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

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

An Atlas of Warm AGN and Starbursts from the IRAS Deep Fields

We present 180 AGN candidates based on color selection from the IRAS slow-scan deep observations, with color criteria broadened from the initial Point-Source Catalog samples to include similar objects with redshifts up to z=1 and allowing for two-band detections. Spectroscopic identifications have been obtained for 80 (44%); some additional ones are secure based on radio detections or optical morphology, although yet unobserved spectroscopically. These spectroscopic identifications include 13 Sy 1 galaxies, 17 Sy 2 Seyferts, 29 starbursts, 7 LINER systems, and 13 emission-line galaxies so heavily reddened as to remain of ambiguous classification. The optical magnitudes range from R=12.0-20.5; counts suggest that incompleteness is important fainter than R=15.5. Redshifts extend to z=0.51, with a significant part of the sample at z>0.2. The sample includes slightly more AGN than star-forming systems among those where the spectra contain enough diagnostic feature to make the distinction. The active nuclei include several broad-line objects with strong Fe II emission, and composite objects with the absorption-line signatures of fading starbursts. These AGN with warm far-IR colors have little overlap with the "red AGN" identified with 2MASS; only a single Sy 1 was detected by 2MASS with J-K > 2. Some reliable IRAS detections have either very faint optical counterparts or only absorption-line galaxies, potentially being deeply obscured AGN. The IRAS detections include a newly identified symbiotic star, and several possible examples of the "Vega phenomenon", including dwarfs as cool as type K. Appendices detail these candidate stars, and the optical-identification content of a particularly deep set of high-latitude IRAS scans (probing the limits of optical identification from IRAS data alone).Comment: ApJ Suppl, in press. Figures converted to JPEG/GIF for better compression; PDF with full-resolution figures available before publication at http://www.astr.ua.edu/keel/aoagn.pd

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction

Concerning the Wave equation on Asymptotically Euclidean Manifolds

We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on $(\R^d, \mathfrak{g})$, $d \geq 3$, when metric $\mathfrak{g}$ is non-trapping and approaches the Euclidean metric like $x ^{- \rho}$ with $\rho>0$. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for $\rho> 1$ and $d=3$. Also, we establish the Strauss conjecture when the metric is radial with $\rho>0$ for $d= 3$.Comment: Final version. To appear in Journal d'Analyse Mathematiqu

The fundamental solution and Strichartz estimates for the Schr\"odinger equation on flat euclidean cones

We study the Schr\"odinger equation on a flat euclidean cone $\mathbb{R}_+ \times \mathbb{S}^1_\rho$ of cross-sectional radius $\rho > 0$, developing asymptotics for the fundamental solution both in the regime near the cone point and at radial infinity. These asymptotic expansions remain uniform while approaching the intersection of the "geometric front", the part of the solution coming from formal application of the method of images, and the "diffractive front" emerging from the cone tip. As an application, we prove Strichartz estimates for the Schr\"odinger propagator on this class of cones.Comment: 21 pages, 4 figures. Minor typos corrected. To be published in Comm. Math. Phy

Asymptotic behavior of small solutions for the discrete nonlinear Schr\"odinger and Klein-Gordon equations

We show decay estimates for the propagator of the discrete Schr\"odinger and Klein-Gordon equations in the form \norm{U(t)f}{l^\infty}\leq C (1+|t|)^{-d/3}\norm{f}{l^1}. This implies a corresponding (restricted) set of Strichartz estimates. Applications of the latter include the existence of excitation thresholds for certain regimes of the parameters and the decay of small initial data for relevant $l^p$ norms. The analytical decay estimates are corroborated with numerical results.Comment: 13 pages, 4 figure

Carbon allocation and carbon isotope fluxes in the plant-soil-atmosphere continuum: a review

The terrestrial carbon (C) cycle has received increasing interest over the past few decades, however, there is still a lack of understanding of the fate of newly assimilated C allocated within plants and to the soil, stored within ecosystems and lost to the atmosphere. Stable carbon isotope studies can give novel insights into these issues. In this review we provide an overview of an emerging picture of plant-soil-atmosphere C fluxes, as based on C isotope studies, and identify processes determining related C isotope signatures. The first part of the review focuses on isotopic fractionation processes within plants during and after photosynthesis. The second major part elaborates on plant-internal and plant-rhizosphere C allocation patterns at different time scales (diel, seasonal, interannual), including the speed of C transfer and time lags in the coupling of assimilation and respiration, as well as the magnitude and controls of plant-soil C allocation and respiratory fluxes. Plant responses to changing environmental conditions, the functional relationship between the physiological and phenological status of plants and C transfer, and interactions between C, water and nutrient dynamics are discussed. The role of the C counterflow from the rhizosphere to the aboveground parts of the plants, e.g. via CO<sub>2</sub> dissolved in the xylem water or as xylem-transported sugars, is highlighted. The third part is centered around belowground C turnover, focusing especially on above- and belowground litter inputs, soil organic matter formation and turnover, production and loss of dissolved organic C, soil respiration and CO<sub>2</sub> fixation by soil microbes. Furthermore, plant controls on microbial communities and activity via exudates and litter production as well as microbial community effects on C mineralization are reviewed. A further part of the paper is dedicated to physical interactions between soil CO<sub>2</sub> and the soil matrix, such as CO<sub>2</sub> diffusion and dissolution processes within the soil profile. Finally, we highlight state-of-the-art stable isotope methodologies and their latest developments. From the presented evidence we conclude that there exists a tight coupling of physical, chemical and biological processes involved in C cycling and C isotope fluxes in the plant-soil-atmosphere system. Generally, research using information from C isotopes allows an integrated view of the different processes involved. However, complex interactions among the range of processes complicate or currently impede the interpretation of isotopic signals in CO<sub>2</sub> or organic compounds at the plant and ecosystem level. This review tries to identify present knowledge gaps in correctly interpreting carbon stable isotope signals in the plant-soil-atmosphere system and how future research approaches could contribute to closing these gaps

The pre-WDVV ring of physics and its topology

We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the Whitehouse complex. Using discrete Morse theory, we give an elementary proof that the Whitehouse complex $\Delta_n$ is homotopy equivalent to a wedge of $(n-2)!$ spheres of dimension $n-4$. We also verify the Cohen-Macaulay property. Additionally, recurrences are given for the face enumeration of the complex and the Hilbert series of the associated pre-WDVV ring.Comment: 13 pages, 4 figures, 2 table