Understanding the relationship between the environment of the black hole and the radio jet: optical spectroscopy of compact AGN

We aim to investigate the relationship between radio jet activity on parsec-scales and the characteristics of both the bright active galactic nuclei (AGN) and their broad line regions (BLR). For this purpose, we combine 2cm Very Long Baseline Array observations of AGN with their optical spectral observations. This would enable us to investigate the optical spectra of a set of 172 relativistically beamed, flat-spectrum AGN with the nuclear disk oriented near to the plane of sky. Here, we present first results from optical spectroscopic observations of the brightest AGN from the 2 cm VLBA survey, and show a diversity of their spectral morphologies.Comment: 2 pages, to be published in the Proceedings of "Multiwavelength AGN Surveys", Cozumel, Dec 8 - 12, 200

Radio-optical scrutiny of the central engine in compact AGN

We combine Very-Long-Baseline Interferometry (VLBI) data for $\sim100$ active galactic nuclei (AGN) available from the Very Large Baseline Array (VLBA) 2 cm imaging survey and optical spectroscopy to investigate the relationships in the emission-line region--central engine--radio jet system. Here, we present the diversity of spectral types among the brightest AGN in our sample. We also discuss correlations between the mass of the central engine and properties of the parsec-scale radio jet for 24 AGN selected by the presence of H$\beta$ broad-emission lines in their spectra.Comment: 4 pages, 5 figures, to appear in the proceedings of the Workshop on "Multiband Approach to AGN" held in Bonn (Germany), 30 September - 2 October 2004, to be published in "Memorie della Societa Astronomica Italiana

Effects of noise on hysteresis and resonance width in graphene and nanotubes resonators

We investigate the role that noise plays in the hysteretic dynamics of a suspended nanotube or a graphene sheet subject to an oscillating force. We find that not only the size but also the position of the hysteresis region in these systems can be controlled by noise. We also find that nano-resonators act as noise rectifiers: by increasing the noise in the setup, the resonance width of the characteristic peak in these systems is reduced and, as a result, the quality factor is increased.Comment: 15 pages, 6 figures. Sent to PRB (in revision

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

H^s versus C^0-weighted minimizers

We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology.Comment: 15 page

A family of complex potentials with real spectrum

We consider a two-parameter non hermitean quantum-mechanical hamiltonian that is invariant under the combined effects of parity and time reversal transformation. Numerical investigation shows that for some values of the potential parameters the hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other PT symmetric models, which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.Comment: Six figures and four table

Dynamics of a map with power-law tail

We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both regular and chaotic behavior. We study numerically and, in part, analytically different bifurcation structures. Particularly interesting is the description of the abrupt transition order-to-chaos mediated by an attractor made of an infinite number of limit cycles with only a finite number of different periods. It is shown that the power-law piece in the map is at the origin of this type of bifurcation. The system exhibits interior crises and crisis-induced intermittency.Comment: 28 pages, 17 figure