On the notion of Weyl system

We review the standard notion of Weyl system, which stems from the Weyl formulation of the canonical commutation relations of quantum mechanics, and propose an alternative definition based on the theory of projective representations. Next, we discuss some conceptual advantages of this alternative definition. Finally, we introduce a notion of physical equivalence of group representations and propose a further ‘purely conceptual’ definition of Weyl system based on this notion.     

On discrete frames associated with semidirect products

For groups which are the semidirect product of some vector group with a unimodular group we prove that the existence of a discrete frame obtained from an at-most countable set of vectors through the action of a given unitary representation implies that the representation in use has to be square-integrable.     

Resonances and spectral properties of detuned OPOs pumped by fluctuating sources

Twin-beam fluctuations are analyzed for detuned and mismatched OPO configurations. Resonances and frequency responses to the quantum noise sources (quantum and pump amplitude/phase fluctuations) are examined as functions of cavity decay rates, excitation parameters and detuning. The dependence of self- and mutual correlations of beam amplitudes and phases on detuning, mismatch and damping parameters is discussed. Received: 25 January 2002 / Revised version: 28 May 2002 / Published online: 15 November 2002 RID="*" ID="*"Corresponding author. Fax: +39-81/676-346, E-mail: alberto.porzio@na.infn.it     

The first entry to 5,6-dihydroxy-3-mercaptoindole, 5-hydroxy-3-mercaptoindole and their 2-carbomethoxy derivatives by a mild thiocyanation/reduction methodology

The hitherto unknown 5,6-dihydroxy-3-mercaptoindole (4a) and its 2-carbomethoxy derivative (4b), as well as the analogous 5-hydroxy 3-mercaptoindoles, have been conveniently obtained as O,S-acetyl derivatives 3a-d by thiocyanation of the corresponding acetoxyindoles 1a-d with the NH₄SCN/oxone system followed by SmI₂ reduction and acetylation.     

Nonlinear frequency response curves estimation and stability analysis of randomly excited systems in the subspace framework

Nonlinear Dynamics - In this paper, the periodic solutions of nonlinear mechanical systems are studied starting from the nonlinear state-space model estimated using the nonlinear subspace...