On the automorphisms of moduli spaces of curves

In the last years the biregular automorphisms of the Deligne-Mumford's and Hassett's compactifications of the moduli space of n-pointed genus g smooth curves have been extensively studied by A. Bruno and the authors. In this paper we give a survey of these recent results and extend our techniques to some moduli spaces appearing as intermediate steps of the Kapranov's and Keel's realizations of $\bar{M}_{0,n}$, and to the degenerations of Hassett's spaces obtained by allowing zero weights.Comment: 15 pages. The material of version 1 has been reorganized and expanded in this paper and in arXiv:1307.6828 on automorphisms of Hassett's moduli space

Properties of the unusual galaxy PSC 09104+4109

The IRAS source PSC 09104+4109 is tentatively identified with a faint emission line galaxy having z = 0.442. Assuming this identification is correct, the total infrared luminosity of this galaxy is estimated to be 5 x 10 to the 12th power L sub 0, among the highest for galaxies detected by IRAS. This energy is concentrated at wavelengths less than 30 micrometers, and is approx. 50 times greater than the estimated optical luminosity. The serendipitous way in which this source was found in the PSC catalog suggests that many more similar objects may be found at the lowest levels of the IRAS survey

Stability margins for multilinear interval systems by way of phase conditions: A unified approach

A simple way of checking the stability with respect to an arbitrary stability region of a family of polynomials containing a vector of parameters varying within prescribed intervals is discussed. It is assumed that the parameters appear affine multilinearly in the characteristic polynomial coefficients. The condition proposed is simply to check the phase difference of the vertex polynomials. This test based on the mapping theorem significantly reduces computational complexity. Mathematical proofs are omitted. The results can be used to determine various stability margins of control systems containing interconnected interval subsystems. These include the gain, phase, time-delay, H(sup infinity), and nonlinear sector bounded stability margins of multilinear interval systems

Parametric stability margin for multilinear interval control systems

Recently, a necessary and sufficient condition to determine the robust stability of a multilinear interval control system has been reported as an extension of the well-known Box theorem which deals with the linear affine case. A simple but computationally efficient algorithm, based on the above result, to check the robust stability of such systems is introduced. The method is also extended to find the parametric stability margin of such a system

The 32nd CDC: Robust stabilizer synthesis for interval plants using Nevanlina-pick theory

The synthesis of robustly stabilizing compensators for interval plants, i.e., plants whose parameters vary within prescribed ranges is discussed. Well-known H(sup infinity) methods are used to establish robust stabilizability conditions for a family of plants and also to synthesize controllers that would stabilize the whole family. Though conservative, these methods give a very simple way to come up with a family of robust stabilizers for an interval plant

On the uniqueness of solutions to the Gross-Pitaevskii hierarchy

We give a new proof of uniqueness of solutions to the Gross-Pitaevskii hierarchy, first established by Erdos, Schlein and Yau, in a different space, based on space-time estimates

A simulation survey of galaxy interactions

Many carefully selected samples of interacting galaxies have been observed extensively in attempts to clarify whether interaction produces activity in galaxies. Because the sample members represent a wide range of encounter parameters and times, one can then study whether there are correlations between observable encounter features and, for example, Seyfert activity. On the other hand, in theoretical studies, simulations typically deal with either time-consuming detailed modelling of single galaxy pairs or tracing a few model encounters over time. The authors extend the observational survey approach by combining it with a simulation survey. The authors are conducting a survey of model encounters, covering the most important encounter parameters over a wide range. Some parameters, such as companion structure and initial velocity, are demonstratably less important and can be ignored in a first pass. The parameter range must be richly enough sampled so that the authors can evaluate the uniqueness of the observable morphology and velocity structure of the resulting simulated pairs to diagnose unobservable companion orbit parameters. They are using a self-gravitating polar n-body code run on the Cray X-MP at the Alabama Supercomputer Network. For each simulation, the authors have stellar and gas distributions predicted over, typically, a billion years, along with information on gas motions within the disk and any material captured by the companion or lost to the system. Features of disturbed spiral galaxies are sensitive enough to time and encounter parameters so that a match of the simulation survey results to observations can be applied as starting points to infer unobservable orbital or system parameters in actual sample members. This should enable them to examine whether interesting observed properties (Seyfert activity, nuclear star-formation rate) are functions of unobservable dynamical properties which characterize each encounter. Any correlations (or lack of some expected ones) will provide strong clues as to how or whether these phenomena are related to interactions. Aside from its use with such observed samples, this survey should greatly speed determination of initial orbital parameters for more detailed subsequent simulations of individual systems

The cone of pseudo-effective divisors of log varieties after Batyrev

In these notes we investigate the cone of nef curves of projective varieties, which is the dual cone to the cone of pseudo-effective divisors. We prove a structure theorem for the cone of nef curves of projective $\mathbb Q$-factorial klt pairs of arbitrary dimension from the point of view of the Minimal Model Program. This is a generalization of Batyrev's structure theorem for the cone of nef curves of projective terminal threefolds.Comment: 15 pages. v2: Completely rewritten paper. Structure theorem for the cone of nef curves proved in arbitrary dimension using results of Birkar, Cascini, Hacon and McKernan. To appear in Mathematische Zeitschrif

Seeing Galaxies Through Thick & Thin. III. HST Imaging of the Dust in Backlit Spiral Galaxies

We present analysis of WFPC2 imaging of two spiral galaxies partially backlit by E/S0 systems in the pairs AM1316-241 and AM0500-620, and the spiral foreground system in NGC 1275. Images in B and I are used to determine the reddening curve of in these systems. The spiral component of AM1316-241 shows dust strongly concentrated in discrete arms, with a reddening law very close to the Milky Way mean. The dust distribution is scale-free between about 100 pc and the arm scale. The spiral in AM0500-620 shows dust concentrated in arms and interarm spurs, with measurable interarm extinction as well. Although its dust properties are less well-determined, we find evidence for a steeper extinction law here. The shape of the reddening law suggests that, at least in AM1316-241, we have resolved most of the dust structure. In AM0500-620, the slope of the fractal perimeter-scale relation steepens systematically from low to high extinction. In AM1316-241, we cannot determine a unique fractal dimension from the defining area-perimeter relation, so the projected dust distribution is best defined as fractal-like. In neither galaxy do we see regions even on single-pixel scales in spiral arms with AB > 2.5. The measurements in NGC 1275 are compromised by our lack of independent knowledge of the foreground system's light distribution, but masked sampling of the absorption suggests an effective reddening curve much flatter than the Milky Way mean (perhaps indicating that the foreground system has been affected by immersion in the hot intracluster gas).Comment: Astronomical Journal, in press. 13 figures. Full-size PostScript figures available at http://www.astr.ua.edu/preprints/kee