Asymptotic Properties of Quasi-Maximum Likelihood Estimators for ARMA Models with Time-Dependent Coefficients

For about thirty years, time series models with time-dependent coefficients have sometimes been considered as an alternative to models with constant coefficients or non-linear models. Analysis based on models with time-dependent models has long suffered from the absence of an asymptotic theory except in very special cases. The purpose of this paper is to provide such a theory without using a locally stationary spectral representation and time rescaling. We consider autoregressive-moving average (ARMA) models with time-dependent coefficients and a heteroscedastic innovation process. The coefficients and the innovation variance are deterministic functions of time which depend on a finite number of parameters. These parameters are estimated by maximising the Gaussian likelihood function. Deriving conditions for consistency and asymptotic normality and obtaining the asymptotic covariance matrix are done using some assumptions on the functions of time in order to attenuate non-stationarity, mild assumptions for the distribution of the innovations, and also a kind of mixing condition. Theorems from the theory of martingales and mixtingales are used. Some simulation results are given and both theoretical and practical examples are treated. Received 2004; Final version 23 December 2004     

Optical emissions of products sputtered from Fe, Fe2O3 and Fe3O4 powders

Powder iron has been bombarded by a 5 keV Kr⁺ ions in a vacuum better than 10^-7 torr and under few 10^-6 torr ultra pure oxygen partial pressure. The optical spectra of the sputtered particles were recorded between 340.0 nm and 410.0 nm. These spectra exhibit discrete lines, which are attributed to neutral excited atoms of iron. Two iron oxides, namely hematite (Fe₂O₃)_{3}) and magnetite (Fe₃O₄)_{4}), in powder form, were studied under the same experimental conditions and identical lines were observed in the obtained spectra. The absolute intensities of the spectral lines in all spectra were measured and the differences in the recorded yield photons were discussed in term of electron-transfer processes between the excited sputtered atom and the bombarded surface. In accordance with the proposed interpretation, we suggest values for the energy gaps and electronic affinities for the studied oxides and for the oxide layer that might be formed by the adsorption of oxygen atoms.     

Linear recurrence relations in the algebra of matrices and applications

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for Aⁿ (nr) and e^tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A^j, where 0jr−1.     

Palladium-catalyzed stereoconvergent formylation of (E/Z)-β-bromo-β-fluorostyrenes: straightforward access to (Z)-α-fluorocinnamic aldehydes and (Z)-β-fluorocinnamic alcohols

We report here the stereoconvergent formylation of (E/Z)-β-bromo-β-fluorostyrene mixtures with carbon monoxide and sodium formate catalyzed by palladium. Optimization of reaction conditions leads to the corresponding pure (Z)-α-fluorocinnamaldehydes in good yields. The reaction was extended to styrenes bearing electro-attracting or electro-donating groups. The obtained α-fluoroaldehydes were smoothly reduced to the corresponding (Z)-β-fluorocinnamic alcohol by NaBH(4). The reaction could be performed on functionalized substrates as demonstrated by the access to the glucoside of β-fluoroconiferyl alcohol, (Z)-β-fluoroconiferin, a strong inhibitor of lignin polymerization.     

Complexation of α, ω-dicarboxylates by 3,3′-bis(5-phenyl-1,4-dioxo-2,3,5-triaza)-2,2′-bipyridine

A new bipyridine derivative has been synthesized and characterized. The UV spectra of the prepared ligand are strongly dependent on the solvent, probably due to the different conformations present in each solvent. The ability of this ligand to act as chemosensor for α,ω-dicarboxylates has been evaluated by UV–vis and fluorescence studies. The stoichiometry of the formed complexes was always 1:2. The rigidity induced by the complexation gives rise to an enhancement of the fluorescence emission when DMSO was used.     

A decoupled algorithm for a drift‐diffusion model

This paper suggests a decoupled method in order to approximate a free boundary separating the depletion region and the charge neutrality region in a field effect transistor of MESFET type. In order to do that, a simplified drift‐diffusion model is used. A decoupled algorithm is presented in (Math. Comput. Simulat. 1998; 47 (6):531–539). In this work an existence theorem is proved, and the study of the convergence of the previous algorithm is presented with some numerical results. Copyright © 2005 John Wiley & Sons, Ltd.     

An efficient access to (Z)-β-fluoroallyl alcohols based on the two carbon homologation of aromatic aldehydes by Horner–Wadsworth–Emmons reaction with 2-(diethoxyphosphinyl)-2-fluoro-ethanethioic acid,S-ethyl ester followed by reduction with sodium borohydride

We describe a biomimetic approach to (Z)-β-fluoroallyl alcohols based on the two carbon homologation of aromatic aldehydes to α-fluorocinnamic thioesters by Horner–Wadsworth–Emmons reaction with 2-(diethoxyphosphinyl)-2-fluoro-ethanethioic acid, S-ethyl ester, followed by reduction with sodium borohydride in mild conditions. The α-fluorothioesters were obtained in a good yield by condensing the aldehydes with the lithium anion of 2-(diethoxyphosphinyl)-2-fluoro-ethanethioic acid, S-ethyl ester in THF at ?78 °C. The (E,Z)-α-fluorocinnamic thioester mixtures were then cleanly reduced with double bond isomerisation to the corresponding (Z)-β-fluoroallyl alcohols by NaBH₄ at room temperature. This methodology may be applied to highly functionalized aldehydes as exemplified by the straightforward access to (Z)-β-fluoroconiferin, a strong inhibitor of lignin polymerization from O-glucosylated vanillin.