Weinstein–Sobolev Spaces of Exponential Type and Applications

In this paper, we introduce and study the Sobolev spaces of exponential type associated with the Weinstein operator, via some elements of harmonic analysis related to this operator. In particular, some properties, including completeness and imbedding theorem, are proved. Finally, using the theory of reproducing kernels, some applications are given for these spaces.     

Reactivity of RCu,BF3 and R2 CuLi,BF3 towards allylic acetals and ethers

Organocopper and cuprate reagents associated with Lewis acids, are highly reactive towards allylic acetals and ethers. Displacements of the alkoxy group occurs by SN₂' attack according to the various parameters of the reaction.     

Localization for the Random Displacement Model at Weak Disorder

This paper is devoted to the study of the random displacement model on ${\mathbb{R}^d}$ . We prove that, in the weak displacement regime, Anderson and dynamical localization hold near the bottom of the spectrum under a generic assumption on the single-site potential and a fairly general assumption on the support of the possible displacements. This result follows from the proof of the existence of Lifshitz tails and of a Wegner estimate for the model under scrutiny.     

Asymmetric cleavage of chiral acetals by R2CuLi,BF3 reagents

The title reagents cleave diastereoselectively the acetals derived from various aldehydes and chiral 2–3 butane diol (or higher homologs). This reaction affords an asymetric synthesis of secondary alcohols from an aldehyde and a trivial organolithium reagent.     

Lifshits Tails for Random Schrödinger Operators with Nonsign Definite Potentials

This paper is devoted to the study of Lifshits tails for random Schr?dinger operator acting on of the form , where H ₀ is a -periodic Schr?dinger operator, λ is a positive coupling constant, are i.i.d and bounded random variables and V is the single site potential with changing sign. We prove that, in the weak disorder regime, at an open band edge, a true Lifshits tail for the random Schr?dinger operator occurs under a certain set of conditions on H ₀ and on V. Submitted: April 17, 2007. Accepted: December 13, 2007.     

Reactivity of RCu,BF3 and R2CuLi,BF3 towards the ether linkage. Epoxides,acetals and orthoformates

The association of BF₃ to organocopper and cuprate reagents increases dramatically their reactivity towards epoxides. The same reagents cleave acetals to afford the product of substitution of one alkoxy group, whereas orthoformates lead to acetals under conditions where no further attack occurs.     

Internal Lifshits tails for random magnetic Schrödinger operators

This paper is devoted to the study of Lifshits tails for weak random magnetic perturbations of periodic Schrödinger operators acting on L²(Rd) of the form Hλ,w=(−i∇−λ_∑γ∈ZdwγA²(⋅−γ))+V, where V is a Zd-periodic potential, λ is positive coupling constants, (wγ)_γ∈Zd are i.i.d and bounded random variables and is the single site vector magnetic potential. We prove that, for λ small, at an open band edge, a true Lifshits tail for the random magnetic Schrödinger operator occurs if a certain set of conditions on H₀=−Δ+V and on A holds.     

Conception of a 90-GHz metamaterial-based coupler for astrophysical applications

Designed for astrophysical applications, this coupler must be as small as possible to be integrated in a low temperature superconducting detection chain. By using metamaterials, dimensions can be reduced and performances enhanced compared with a conventional coupler. The novelty of the work presented in this paper is a coupler that operates at millimeter waves (W band) and cryogenic temperatures (4 K) for astrophysics applications and more precisely for the detection of the cosmological microwave background radiation.     

A wavelet-based forward BSS algorithm for acoustic noise reduction and speech enhancement

In this paper, we address the problem of noise reduction and speech enhancement by adaptive filtering algorithm. Recently, the well known forward blind source separation (FBSS) structure has been largely studied and intensively used to reduce acoustic noise components and to enhance speech signal. The FBSS structure is often combined with adaptive algorithms to accelerate the adaptation of the cross-filters, and to improve noise suppression at the output. In this paper, we propose to use a wavelet transform decomposition in the FBSS structure by using a two-channel forward wavelet symmetric adaptive decorrelating (WFSAD) algorithm. The proposed WFSAD algorithm provides a better compromise between time and frequency resolution and improves robustness of the noise reduction process when compared with the classical two-channel forward symmetric adaptive decorrelating (FSAD) algorithm. Simulation results prove the efficiency of the proposed WFBSS algorithm in comparison with conventional ones in terms of several objective and subjective criteria.