New insight into solid-state molecular dynamics: mechanochemical synthesis of azobenzene/triphenylphosphine palladacycles

Solid-state reactions of dicyclopalladated azobenzenes and triphenylphosphine lead to the thermodynamically favorable bridged complexes. It was demonstrated for the first time that very complex molecular dynamics involving a series of structural transformations is also feasible in the solid state.     

Titania supported gold nanoparticles as photocatalyst

This Perspective is focused on the photocatalytic activity of gold nanoparticles supported on titania (Au/TiO(2)). Titania is the most widely used photocatalyst, but its limited activity under visible light irradiation has motivated the quest for modified titania materials absorbing visible light. The review starts by justifying how doping with metallic elements is a related strategy, but different, to that leading to the use of Au/TiO(2) in photocatalysis. Data supporting and confirming the photoactivity of gold nanoparticles in colloidal solutions are briefly presented to justify the possibility of gold photosensitization of titania by electron injection into the conduction band. After describing the most common procedures used to prepare Au/TiO(2), the central part of this article is focused on the photocatalytic activity reported for Au/TiO(2) for hydrogen generation, dye decoloration, phenol decomposition and carboxylic acid degradation, among other processes. Emphasis is given to the role that parameters like Au loading, particle size, surface area, spatial structuring and others play on the photocatalytic activity. One important issue has been to distinguish those reports using visible light from those other in which direct titania excitation by UV light has been used. These Au/TiO(2) photocatalysts can find real applications in the near future for environmental remediation and for hydrogen generation.     

Time Decay of Scaling Critical Electromagnetic Schrödinger Flows

We obtain a representation formula for solutions to Schrödinger equations with a class of homogeneous, scaling-critical electromagnetic potentials. As a consequence, we prove the sharp ${L^1 \to L^\infty}$ time decay estimate for the 3D-inverse square and the 2D-Aharonov–Bohm potentials.     

Groups of prime power order and their nonabelian tensor squares

We prove that the nonabelian tensor square of a powerful p-group is again a powerful p-group. Furthermore, If G is powerful, then the exponent of G ⊕ G divides the exponent of G. New bounds for the exponent, rank, and order of various homological functors of a given finite p-group are obtained. In particular, we improve the bound for the order of the Schur multiplier of a given finite p-group obtained by Lubotzky and Mann.     

Sull'estensione dell'integrale debole alla Burkill-Cesari ad una misura

We extend the weak Burkill-Cesari integral of a vector valued set function, with values in a Banach space, to a measure, following an idea developed by Cesari ([4], [5]) in Euclidean spaces.     

Un teorema di rappresentazione per l'integrale parametrico del Calcolo delle Variazioni alla Weierstrass

Summary We prove that the Weierstrass integral over a variety ([5]),in Banach spaces, can be represented as a Bochner integral. This result was given by Cesari ([6])in Euclidean spaces.

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Lavoro eseguito nell'ambito del Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni del C.N.R.Desideriamo ringraziare i Proff. L.Cesari e C.Vinti per le conversazioni avute con loro sull'argomento.     

Elliptic problems with a Hardy potential and critical growth in the gradient: Non-resonance and blow-up results

In this article we analyze existence and nonexistence of positive solutions to problem

     

Error growth patterns in systems with spatial chaos: from coupled map lattices to global weather models

Error growth in spatiotemporal chaotic systems is investigated by analyzing the interplay between temporal and spatial dynamics. The spatial correlation and localization of relative fluctuations grow and decay indicating two different regimes, before and after saturation by nonlinear effects. This general behavior is shown to hold both in simple coupled map lattices and in global weather models. This explains the increasing or decreasing trends previously observed in the exponential growth rate of these spatiotemporal systems.