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.     

5- and 6-pulse electron spin echo envelope modulation (ESEEM) of multi-nuclear spin systems

In 3-pulse ESEEM and the original 4-pulse HYSCORE, nuclei with large modulation depth (k approximately 1) suppress spectral peaks from nuclei with weak modulations (k approximately 0). This cross suppression can impede the detection of the latter nuclei, which are often the ones of interest. We show that two extended pulse sequences, 5-pulse ESEEM and 6-pulse HYSCORE, can be used as experimental alternatives that suffer less strongly from the cross suppression and allow to recover signals of k approximately 0 nuclei in the presence of k approximately 1 nuclei. In the extended sequences, modulations from k approximately 0 nuclei are strongly enhanced. In addition, multi-quantum transitions are absent which simplifies the spectra. General analytical expressions for the modulation signals in these sequences are derived and discussed. Numerical simulations and experimental spectra that demonstrate the higher sensitivity of the extended pulse sequences are presented.     

Phase Cycling in Electron Spin Echo Envelope Modulation

We present a general way to devise efficient phase cycles for arbitrary electron spin echo envelope modulation (ESEEM) experiments. The method determines all coherence transfer pathways contributing to the measured signal, selects those of interest and then examines all possible nested phase cycles in order to find those that achieve the required selection. The procedure is used to find efficient nested phase cycles for ESEEM sequences containing up to nine pulses: two-pulse, three-pulse and five-pulse ESEEM, standard and six-pulse hyperfine sublevel correlation (HYSCORE) as well as their extensions including remote echo detection. In addition, it is shown that by shifting the last pulse by 90° three-pulse ESEEM and HYSCORE do not need phase cycling in the case of a symmetrically excited line. Authors' address: Stefan Stoll, Department of Chemistry, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA     

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).