On the uniqueness of limit cycles for Li\'enard equation: the legacy of G. Sansone

We give an account of the results about limit cycle's uniqueness for Li\'enard equations, from Levinson-Smith's one to the most recent ones. We present a new uniqueness theorem in the line of Sansone-Massera's geometrical approach.Comment: 2 figure

Linear water waves with vorticity: rotational features and particle paths

Steady linear gravity waves of small amplitude travelling on a current of constant vorticity are found. For negative vorticity we show the appearance of internal waves and vortices, wherein the particle trajectories are not any more closed ellipses. For positive vorticity the situation resembles that of Stokes waves, but for large vorticity the trajectories are affected

Italy seen through British eyes: a European middle power?

This article analyses the British perceptions of contemporary Italy and Italian politics. Through the use of a number of sources (parliamentary debates, governmental documents, newspaper articles and interviews) it argues that Italy is not perceived, within Great Britain, as a great power within the European system nor it is viewed as a peripheral actor. Rather, it suggests that Italy seems to have finally found in the post-Cold War scenario its proper role–a European middle power, with important responsibilities within a regional sub-system. A frequent request–and expectation–coming from British politics and society is that Italy should take on more international responsibilities, even in the sphere of defence–as the different readings of Italy's role and leadership in Afghanistan and Lebanon reveal. However, Italy's ability to play this role is believed to be hampered by several factors: its uncertain political situation, its unwillingness to engage in military operations, its reluctance to respect international commitments and its structural economic problems. As a result, further possibilities of cooperation with other international partners as well as its potential for autonomous action on the international stage are, in several cases, precluded. Moreover, if the relations between Italy and the UK are usually seen in a positive way, and Italy is viewed as a reliable partner, the nature of the cooperation between the two countries is often considered to be fragile and based on short-term common interests and strategies

Ecological correlation between diabetes hospitalizations and fine particulate matter in Italian provinces

Background: Exposure to particulate matter has been associated with increased risk of cardiovascular and respiratory diseases. We evaluated the ecological correlation between standardized hospital discharges with diabetes in Italian provinces and fine particulate matter (PM2.5) adjusting for common risk factors, socioeconomic factors and differences in hospitalization appropriateness. Methods: We used cross sectional data aggregated at the province level and available from official institutional databases for years 2008–2010. Covariates included prevalence of adult overweight, obese, smokers, physically inactive, education and income (as average gross domestic product per person, GDP). We reduced the number of covariates to a smaller number of factors for the subsequent statistical model by extracting meaningful components using principal component analysis (PCA). Log-linear multiple regression analysis was used to model diabetes hospital discharges with PCA components and PM2.5 levels and hospitalization appropriateness for men and women. Results: The first PCA components for both men and women were characterized by larger loadings of risk factors (obesity, overweight, physical inactivity, cigarette smoking) and lower socioeconomic factors (educational level and mean GDP). Diabetes hospitalization increases with the first PCA component and decreases with the index of hospitalization appropriateness. In fully adjusted models, diabetes hospitalizations increase with increasing annual PM2.5 concentrations, with a rise of 3.5 % (1.3 %–5.6 %) for men and of 4.0 % (1.5 %-6.4 %) for women per unit of PM2.5 increase. Conclusions: We found a significant ecological relationship between sex and age standardised hospital discharge with diabetes as principle diagnosis and mean annual PM2.5 concentrations in Italian provinces, once that covariates have been accounted for. The relationship was robust to different means of estimating PM2.5 exposure. A large portion of the variance of diabetes hospitalizations was linked to differences of hospital care appropriateness between Italian regions and this variable should routinely be included in ecological analyses of hospitalizations

On the Topological Nature of the Hawking Temperature of Black Holes

In this work we determine that the Hawking temperature of black holes possesses a purely topological nature. We find a very simple but powerful formula, based on a topological invariant known as the Euler characteristic, which is able to provide the exact Hawking temperature of any two-dimensional black hole -- and in fact of any metric that can be dimensionally reduced to two dimensions -- in any given coordinate system, introducing a covariant way to determine the temperature only using virtually trivial computations. We apply the topological temperature formula to several known black hole systems as well as to the Hawking emission of solitons of integrable equations.Comment: Updated version with more relevant reference

Universal quantum Hawking evaporation of integrable two-dimensional solitons

We show that any soliton solution of an arbitrary two-dimensional integrable equation has the potential to eventually evaporate and emit the exact analogue of Hawking radiation from black holes. From the AKNS matrix formulation of integrability, we show that it is possible to associate a real spacetime metric tensor which defines a curved surface, perceived by the classical and quantum fluctuations propagating on the soliton. By defining proper scalar invariants of the associated Riemannian geometry, and introducing the conformal anomaly, we are able to determine the Hawking temperatures and entropies of the fundamental solitons of the nonlinear Schroedinger, KdV and sine-Gordon equations. The mechanism advanced here is simple, completely universal and can be applied to all integrable equations in two dimensions, and is easily applicable to a large class of black holes of any dimensionality, opening up totally new windows on the quantum mechanics of solitons and their deep connections with black hole physics