Prediction of Continuous Time Processes by C[0,1]‐Valued Autoregressive Process

In order to predict a continuous time process on an entire‐time interval, we introduce the C_[0,1]‐valued autoregressive process of first order. We show, under mild regularity conditions the convergence almost sure of the predictor. We propose an estimator of the dimension of the projecting space of observations and illustrate the results by a numerical example. This revised version was published online in June 2006 with corrections to the Cover Date.     

Theoretical study of the chemisorption of H2 on boron cluster surfaces

“Ab initio” RHF calculations are used to investigate the chemisorption of a H₂ molecule on boron cluster surfaces. Potential energy surfaces and electron charge difference density plots are given. The results obtained indicate that the H₂ molecule in certain cases is dissociated on the surface, and that the hydrogen atoms are individually bound to different boron atoms. It is also found that the chemisorbed hydrogen atoms can move almost freely in certain directions parallel to the boron surface.     

Gap equations for molecular systems

The gap equations for different Fukutome classes are derived in the formalism of second quantization. Compact orbital forms are given for the gap and related to energy difference of the new LUMO and HOMO , ?_LU –?_HO , obtained from the old RHF molecular orbitals. Approximate expressions are obtained by maximizing the average electron–electron repulsion energy. The simplifications obtained and possible applications to molecular systems are discussed and compared with the instability analysis of an RHF state.     

Estimation spatio-temporelle d'un modèle de système de particules

Let X be a discrete time contact process (CP) on ${\mathbb{Z}}^2$ as defined by Durrett and Levin (1994). We study the estimation of the model based on space–time evolution of X, that is, $T+1$ successive observations of X on a finite subset S of sites. We consider the maximum marginal pseudo-likelihood (MPL) estimator and show that, when $T\to \infty$, this estimator is consistent and asymptotically normal for a non vanishing supercritical CP. To cite this article: X. Guyon, B. Pumo, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Probing Hydrogen Bonding to Bound Dioxygen in Synthetic Models for Heme Proteins: The Importance of Precise Geometry

Distal hydrogen bonding in natural dioxygen binding proteins is crucial for the discrimination between different potential ligands such as O₂ or CO. In the present study, we probe the chemical requirements for proper distal hydrogen bonding in a series of synthetic model compounds for dioxygen‐binding heme proteins. The model compounds 1‐Co to 7‐Co bear different distal residues. The hydrogen bonding in their corresponding dioxygen adducts is directly measured by pulse EPR spectroscopy. The geometrical requirements for this interaction to take place were found to be narrow and very specific. Only two model complexes, 1‐Co and 7‐Co , form a hydrogen bond to bound dioxygen, which was characterized in terms of geometry and nature of the bond. The geometry and dipolar nature of this interaction in 1‐Co ‐O₂ is more similar to the one in natural cobalt myoglobin (Co‐Mb), making 1‐Co the best model compound in the entire series.     

Pulse EPR Methods for Studying Chemical and Biological Samples Containing Transition Metals

This review discusses the application of pulse EPR to the characterization of disordered systems, with an emphasis on samples containing transition metals. Electron nuclear double‐resonance (ENDOR), electron‐spin‐echo envelope‐modulation (ESEEM), and double electron–electron resonance (DEER) methodologies are outlined. The theory of field modulation is outlined, and its application is illustrated with DEER experiments. The simulation of powder spectra in EPR is discussed, and strategies for optimization are given. The implementation of this armory of techniques is demonstrated on a rich variety of chemical systems: several porphyrin derivatives that are found in proteins and used as model systems, otherwise highly reactive aminyl radicals stabilized with electron‐rich transition metals, and nitroxide–copper–nitroxide clusters. These examples show that multi‐frequency continuous‐wave (CW) and pulse EPR provides detailed information about disordered systems.