Fully representable and *-semisimple topological partial *-algebras

We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome is that, for an appropriate order relation, one recovers the \M-bounded elements introduced in previous works.Comment: 26 pages, Studia Mathematica (2012) to appea

Partial inner product spaces: Some categorical aspects

We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces of practical interest.Comment: 21 page

Experimental observation of the X-shaped near field spatio-temporal correlation of ultra-broadband twin beams

In this work we present the experimental observation of the non factorable near field spatio-temporal correlation of ultra-broadband twin beams generated by parametric down conversion (PDC), in an interferometric-type experiment using sum frequency generation, where both the temporal and spatial degrees of freedom of PDC light are controlled with very high resolution. The revealed X-structure of the correlation is in accordance with the predictions of the theory.Comment: 5 pages, 3 figure

IL DESIGN DEI BENI CULTURALI.CRISI TERRITORIO, IDENTITÀ

Sino a pochi anni fa accostare il termine Design a quello di Beni Culturali avrebbe avuto il sapore di una provocazione. Un evidente ossimoro, insomma, tra una parola -Design- per sua natura legata all’idea del nuovo e un’altra -Beni Culturali- evidentemente connessa alla conservazione dell’antico. Se il Design inoltre rimandava quasi automaticamente a una modalità del progetto fondata ancora largamente sul riferimento al paradigma industriale, i Beni Culturali evocavano una concezione “patrimoniale” del lascito storico, per la massima parte individuato nel paesaggio e nei “beni” ereditati dalla cultura delle età preindustriali. E’ dunque evidente che la nuova dizione di Design dei Beni Culturali è il frutto di una progressiva, doppia rivoluzione che ha modificato sia la nostra percezione del concetto di “bene” legato al passato, sia il campo di significati attribuiti alle pratiche del progetto industriale. Il design investe i Beni Culturali con tutto il peso delle nuove tecnologie -del digitale e del virtuale innanzitutto- facendole entrare prepotentemente nel territorio dei musei, dell’archeologia, dell’archivistica, ma anche nella valorizzazione in tempo di crisi delle risorse territoriali diffuse nei contesti urbani e territoriali.Up until just a few years ago, putting the terms “design” and “cultural heritage” together would have sounded like a provocation. An obvious oxymoron, really, between one word – design - by its nature tied to the idea of the new and another – cultural heritage – clearly connected to the conservation of the old. Furthermore, while “design” almost automatically turned to a design process still largely based on the industrial paradigm, “cultural heritage” evoked an interpretation of history’s legacy as “endowments”, for the most part identified in the landscape and in assets inherited from pre-industrial cultures. This new wording of the “design of cultural heritage is the result of a progressive double revolution, which has changed both our perception of the concept of “asset” tied to the past, as well as the range of meanings attributed to the industrial design process. Today, design invests cultural heritage in particular with an armament of new technologies – spanning from digital to virtual,– makes them important protagonists in the fields of museums, archaeology, archiving, but also in the development, in times of crisis, of cultural recourses spread throughout the urban and regional context

Cross-spectral analysis of the X-ray variability of Mrk 421

Using the cross-spectral method, we confirm the existence of the X-ray hard lags discovered with cross-correlation function technique during a large flare of Mrk 421 observed with BeppoSAX . For the 0.1--2 versus 2--10keV light curves, both methods suggest sub-hour hard lags. In the time domain, the degree of hard lag, i.e., the amplitude of the 3.2--10 keV photons lagging the lower energy ones, tends to increase with the decreasing energy. In the Fourier frequency domain, by investigating the cross-spectra of the 0.1--2/2--10 keV and the 2--3.2/3.2--10 keV pairs of light curves, the flare also shows hard lags at the lowest frequencies. However, with the present data, it is impossible to constrain the dependence of the lags on frequencies even though the detailed simulations demonstrate that the hard lags at the lowest frequencies probed by the flare are not an artifact of sparse sampling, Poisson and red noise. As a possible interpretation, the implication of the hard lags is discussed in the context of the interplay between the (diffusive) acceleration and synchrotron cooling of relativistic electrons responsible for the observed X-ray emission. The energy-dependent hard lags are in agreement with the expectation of an energy-dependent acceleration timescale. The inferred magnetic field (B ~ 0.11 Gauss) is consistent with the value inferred from the Spectral Energy Distributions of the source. Future investigations with higher quality data that whether or not the time lags are energy-/frequency-dependent will provide a new constraint on the current models of the TeV blazars.Comment: 11 pages, 6 figures, accepted by MNRA

Detection of the ultranarrow temporal correlation of twin beams via sum-frequency generation

We demonstrate the ultranarrow temporal correlation (6 fs full width half maximum) of twin beams generated by parametric down-conversion, by using the inverse process of sum-frequency generation. The result relies on an achromatic imaging of a huge bandwith of twin beams and on a careful control of their spatial degrees of freedom. The detrimental effects of spatial filtering and of imperfect imaging are shown toghether with the theoretical model used to describe the results

SVEP and local spectral radius formula for unbounded operators

In this paper we study the localized single valued extension property for an unbounded operator T. Moreover, we provide sufficient conditions for which the formula of the local spectral radius holds for these operators