Cafiero approach to the Dieudonné type theorems

AbstractAn algebra of subsets of a normal topological space containing the open sets is considered and in this context the uniform exhaustivity and uniform regularity for a family of additive functions are studied. Based on these results the Cafiero convergence theorem with the Dieudonné type conditions is proved and in this way also the Nikodým–Dieudonné convergence theorem is obtained

Analytical and experimental FWHM of a gamma camera: theoretical and practical issues

It is well known that resolution on a gamma camera varies as a function of distance, scatter and the camera\u2019s characteristics (collimator type, crystal thickness, intrinsic resolution etc). Manufacturers frequently provide only a few pre-calculated resolution values (using a line source in air, 10\u201315 cm from the collimator surface and without scattering). However, these are typically not obtained in situations resembling a clinical setting. From a diagnostic point of view, it is useful to know the expected resolution of a gamma camera at a given distance from the collimator surface for a particular setting in order to decide whether it is worth scanning patients with \u201csmall lesion\u201d or not. When dealing with absolute quantification it is also mandatory to know precisely the expected resolution and its uncertainty in order to make appropriate corrections. Aim. Our aims are: to test a novel mathematical approach, the cubic spline interpolation, for the extraction of the full width at half maximum (FWHM) from the acquisition of a line source (experimental resolution) also considering measurement uncertainty; to compare it with the usually adopted methods such as the gaussian approach; to compare it with the theoretical resolution (analytical resolution) of a gamma camera at different distances; to create a web-based educational program with which to test these theories. Methods. Three mathematical methods (direct calculation, global interpolation using gaussian and local interpolation using splines) for calculatingFWHMfroma line source (planar scintigraphy) were tested and compared. A NEMA Triple Line Source Phantom was used to obtain static images both in air and with different scattering levels. An advanced, open-source software (MATLAB/Octave and PHP based) was created \u201cad hoc\u201d to obtain and compareFWHMvalues and relative uncertainty. Results and Conclusion. Local interpolation using splines proved faster and more reliable than the usually-adopted Gaussian interpolation. The proposed freely available software proved effective in assessing bothFWHMand its uncertainty

Un caso celebre di corrispondenza tra filosofi: il carteggio Croce-Gentile

In this article, we examine the first volume of the correspondence between Croce and Gentile, the most important Italian philosophers of the 20th century. This volume was published in Turin in 2014. The author analyzes the strenghts and weaknesses of this edition by emphasizing that just in the letters emerges the first considerable contrast between the two great thinkers. It is the dispute about the review of Windelband on which Gennaro Sasso, Girolamo Cotroneo and Francesca Rizzo have focused during the years. At the end of the dispute Gentile comes to one of the cornerstones of his thinking: the perfect identity between philosophy and history of philosophy. Nonetheless, it must be recognised that the constant exchange of letters with the younger friend made Croce feel the need to overcome the level of erudition and historiography towards a speculative framework of the 20th-century crisis. Also starting from this correspondence one can finally understand that compared to others the Italian tradition is more suitable to think about life philosophically

The Pollino seismic sequence: Can shear wave anisotropy monitoring help earthquakes forecast?

Since the late the late ’60s-early ’70s era seismologists started developed theories that included variations of the elastic property of the Earth crust and the state of stress and its evolution crust prior to the oc- currence of a large earthquake. Among the others the theory of the dilatancy (Scholz et al., 1973): when a rock is subject to stress, the rock grains are shifted generating micro-cracks, thus the rock itself in- creases its volume. Inside the fractured rock, fluid saturation and pore pressure play an important role in earthquake nucleation, by modulating the effective stress. Thus measuring the variations of wave speed and of anisotropic parameter in time can be highly informative on how the stress leading to a major fault failure builds up. In 80s and 90s such kind of research on earthquake precursor slowed down and the priority was given to seismic hazard and ground motions studies, which are very important since these are the basis for the building codes in many countries. Today we have dense and sophisticated seismic networks to measure wave-fields characteristics: we archive continuous waveform data recorded at three components broad-band seismometers, we almost routinely obtain high resolution ear- thquake locations. Therefore we are ready to start to systematically look at seismic-wave propagation properties to possibly reveal short-term variations in the elastic properties of the Earth crust. In active fault areas and volcanoes, tectonic stress variation influences fracture field orientation and fluid migration processes, whose evolution with time can be monitored through the measurement of the anisotropic pa- rameters ( Piccinini et al., 2006). Through the study of S waves anisotropy it is therefore potentially possible to measure the presence, migration and state of the fluid in the rock traveled by seismic waves, thus providing a valuable route to understanding the seismogenic phenomena and their precursors (Crampin & Gao, 2010). Variations of anisotropic parameter and of the ratio between the compressional (P-wave) and the shear (S-wave) seismic velocities, the Vp/Vs (Nur, 1972) have been recently observed and measured during the preparatory phase of a major earthquake (Lucente et al. 2010). Here we show the anisotropic parameters at station MMN during the Pollino seismic sequence 2010-2013