NGC1052 - A study of the pc-scale twin jet

We present results of a VLBA multi-frequency study of the pc-scale twin jet in NGC1052. We observed this object at epoch 1998.99 with the VLBA at 5, 8.4, 22 and 43 GHz both in total and linearly polarized intensity. The spectral analysis confirms the necessity of a free-free absorbing medium, obscuring the innermost part of both jets. At 5 GHz we found a compact linearly polarized emission region at the base of the eastern jet with a degree of polarization of 1.5%. At higher frequencies there is no evidence for polarization in our data. A core shift analysis constrains the position of the central engine to ~0.03 pc. The shift rates of the apparent core position with frequency confirm the strong influence of free-free absorption in conjunction with steep pressure gradients at the bases of both jets.Comment: Proceedings of the conference "SRT: the impact of large antennas on Radio Astronomy and Space Science", Cagliari, Italy, 7-10 November 2001, in press; 6 pages, 5 figures, needs srt_style.st

The Twin--Jet System in NGC 1052: VLBI-Scrutiny of the Obscuring Torus

NGC 1052 offers the possibility to study the obscuring torus around a supermassive black hole, predicted by the standard model of active galactic nuclei, over a wide range of wavelengths from the radio to the X-ray regime. We present a detailed VLBI study of the parsec-scale structure of the ``twin-jet'' system in NGC 1052 in both total and polarized intensity and at multiple frequencies. We report the detection of linearly polarized emission from the base of the eastern jet at 5 GHz. While the radio spectrum in this region might be still consistent with synchrotron self absorption, the highly inverted spectrum of the western jet base represents a clear sign of pronounced free-free absorption in a circumnuclear torus. We observe an abrupt change of the brightness temperature gradient at a distance of $\sim 0.2$ pc to 0.3 pc from the central engine. This might provide an observational signature of the edge of the central torus, where the transition from an external pressure-dominated jet regime to a more or less freely expanding jet takes place. We determine the absorbing column density towards the western jet core to be $\sim 2.2 \times 10^{22}$ cm$^{-2}$ in good agreement with the values derived from various X-ray observations. This suggests that the nuclear X-ray emission and the jet emission imaged by VLBI originate on the same scales.Comment: 14 pages, 11 figures, needs aa.cls, accepted for publication in Astronomy & Astrophysics, note that the resolution of figure 2 has been decreased in comparison to the journal versio

A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

The Wow Factor? A Comparative Study of the Development of Student Music Teachers' Talents in Scotland and Australia

For some time there has been debate about differing perspectives on musical gift and musical intelligence. One view is that musical gift is innate: that it is present in certain individuals from birth and that the task of the teacher is to develop the potential which is there. A second view is that musical gift is a complex concept which includes responses from individuals to different environments and communities (Howe and Sloboda, 1997). This then raises the possibility that musical excellence can be taught. We have already explored this idea with practising musicians (Stollery and McPhee, 2002). Our research has now expanded to include music teachers in formation, and, in this paper, we look at the influences in their musical development which have either 'crystallised' or 'paralysed' the musical talent which they possess. Our research has a comparative dimension, being carried out in Scotland and in Australia. We conclude that there are several key influences in the musical development of the individual, including home and community support, school opportunities and teaching styles and that there may be education and culture-specific elements to these influences

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

Electron Bernstein waves emission in the TJ-II Stellarator

Taking advantage of the electron Bernstein waves heating (EBWH) system of the TJ-II stellarator, an electron Bernstein emission (EBE) diagnostic was installed. Its purpose is to investigate the B-X-O radiation properties in the zone where optimum theoretical EBW coupling is predicted. An internal movable mirror shared by both systems allows us to collect the EBE radiation along the same line of sight that is used for EBW heating. The theoretical EBE has been calculated for different orientations of the internal mirror using the TRUBA code as ray tracer. A comparison with experimental data obtained in NBI discharges is carried out. The results provide a valuable information regarding the experimental O-X mode conversion window expected in the EBW heating experiments. Furthermore, the characterization of the radiation polarization shows evidence of the underlying B-X-O conversion process.Comment: 21 pages, 14 figure

Rigidity of compact Riemannian spin Manifolds with Boundary

In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake \cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy