A Sampling Theorem for Rotation Numbers of Linear Processes in R2{\R}^{2}

We prove an ergodic theorem for the rotation number of the composition of a sequence os stationary random homeomorphisms in $S^{1}$. In particular, the concept of rotation number of a matrix $g\in Gl^{+}(2,{\R})$ can be generalized to a product of a sequence of stationary random matrices in $Gl^{+}(2,{\R})$. In this particular case this result provides a counter-part of the Osseledec's multiplicative ergodic theorem which guarantees the existence of Lyapunov exponents. A random sampling theorem is then proved to show that the concept we propose is consistent by discretization in time with the rotation number of continuous linear processes on ${\R}^{2}.

Topics on the geometry of D-brane charges and Ramond-Ramond fields

In this paper we discuss some topics on the geometry of type II superstring backgrounds with D-branes, in particular on the geometrical meaning of the D-brane charge, the Ramond-Ramond fields and the Wess-Zumino action. We see that, depending on the behaviour of the D-brane on the four non-compact space-time directions, we need different notions of homology and cohomology to discuss the associated fields and charge: we give a mathematical definition of such notions and show their physical applications. We then discuss the problem of corretly defining Wess-Zumino action using the theory of p-gerbes. Finally, we recall the so-called *-problem and make some brief remarks about it.Comment: 29 pages, no figure

Lyapunov exponents for stochastic differential equations on semi-simple Lie groups

summary:With an intrinsic approach on semi-simple Lie groups we find a Furstenberg–Khasminskii type formula for the limit of the diagonal component in the Iwasawa decomposition. It is an integral formula with respect to the invariant measure in the maximal flag manifold of the group (i.e. the Furstenberg boundary $B=G/MAN$). Its integrand involves the Borel type Riemannian metric in the flag manifolds. When applied to linear stochastic systems which generate a semi-simple group the formula provides a diagonal matrix whose entries are the Lyapunov spectrum. Some Brownian motions on homogeneous spaces are discussed

Hartman-Grobman Theorems along Hyperbolic Stationary Trajectories

We extend the Hartman-Grobman theorems on discrete random dynamical systems (RDS), proved in [7], in two directions: For continuous RDS and for hyperbolic stationary trajectories. In this last case there exists a conjugacy between traveling neighbourhoods of trajectories and neighbourhoods of the origin in the corresponding tangent bundle. We present applications to deterministic dynamical systems

Etiological diagnosis, prognostic significance and role of electrophysiological study in patients with Brugada ECG and syncope.

BACKGROUND: Syncope is considered a risk factor for life-threatening arrhythmias in Brugada patients. Distinguishing a benign syncope from one due to ventricular arrhythmias is often difficult, unless an ECG is recorded during the episode. Aim of the study was to analyze the characteristics of syncopal episodes in a large population of Brugada patients and evaluate the role of electrophysiological study (EPS) and the prognosis in the different subgroups. METHODS AND RESULTS: One hundred ninety-five Brugada patients with history of syncope were considered. Syncope were classified as neurally mediated (group 1, 61%) or unexplained (group 2, 39%) on the basis of personal and family history, clinical features, triggers, situations, associated signs, concomitant therapy. Most patients underwent EPS; they received ICD or implantable loop-recorder on the basis of the result of investigations and physician's judgment. At 62±45months of mean follow-up, group 1 showed a significantly lower incidence of arrhythmic events (2%) as compared to group 2 (9%, p<0.001). Group 2 patients with positive EPS showed the highest risk of arrhythmic events (27%). No ventricular events occurred in subjects with negative EPS. CONCLUSION: Etiological definition of syncope in Brugada patients is important, as it allows identifying two groups with different outcome. Patients with unexplained syncope and ventricular fibrillation induced at EPS have the highest risk of arrhythmic events. Patients presenting with neurally mediated syncope showed a prognosis similar to that of the asymptomatic and the role of EPS in this group is unproven

Geophysical Monitoring at Laboratory Scale of Aerobic Degradation of Diesel Oil

The study is aimed to monitor bioremediation of hydrocarbon-polluted soils by measuring geophysical electromagnetic parameters. A previous study at lab scale showed that biostimulated indigenous microorganisms can remove diesel oil from soil successfully. Herein, we focused on the result of a laboratory test using Time Domain Reflectometry (TDR) probes to measure electrical conductivity and dielectric permittivity in a column of sandy soil artificially contaminated with diesel oil. To simulate aerobic degradation of hydrocarbons, mesocosms were set-up in two Plexiglas columns (inner diameter = 13.8 cm) with 3.4 kg of soil (layer height = 14 cm) spiked with 0.24 kg of diesel oil and hydrated with 0.4 kg of Mineral Salt Medium for Bacteria. One mesocosm was aerated by air injection from the bottom of the column, while the other had only natural aeration due to air diffusion through the soil itself. In each column, electrical conductivity and dielectric permittivity were monitored by TDR probes for 105 days. TDR measurements were supported by microbiological and gas chromatographic analyses, along with SEM images. The findings showed that air injection heavily influenced the TDR monitoring, probably due to generation of air bubbles around the probe that interfered with probe-soil coupling. Therefore, the measurement accuracy was reduced in an irreversible way. In the non-aerated system, a slight (2%) and linear decrease of dielectric permittivity was observed over time, meanwhile electrical conductivity decreased by about 30%

Fly fishing no-kill zones: a possible way to conjugate conservation issues, sustainable sport enhancement and local development in Alpine areas?

The promotion of sustainable tourism and outdoor sports can represent an important way to couple environmental conservation strategies and economic enhancement in marginal and Alpine areas. In this context catch and release fly fishing zones can represent an interesting tool, although no data is available on the effectiveness of these practices on Alpine salmonid population dynamics. Salmonids are the main group of fish in alpine rivers and they are the only actively targeted by anglers. Aim of this work is filling this gap, with a pilot study on two no-kill zones (Po and Pellice rivers, NW Italy). We conducted a temporal and spatial comparison between free-fishing and catch and release management river sections, with a detailed analysis on the Po River site. Our results support the hypothesis that catch and release management allows a numerical increase in wild trout populations. In particular, we detected a massive and rapid increase in younger individuals, possibly linked to a stop on the removal of large-sized reproducers. Protecting trout by the implementation of this practice can at the same time allow the increase of sustainable economic development and sport in marginal areas

Production and destination of sewage sludge in the piemonte region (Italy): The results of a survey for a future sustainable management

The management of sewage sludge originated from municipal wastewater treatment plants (WWTPs) is an urgent issue. In 2019, the local authority of the Piemonte region started a survey with the aim of collecting recent data concerning wastewater and sludge management in the WWTPs located in its own territory. The survey’s results revealed that 60% of the sludge (51,000 t, as dry substance, d.s.) produced by the local WWTPs was recovered or disposed of outside of the region, and a similar amount of sludge was recovered in agriculture directly or after composting. The increase in the costs to accommodate sewage sludge in recovery or disposal plants, followed to a recent Italian Sentence (27958/2017), and the more and more stringent requirements fixed by lots of European countries for the application of sludge in agriculture, are pushing the Piemonte region authority to re-organize its own network for sludge management, with solutions based onto proximity and diversification. Whether the provisions of the current German legislation are applied in the future also in Italy, approx. 90% of sewage sludge produced into the Piemonte region should be incinerated, with a subsequent step of phosphorous recovery. The new regional plan, according to the Regional Address Deed, should consider a diversification of sludge treatment and recovery practices. On this basis, a need for new plants for around 40,000 t d.s./y could be planned