Design and synthesis of new ethylenediamine or propylenediamine diacetic acid derivatives for Re(I) organometallic chemistry

A general synthetic approach for a novel range of bifunctional chelating agent (BCA) for the ‘fac-[M(CO)₃]⁺‘ core (M=^99mTc, ⁹⁹Tc or Re) has been developed. The strategy includes the facile preparation of these tridentate ligands possessing a tertiary amine bearing two carboxylic acid functions as coordinating site and an aromatic amino group for coupling to a biovector. First complexation study has shown that these compounds act exclusively as tridentate ligands (via the two acids and the tertiary amine functions). The convenient synthesis of these new ligands coupled with their high affinity for Re(I) make them quite promising for biomedical applications.     

Itération de pliages de quadrilatères

Iteration of quadrilateral foldings. Starting with a quadrilateral q₀=(A₁,A₂,A₃,A₄) of 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 (see Fig. 1).We study the dynamical behavior of this sequence. In particular, we prove that:– The drift exists.– When none of the q_n is isometric to q₀, then the drift v is zero if and only if one has maxa_j+mina_j1/2a_j where a₁,...,a₄ are the sidelengths of q₀.– For Lebesgue almost all q₀ the sequence (q_n-nv)_n1 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)_n1 is unbounded (see Figs. 2 to 7).      

Approximation and regularisation of arbitrary sets in finite dimension

We define the regularisation of a set by using two kernels. This procedure generalizes that defined by Laory-Lions for the functions. We privilege the geometrical point of view and we obtain in particular some new results about the asymptotic behaviour of Clarke's normal cone at a point of a set belonging to the regularized family     

Analyse harmonique sur les espaces symétriques nilpotents

Let G be a connected simply connected nilpotent Lie group and H the set of fixed points of an involution of G; we give the Plancherel formula of the representation Ind_H^G(1) and infer from it the existence of an H-invariant tempered elementary solution for every nonzero G-invariant differential operator on $\text{G}\text{H}$.     

Energy Statistics in Open Harmonic Networks

We relate the large time asymptotics of the energy statistics in open harmonic networks to the variance-gamma distribution and prove a full large deviation principle. We consider both Hamiltonian and stochastic dynamics, the later case including electronic RC networks. We compare our theoretical predictions with the experimental data obtained by Ciliberto et al. (Phys. Rev. Lett. 110:180601, 2013).     

Automorphismes des cônes convexes

One studies the subgroups of GL(m,ℝ) which preserve a properly convex cone of ℝ ^m and whose action on ℝ ^m is irreducible. In particular, one describes the Zariski closure of these subgroups. As an application, one describes the Zariski closure G of the subgroups of GL(m,ℝ) all of whose elements have nothing but positive eigenvalues. For instance, one can get the group G=GL(m,ℝ) if and only if m≠≡2 modulo4.

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Automorphismes des c?nes convexes

Résumé. On étudie les sous-groupes de GL(m,ℝ) qui préservent un c?ne convexe saillant de ℝ ^m et dont l’action sur ℝ ^m est irréductible. En particulier, on décrit les adhérences de Zariski possibles pour ces sous-groupes. Comme application, on décrit les adhérences de Zariski G possibles pour les sous-groupes de GL(m,ℝ) dont tous les éléments ont toutes leurs valeurs propres positives. Par exemple, le groupe G=GL(m,ℝ) convient si et seulement si m≠≡2 modulo4.

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Oblatum 22-I-1999 & 10-XI-1999?Published online: 21 February 2000     

Band structure and atomic sum rules for X-ray dichroism

Corrections to the atomic orbital sum rule for circular magnetic X-ray dichroism in solids are derived using orthonormal LMTOs as a single-particle basis for electron band states. Received 4 September 2000     

The period-index problem for real surfaces

Publications mathématiques de l'IHÉS - We study when the period and the index of a class in the Brauer group of the function field of a real algebraic surface coincide. We prove that...