Operators in Rigged Hilbert spaces: some spectral properties

A notion of resolvent set for an operator acting in a rigged Hilbert space \D \subset \H\subset \D^\times is proposed. This set depends on a family of intermediate locally convex spaces living between \D and \D^\times, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.Comment: 29 page

Markus Gabriel, Il senso dell'esistenza.

La recensione si configura nei termini di una presentazione critica dei nuclei tematici centrali del testo di Markus Gabriel, ed \ue8 essenzialmente orientata all'individuazione dei passaggi fondamentali attraverso i quali l'autore delinea il profilo teorico del nuovo realismo. Nello specifico, la recensione mette in rilievo le modalit\ue0 attraverso le quali l'autore esibisce le caratteristiche strutturali del dispositivo ontologico su cui si basa la proposta teorica neo-realista

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

Space-time coupling in the up-conversion of broadband down-converted light

We investigate the up-conversion process of broadband light from parametric down-conversion (PDC), focusing on the spatio-temporal spectral properties of the sum-frequency generated (SFG) radiation. We demonstrate that the incoherent component of the SFG spectrum is characterized by a skewed geometry in space-time, which originates from a compensation between the group-velocity mismatch and the spatial walk-off of the fundamental and the SFG fields. The results are illustrated both by a theoretical modeling of the optical system and by experimental measurements.Comment: 11 pages, 9 figures. arXiv admin note: text overlap with arXiv:1308.236

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

Evaluation of biomass activity in membrane bioreactors by means of respirometric techniques

The paper reports the main results of a respirometric experimental survey carried out on several membrane bioreactor pilot plants, characterized by different pilot plant layouts as well as operational conditions. The main aim was to assess the influence of specific conditions on biokinetic/stoichiometric parameters. In particular, the respirometric tests were specifically aimed at investigating the activity of both heterotrophic and autotrophic bacterial species. The achieved results showed that the plant configuration and the features of the feeding wastewater and operational conditions determine significant variation of the kinetic coefficients. The respirometric analysis was confirmed to be a simple and effective tool for the evaluation of the actual biomass kinetic parameters, to be used in mathematical models for the design phase as well as for monitoring the biomass viability during plant operations