On the concentration of entropy for scalar conservation laws

We prove that the entropy for an $L^\infty$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution

Detection of Faint BLR Components in the Starburst/Seyfert Galaxy NGC 6221 and Measure of the Central BH Mass

In the last decade, using single epoch virial based techniques in the optical band, it has been possible to measure the central black hole mass on large AGN1 samples. However these measurements use the width of the broad line region as a proxy of the virial velocities and are therefore difficult to be carried out on those obscured (type 2) or low luminosity AGN where the nuclear component does not dominate in the optical. Here we present the optical and near infrared spectrum of the starburst/Seyfert galaxy NGC 6221, observed with X-shooter/VLT. Previous observations of NGC 6221 in the X-ray band show an absorbed (N_H=8.5 +/- 0.4 x 10^21 cm^-2) spectrum typical of a type 2 AGN with luminosity log(L_14-195 keV) = 42.05 erg/s, while in the optical band its spectrum is typical of a reddened (A_V=3) starburst. Our deep X-shooter/VLT observations have allowed us to detect faint broad emission in the H_alpha, HeI and Pa_beta lines (FWHM ~1400-2300 km/s) confirming previous studies indicating that NGC 6221 is a reddened starburst galaxy which hosts an AGN. We use the measure of the broad components to provide a first estimate of its central black hole mass (M_BH = 10^(6.6 +/- 0.3) Msol, lambda_Edd=0.01-0.03), obtained using recently calibrated virial relations suitable for moderately obscured (N_H<10^24 cm^-2) AGN.Comment: 13 pages, 3 figures, 1 table. Published in Frontiers in Astronomy and Space Science

The fundamental relation between supermassive black holes and their host galaxies

We study the correlations between supermassive black holes (BHs) and their host galaxies, using a sample of 83 BH masses collected from the most recent and reliable spatially resolved estimates available from the literature. We confirm the mono- and bivariate correlations between SMBHs and the bulges of their host galaxies, confirming that the correlation with the effective velocity dispersion is not significantly improved by higher dimensionality. Instead, pseudo-bulges do not seem to correlate with their SMBHs, probably because their secular evolution is often unable to trigger accretion onto the central BH. We then present a novel approach aimed at finding the fundamental relation between SMBHs and their host galaxies. For the first time, we analytically combine BH masses with the Fundamental Plane (FP), showing that M_(BH)–σ_e appears to be the fundamental relation rather than a putative ‘BH Fundamental Plane’ of the kind M_(BH)–σ_e–R_e. These results can be explained by a picture which sees the M_(BH)–σ_e relation as a natural outcome of the change in AGN feedback from momentum-driven to energy-driven. The other scaling relations are then established through the FP

The Fundamental Relation between Supermassive Black Holes and Their Host Galaxies

We study the correlations between Supermassive Black Holes (BH) and their host galaxies, using a sample of 83 BH masses collected from the most recent and reliable spatially resolved estimates available from the literature. We confirm the mono- and bivariate correlations between SMBHs and the bulges of their host galaxies, confirming that the correlation with the effective velocity dispersion is not significantly improved by higher dimensionality. Instead, pseudobulges do not seem to correlate with their SMBHs, probably because their secular evolution is often unable to trigger accretion onto the central BH. We then present a novel approach aimed at finding the fundamental relation between SMBHs and their host galaxies. For the first time, we analytically combine BH masses with the Fundamental Plane (FP), showing that Mbh-sigma_e appears to be the fundamental relation rather than a putative "BH Fundamental Plane" of the kind Mbh-sigma_e-R_e. These results can be explained by a picture which sees the Mbh-sigma_e relation as a natural outcome of the change in AGN feedback from momentum- to energy-driven. The other scaling relations are then established through the FP.Comment: 15 pages, 11 figures, accepted by MNRA

Notch signaling sustains the expression of Mcl-1 and the activity of eIF4E to promote cell survival in CLL

In chronic lymphocytic leukemia (CLL), Notch1 and Notch2 signaling is constitutively activated and contributes to apoptosis resistance. We show that genetic inhibition of either Notch1 or Notch2, through small-interfering RNA, increases apoptosis of CLL cells and is associated with decreased levels of the anti-apoptotic protein Mcl-1. Thus, Notch signaling promotes CLL cell survival at least in part by sustaining Mcl-1 expression. In CLL cells, an enhanced Notch activation also contributes to the increase in Mcl-1 expression and cell survival induced by IL-4.Mcl-1 downregulation by Notch targeting is not due to reduced transcription or degradation by caspases, but in part, to increased degradation by the proteasome. Mcl-1 downregulation by Notch targeting is also accompanied by reduced phosphorylation of eukaryotic translation initiation factor 4E (eIF4E), suggesting that this protein is another target of Notch signaling in CLL cells.Overall, we show that Notch signaling sustains CLL cell survival by promoting Mcl-1 expression and eIF4E activity, and given the oncogenic role of these factors, we underscore the therapeutic potential of Notch inhibition in CLL

Extending Virial Black Hole Mass Estimates to Low-Luminosity or Obscured AGN: the cases of NGC 4395 and MCG -01-24-012

In the last decade, using single epoch (SE) virial based spectroscopic optical observations, it has been possible to measure the black hole (BH) mass on large type 1 Active Galactic Nuclei (AGN) samples. However this kind of measurements can not be applied on those obscured type 2 and/or low luminosity AGN where the nuclear component does not dominate in the optical. We have derived new SE relationships, based on the FWHM and luminosity of the broad line region component of the Pabeta emission line and/or the hard X-ray luminosity in the 14-195 keV band, which have the prospect of better working with low luminosity or obscured AGN. The SE relationships have been calibrated in the 10^5-10^9 M_sol mass range, using a sample of AGN whose BH masses have been previously measured using reverberation mapping techniques. Our tightest relationship between the reverberation-based BH mass and the SE virial product has an intrinsic spread of 0.20 dex. Thanks to these SE relations, in agreement with previous estimates, we have measured a BH mass of M_BH =1.7^+1.3_-0.7 X 10^5 M_sol for the low luminosity, type 1, AGN NGC 4395 (one of the smallest active galactic BH known). We also measured, for the first time, a BH mass of M_BH = 1.5^+1.1_-0.6 X 10^7 M_sol for the Seyfert 2 galaxy MCG -01-24-012.Comment: 10 pages, 7 figures. Accepted by MNRA

Dwarf spheroidal satellites of M31: I. Variable stars and stellar populations in Andromeda XIX

We present B,V time-series photometry of Andromeda XIX (And XIX), the most extended (half-light radius of 6.2') of Andromeda's dwarf spheroidal companions, that we observed with the Large Binocular Cameras at the Large Binocular Telescope. We surveyed a 23'x 23' area centered on And XIX and present the deepest color magnitude diagram (CMD) ever obtained for this galaxy, reaching, at V~26.3 mag, about one magnitude below the horizontal branch (HB). The CMD shows a prominent and slightly widened red giant branch, along with a predominantly red HB, which, however, extends to the blue to significantly populate the classical instability strip. We have identified 39 pulsating variable stars, of which 31 are of RR Lyrae type and 8 are Anomalous Cepheids (ACs). Twelve of the RR Lyrae variables and 3 of the ACs are located within And XIX's half light radius. The average period of the fundamental mode RR Lyrae stars ( = 0.62 d, \sigma= 0.03 d) and the period-amplitude diagram qualify And XIX as an Oosterhoff-Intermediate system. From the average luminosity of the RR Lyrae stars ( = 25.34 mag, \sigma= 0.10 mag) we determine a distance modulus of (m-M)$_0$=$24.52\pm0.23$ mag in a scale where the distance to the Large Magellanic Cloud (LMC) is $18.5\pm0.1$ mag. The ACs follow a well defined Period-Wesenheit (PW) relation that appears to be in very good agreement with the PW relationship defined by the ACs in the LMC.Comment: accepted for publication in Ap