Information rates in optical channels

Results of numerical computations of the information capacity in a photon communication channels are given and compared for various optical sources of different statistical properties.     

New formulations of linearized elasticity problems,based on extensions of Donati's theorem

The classical Donati theorem is used for characterizing smooth matrix fields as linearized strain tensor fields. In this Note, we give several generalizations of this theorem, notably to matrix fields whose components are only in $H^{\mathrm{?1}}$. We then show that our extensions of Donati's theorem allow to reformulate in a novel fashion linearized three-dimensional elasticity problems as quadratic minimization problems with the strains as the primary unknowns. To cite this article: C. Amrouche et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Computation of Greeks in LIBOR models driven by time–inhomogeneous Lévy processes

The aim of this article is to compute Greeks, i.e. price sensitivities in the framework of the Lévy LIBOR model. Two approaches are discussed. The first approach is based on the integration-by-parts formula, which lies at the core of the application of the Malliavin calculus to finance. The second approach consists of using Fourier-based methods for pricing derivatives. We illustrate the result by applying the formula to a caplet price where the jump part of the driving process of the underlying model is given by a time–inhomogeneous Gamma process and alternatively by a Variance Gamma process.     

Photomagnetic properties of an iron(II) low-spin complex with an unusually long-lived metastable LIESST state

A comprehensive study of the photomagnetic behavior of the [Fe(L222N5)(CN)2].H2O complex has been carried out. This complex is characterized by a low-spin (LS) iron(II)-metal center up to 400 K and exhibits at 10 K the well-known Light-Induced Excited Spin State Trapping (LIESST) effect. The critical LIESST temperature (T(LIESST)) has been measured to be 105 K. The kinetics of the transition from the metastable high-spin (HS) state to the low-spin state have been determined and used for reproducing the experimental T(LIESST) curve. This study represents a second example of a fully low-spin iron(II)-metal complex up to 400 K, which can be photoexcited at low temperature with an atypical long-lived metastable HS state. This underlines the preponderant role of the inner coordination sphere for stabilizing the lifetime of the photoinduced HS state.     

Desilylation procedure via a naphthalene-catalysed lithiation reaction

The reaction of silyl protected alcohols, amines and thiols with lithium powder and a catalytic amount of naphthalene, in THF, at 0 °C led, after hydrolysis, to the recovery of the free alcohols, amines and thiols in very good yields. At least a phenyl group was required in the silyl protecting group for the success of the reaction. Some polyfunctionalised starting materials have successfully been deprotected. The stereochemical outcome of the deprotection of a silylated chiral secondary alcohol has also been studied and no racemization was observed. The process has shown to be a good alternative to the acid-catalysed desilylation procedures, the latter being not useful for the deprotection of some silylated tertiary alcohols.     

Deallyloxy- and debenzyloxycarbonylation of protected alcohols, amines and thiols via a naphthalene-catalysed lithiation reaction

The naphthalene-catalysed lithiation of Alloc- and Cbz-protected alcohols, amines and thiols in THF at 0 °C led, after quenching with methanol, to the recovery of the free alcohols, amines and thiols in short reaction times and with very good yields. The selectivity for the removal of the Alloc- or the Cbz- group in a polyfunctionalised substrate has been studied. The selective reductive cleavage of a benzylic carbon-oxygen bond was achieved in the presence of an allylic carbon-oxygen or carbon-nitrogen bond. This method represents a great improvement in comparison with the previously reported deprotection procedures by dissolving metals, since it avoids the use of the toxic liquid ammonia and, therefore, the need to perform the reaction at low temperatures.     

Autocorrelation function of scattered light for a binary fluid near the critical mixing point

Using a time-to-amplitude conversion method the second order correlation function of the central component in light scattered by a binary fluid was measured very close to the critical point. At kξ?7 deviation from a exponential decay of the concentration fluctuations turns out to be smaller than one percent.