Pasquale del Pezzo, Duke of Caianello, Neapolitan mathematician

This article is dedicated to a reconstruction of some events and achievements, both personal and scientific, in the life of the Neapolitan mathematician Pasquale del Pezzo, Duke of Caianello

The first Long Period earthquake detected in the background seismicity at Mt. Vesuvius

The typical earthquakes occurring at Mt. Vesuvius are Volcano-Tectonic. On July 20, 2003, an unusual earthquake with low and narrow frequency content was detected. The seismograms presented an emergent onset and a nearly monochromatic spectrum at all stations of the Osservatorio Vesuviano(Istituto Nazionale di Geofisica e Vulcanologia) seismic network. The event was located at about 4 km b.s.l. close to the crater axis and an equivalent duration magnitude of 0.6 was estimated. The nature of this event was investigated by comparing its features with those of two typical Volcano-Tectonic earthquakes occurred inside the same source volume. We compared the spectral content calculating the spectrograms and the coda patterns using the Hilbert Transform. A Seismic Moment Tensor inversion was performed on the low frequency earthquake. The focal mechanisms for the two Volcano-Tectonic earthquakes were estimated with a classical technique and resulted compatible with the stress field acting on the volcano. Taking into account the clear differences with the typical Volcano-Tectonic events as well as the peculiarities retrieved from our analyses (monochromatic, low frequency spectral content, and sustained coda) and also some geochemical observations, we classify the unusual low frequency seismic event detected at Mt. Vesuvius as Long Period earthquake and propose that its origin could be linked to a pressure drop in the deep hydrothermal system

Fermat hypersurfaces and Subcanonical curves

We extend the classical Enriques-Petri Theorem to $s$-subcanonical projectively normal curves, proving that such a curve is $(s+2)$-gonal if and only if it is contained in a surface of minimal degree. Moreover, we show that any Fermat hypersurface of degree $s+2$ is apolar to an $s$-subcanonical $(s+2)$-gonal projectively normal curve, and vice versa.Comment: 18 pages; AMS-LaTe

Subsurface structure of the Solfatara volcano (Campi Flegreicaldera, Italy) as deduced from joint seismic-noise array,volcanological and morphostructural analysis

The joint application of different seismological techniques for seismic noise analysis, and the results of a volcanological and morphostructural survey, have allowed us to obtain a detailed and well constrained image of the shallow crustal structure of the Solfatara volcano (Campi Flegrei caldera, Italy). Horizontal-to-vertical spectral ratios, inversion of surface wave dispersion curves and polarization analysis provided resonance frequencies and peak amplitudes, shear wave velocity profiles and polarization pattern of coherent ambient noise. These results, combined in a unique framework, indicate that the volcanic edifice is characterized by lateral and vertical discontinuities and heterogeneities in terms of shear wave velocity, lithological contrasts and structural setting. The interpretation of the seismological results, with the volcanological and morphostructural constraints, supports the hypothesis that the volcano has been characterized by a complex and intense activity, with the alternation of constructive and destructive phases, during which magmatic and phreatomagmatic explosions built a complex tuff-cone, later reworked by atmospheric agents and altered by hydrothermal activity. The differences in the velocity structure between the central and eastern parts of the crater have been interpreted as resulting from a possible eastward migration of the eruptive vent along the deformational features affecting the area, and to the presence of viscous lava and lithified tuff bodies within the feeding conduits, which are buried under a covering of reworked materials of variable thickness. The observed fault and fracture systems, partially inherited from regional structural setting and exhumed during volcanism and ground deformation episodes also seems to strongly control wave propagation, affecting the noise polarization properties

Clues on the origin of post-2000 earthquakes at Campi Flegrei caldera (Italy)

Acknowledgements We thank the INGV-OV staff involved in the management and maintenance of the seismic and GPS networks and Francesca Di Luccio for the data of the best located earthquakes. We acknowledge Valerio Acocella and an anonymous reviewer for the helpful comments that improved the clarity of the manuscript.This study has benefited from funding provided by INGV (project COHESO) by the Italian Presidenza del Consiglio dei Ministri Dipartimento della Protezione Civile (DPC), INGV-DPC Research Agreement 2012–2014, Progetto V2 “Precursori di eruzioni”. This paper does not necessarily represent DPC official opinion and policies. EdP has been partly supported by Spanish Project Ephestos, CGL2011-29499-C02-01 and KNOWAVES, TEC2015-68752. We wish to acknowledge the former contribution of Lorenzo Casertano, Oliveri del Castillo and Maria Teresa Quagliariello, who, in an early paper published on Nature in 1976, first discussed the importance of fluids in the dynamics of Campi Flegrei Caldera.Peer reviewedPublisher PD

ANNALS OF GEOPHYSICS: AD MAJORA

Annals of Geophysics (ISSN: 1593-5213; from 2010, 2037-416X) is a bimonthly international journal, which publishes scientific papers in the field of geophysics sensu lato. It derives from Annali di Geofisica (ISSN: 0365-2556), which commenced publication in January 1948 as a quarterly periodical devoted to general geophysics, seismology, Earth magnetism, and atmospheric studies...

On the classification of OADP varieties

The main purpose of this paper is to show that OADP varieties stand at an important crossroad of various main streets in different disciplines like projective geometry, birational geometry and algebra. This is a good reason for studying and classifying them. Main specific results are: (a) the classification of all OADP surfaces (regardless to their smoothness); (b) the classification of a relevant class of normal OADP varieties of any dimension, which includes interesting examples like lagrangian grassmannians. Following [PR], the equivalence of the classification in (b) with the one of quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan algebras are explained.Comment: 13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in a special issue of Science in China Series A: Mathematic

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde