Itération de pliages de quadrilatères

Starting with a quadrilateral q₀=(A₁,A₂,A₃,A₄) of $\text{R}{}^2$, one constructs a sequence of quadrilaterals q_n=(A_4n+1,…,A_4n+4) by iteration of foldings: q_n=?₄°?₃°?₂°?₁(q_n?1) where the folding ?_j replaces the vertex number j by its symmetric with respect to the opposite diagonal.We study the dynamical behavior of this sequence. In particular, we prove that:– The drift $\text{v:=}\text{lim}{}_{\mathrm{n\to \infty }}\text{1}\text{n}\text{q}{}_{\mathrm{n}}$ exists.– When none of the q_n is isometric to q₀, then the drift v is zero if and only if one has $\text{max}\text{a}{}_{\mathrm{j}}\text{+}\text{min}\text{a}{}_{\mathrm{j}}\text{?}\text{1}\text{2}\text{∑a}{}_{\mathrm{j}}$, where a₁,…,a₄ are the sidelengths of q₀.– For Lebesgue almost all q₀ the sequence (q_n?nv)_n?1 is dense on a bounded analytic curve with a center, or an axis of symmetry. However, for Baire generic q₀, the sequence (q_n?nv)_n?1 is unbounded. To cite this article: Y. Benoist, D. Hulin, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Propriétés Asymptotiques des Groupes Linéaires

Let G be a reductive linear real Lie group and be a Zariski dense subgroup. We study asymptotic properties of through the set of logarithms of the radial components of the elements of : we prove that the asymptotic cone of this set is a convex cone with non empty interior and is stable by the Cartan involution. Reciprocally any closed convex cone of the positive Weyl chamber whose interior is non empty and which is stable by the opposition involution can be obtained this way.?We relate this limit cone and the limit set of to the set of open semigroups of G which meet .?We also prove similar results over any local fields.

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Propriétés Asymptotiques des Groupes Linéaires

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Submitted: January 1996     

Sur les difféomorphismes d'Anosov affines à feuilletages stable et instable différentiables

Résumé Nous étudions les difféomorphismes d'Anosov topologiquement transitifs sur une variété compacte dont les feuilletages stable et instable sont de classeC . Nous montrons que si un tel difféomorphisme préserve une structure symplectique ou une connexion, il est alorsC conjugué à un infranilautomorphisme hyperbolique.Oblatum 18-III-1992     

New aromatic annulation reaction via a C14 enaminone synthon: synthesis of ‘terpenoid-like chalcones’

Diverse functionalized synthons from a new enaminone are reported. These synthons were easily obtained in a one pot process starting from a compound derived from β-ionone. A new annulation reaction of this C-14 compound with several anions led to new ‘terpenoid-like’ chalcones.     

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 .

     

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.     

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.      

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.     

A note on relative entropy

The quantum-mechanical concept of relative entropy is discussed from an information-theoretic point of view. We show that not all definitions found in the recent literature are equally suitable for the purpose of statistical inference by entropy maximization.