductivity.     

On the Symmetric and Rees algebras of an ideal

Some necessary and sufficient conditions are given for the Rees and Symmetric Algebra of an ideal being canonically isomorphic. Some applications are obtained to the study of the relations between the generators of ideals which are maximal minors of a generic t by (t+1) matrix, prime ideals of finite projective dimension, almost complete intersections or d-sequences.This paper was supported by C. N. R. (Consiglio Nazionale delle Ricerche)