Certain particular solutions of the clairaut equation

A study has been conducted to ascertain conditions on the density distribution within a fluid, rotating planet in order that the deformation of its outer shell be expressible in terms of the Bessel functions of the first kind and the Gaussian hypergeometric series.It has been established that (1) the density must be a solution to an ordinary differential equation of the Riccati type, and (2) two already considered density distributions are the only closed-form solutions of physical relevance.     

Sopra una clorite (penninite) della valle del Dragone nell'appennino emiliano

Riassunto Viene descritta una penninite di Boccassuolo nell'Appennino modenese, e attraverso lo studio ottico, chimico, roentgenografico e termico differenziale ne vengono definite le proprietà caratteristiche. L'esame della curva termico differenziale e degli spettrogrammi Debye ottenuti da polvere di penninite scaldata fra 900° e 950° permette di stabilire che la trasformazione penninite-enstatite inizia già nell'ambito di temperatura compreso fra 910° e 940°.Con 1 figura.     

Migrating sand waves

A simple mathematical model is described, which reproduces the major features of sand waves' appearance and growth and in particular predicts their migration speed. The model is based on the linear stability analysis of the flat configuration of the sea bottom subject to tidal currents. Attention is focused on the prediction of the complex growth rate that bottom perturbations undergo because of both oscillatory fluid motions and residual currents. While the real part _r of controls the amplification or decay of the amplitude of the bedforms, the imaginary part _i is related to their migration speed. Previous works on the migration of the sand waves (Németh etal. 2002) consider a forcing tide made up by the M2 constituent (oscillatory period equal to 12 h) plus the residual current Z0 and predict always a downcurrent migration of the bedforms. However, field cases exist of upcurrent-migrating sand waves (downcurrent/upcurrent-migrating sand waves mean bedforms moving in the direction of the steady residual tidal current or in the opposite direction, respectively). The inclusion of a tide constituent characterized by a period of 6 h (M4) is the main novelty of the present work, which allows for the prediction of the migration of sand waves against the residual current Z0. Indeed, the M4 tide constituent, as does also the residual current Z0, breaks the symmetry of the problem forced only by the M2 tide constituent, and induces sand-wave migration. The model proposed by Besio etal. (2003a) forms the basis for the present analysis. Previous works on the subject (Gerkema 2000; Hulscher 1996a,b; Komarova and Hulscher 2000) are thus improved by using a new solution procedure (Besio etal. 2003a) which allows for a more accurate evaluation of the growth rate for arbitrary values of the parameter r, which is the ratio between the horizontal tidal excursion and the perturbation wavelength. Responsible Editor: Jens Kappenberg     

Improvement of Nakamura technique by singular spectrum analysis

In this work we investigate the application of the Singular Spectrum Analysis to improve Nakamura Technique. The SSA has a wide and multidisciplinary range of applications; it allows a time series to be decomposed into different components, e.g. the signal itself, as well as various noise components, which can be subsequently removed from the data. Removal of the minor component of the data can lead to significant improvements in the identification of the system. In this paper the use of SSA Technique allows to optimize the signal to noise ratio before computing the classical Nakamura spectral ratios. A number of typical applications are also presented.     

Petrogenesis of tourmaline rocks associated with Fe-carbonate–graphite metapelite, metabasite and strata-bound polymetallic sulphide mineralisation, Peloritani Mountains, Sicily, Southern Italy

Tourmalinite and tourmaline-rich rocks associated with Fe-carbonate–graphite phyllite, strata-bound polymetallic sulphide deposits, metabasite and marble were studied, for information on the mechanism of tourmaline formation in the pre-Hercynian low-grade metamorphic sequence of the Mandanici Unit in the Peloritani Mountains of Sicily, southern Italy. The major and trace element compositions of the tourmaline rocks suggest the existence of a sedimentary protolith with pre-metamorphic black shale and bedded chert. Boron was interpreted to be accumulated in a restricted sedimentary basin, between platform carbonate formations, with abundant organic matter and Fe–Al–Ti-rich laterite–bauxite soil-derived clastic supply, under a continental volcano-tectonic extensional regime accompanied by a local convective hydrothermal system along faults. Petrographic, crystal–chemical and δ¹¹B isotopic data are compatible with a model of marine sediment dewatering at temperatures below 200 °C, which caused the removal of boron from clay. Metamorphism led to the development of tourmaline in an Al–Ti-rich environment, in equilibrium with other minerals such as ilmenite, albite and muscovite. The upper temperature of metamorphism (almost 375 °C), estimated on the basis of δ¹¹B, fits geothermometric results from Δ¹³C_{carbonate–graphite} on associated rocks. The estimated value of δ¹¹B in the tourmalinite protolith, − 7.5‰ , is also compatible with continental-derived Al-rich sediments.     

Seismic study of the Mesozoic carbonate basement around Mt. Somma–Vesuvius, Italy

Fifteen seismic reflection lines from AGIP surveys, in and around the Campanian Plain and Mt. Somma–Vesuvius (south Italy) have been interpreted. The attention has been focused to the horizon pertinent to the top of the Mesozoic carbonate sequence and the Quaternary faults dissecting it. As a matter of fact, both are very important elements for understanding the origin of the volcanic activity in the area, that often in the past, has been the topic of debates not supported by reliable data. In the study area, referring to the depth of the carbonate basement, comparison between the result achieved by the seismic prospecting and previous gravity studies has been made. It shows coherence in some areas but large discrepancy within others. Near the town of S. Anastasia, the gravity and seismic depth estimates differ as much as 1000 m or more. Furthermore, the seismic data show that the source of the greatest volcanic eruption in the area (the so-called ‘Campanian Ignimbrite') is probably not located in the Acerra depression, as suggested by other authors. A main NE–SW fault directed toward Vesuvius, considered as playing a primary role on volcanogenetic processes and previously recognised only offshore by marine seismic survey, has been now identified also inland using this new seismic information. The results presented here strengthen the hypothesis that Mt. Vesuvius is located at the crossing point of two regional Quaternary sets of fault heading NW–SE and NE–SW.     

XMM–Newton observations of soft gamma-ray repeaters

All the confirmed Soft Gamma-ray Repeaters have been observed with the EPIC instrument on the XMM–Newton satellite. We review the results obtained in these observations, providing the most accurate spectra on the persistent X-ray emission in the 1–10 keV range for these objects, and discuss them in the context of the magnetar interpretation.