Time behaviour of non-linear stochastic processes in the presence of multiplicative noise: From Kramers' to Suzuki's decay

The diffusional regime of a Brownian particle in a double-well potential in the presence of both additive and multiplicative noise is explored. As a relevant effect of the multiplicative noise, the escape rate from a well is shown to change from the small value of the Kramers theory into the large relaxation rate of the Suzuki regime. It is shown, furthermore, that the time required to get equilibrium in a well after sudden application of multiplicative noise (the activation time) is very much shorter than the Kramers relaxation time. We envisage therefore an operational scheme making available multiplicative noise for a short interval of time (for example using a light pulse) as an efficient tool to get a fast process of escape from a well. These results are obtained by using a continued-fraction algorithm which makes it possible even to successfully deal with the decay of an unstable state at the critical point.     

A reflectometric method to measure the azimuthal anchoring energy of a nematic liquid crystal

Summary A new reflectometric method to measure the azimuthal anchoring energy at the interface between a nematic liquid crystal and an isotropic method is proposed. The spurious contribution to the reflectivity coefficients due to the presence of a director-field distortion near the interface is calculated by using the numerical Berreman algorithm and is shown to be negligible for magnetic fields small enough (H<10 kG). Preliminary measurements of the azimuthal anchoring energy at the interface between the NLC 5CB and a rubbed glass plate are given. Research supported in part by MPI and in part by CNR.     

The palladium-catalyzed reaction of aryl iodides with mono and disubstituted acetylenes: a new synthesis of trisubstituted alkenes.

Mono and disubstituted acetylenes react with aryl iodides containing a variety of functional groups in the presence of palladium catalyst, formic acid and a tertiary amine to give trisubstituted alkenes.     

Equilibrium states for a plane incompressible perfect fluid

We associate to the plane incompressible Euler equation with periodic conditions the corresponding Hopf equation, as an equation for measures on the space of solenoidal distributions. We define equilibrium states as the solutions of the stationary Hopf equation. We find a class of equilibrium states which corresponds to a class of infinitely divisible distributions, and investigate the properties of gaussian and poissonian states. Equilibrium dynamics for a class of poissonian states is constructed by means of the Onsager vortex equations.Research partially supported by C.N.R., G.N.F.M.     

Palladium-catalyzed carbonylation of enol triflates. A novel method for one-carbon homologation of ketones to α,β-unsaturated carboxylic acid derivatives

Ketones can be homologated to α,gb-unsaturated esters or amides via their enol triflates by a palladium-catalyzed reaction with carbon monoxide and alcohols or amines.     

Ru-based oxidation catalysis

Ranging from the oxidative conversion of water to O(2) to the elegant hydroxylation of olefins and to oxidative dehydrogenation of alcohols Ru-mediated oxidations are finding increasing application due to the unique properties of this extremely versatile transition metal, whose oxidation state can vary from -II to +VIII. Covering recent developments in both homogeneously and heterogeneously catalysed oxidations (in liquid-phase as well as in novel reaction media), this tutorial review aims to provide investigators with a general picture of the chemical and structural origins of the excellent performance of many ruthenium catalysts and to promote further advancement that, it is envisaged, will soon benefit society at large.     

Origin of the sphere-to-rod transition in cationic micelles with aromatic counterions: specific ion hydration in the interfacial region matters

Sphere-to-rod transitions of cetyltrimethylammonium (CTA+) micelles with dichlorobenzoate counterions are remarkably substituent dependent. Simultaneous estimates of the interfacial molarities of H2O, MeOH, and Cl- and 2,6- and 3,5-dichlorobenzoate (2,6OBz and 3,5OBz) counterions were obtained by the chemical trapping method in mixed micelles of CTACl/CTA3,5OBz and CTACl/CTA2,6OBz without added salt. Increasing the CTA3,5OBz mole fraction produces a marked concurrent increase in interfacial 3,5OBz- and a decrease in interfacial H2O concentrations through the sphere-to-rod transition. No abrupt concentration changes are observed with increasing CTA2,6OBz mole fraction. Counterion-specific changes in the interfacial water concentration may be a major contributor to the delicate balance of forces governing micellar morphology.     

Some properties of nonnegative solutions of parabolic differential operators

Sunto In questo lavoro vengono prese in considerazione soluzioni deboli non-negative di equazioni paraboliche lineari del secondo ordine in forma di divergenza in un dominio cilindrico diR ⁿ×R. Per tali soluzioni si stabilisce un principio di tipo Harnach che si estende sino alla frontiera del dominio. Si prova poi che tale principio è équivalente ad una stima uniforme per la misura calorica associata ad ogni operatore del tipo suddetto. Per soluzioni continue nella chiusura del dominio è poi provata una versione più forte del prineipio di cut sopra.

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Lavoro eseguito nell'ambito del G.N.A.F.A.     

Retrieving information about a group from its character degrees or from its class sizes

We prove that knowledge of the character degrees of a finite group and of their multiplicities determines whether has a Sylow -subgroup as a direct factor. An analogous result based on knowledge of the conjugacy class sizes is known. We prove variations of both results and discuss their similarities.