Root asymptotics of spectral polynomials for the Lame operator

The study of polynomial solutions to the classical Lam\'e equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schr\"odinger equation with finite gap potential given by the Weierstrass $\wp$-function on the real line. In this paper we establish several natural (and equivalent) formulas in terms of hypergeometric and elliptic type integrals for the density of the appropriately scaled asymptotic distribution of these eigenvalues when the integer-valued spectral parameter tends to infinity. We also show that this density satisfies a Heun differential equation with four singularities.Comment: final version, to appear in Commun. Math. Phys.; 13 pages, 3 figures, LaTeX2

La movilización como comunicación: Una contribución latinoamericana al estudio de los movimientos sociales

Many scholars have noted the lack of interdisciplinary dialogue and research between the areas of social movements studies and that of media and communications. While social movement studies fail to fully analyse media practices and communicative processes in relation to mobilization, in media and communication the social and political aspects of mobilization are seldom taken into account when analysing communication in social movements. This apparent lack of dialogue is presented in the paper as a consequence of north-centred theorization in the fields of social movement studies and media and communication, which is addressed by spelling out the contribution of Latin American communication scholarship and a view of mobilization as anchored in communication.Muchos académicos han observado la ausencia de diálogo interdisciplinario entre los estudios de los movimientos sociales y de los medios y la comunicación. Mientras que los estudios de los movimientos sociales no analizan de manera integral las prácticas mediáticas y los procesos comunicacionales en relación con la movilización, los estudios de medios y comunicación raras veces toman en cuenta los aspectos socio-políticos cuando analizan la comunicación en los movimientos sociales. Este artículo plantea esa aparente falta de diálogo como una consecuencia de una teorización eurocéntrica, explica en detalle la contribución de los estudios latinoamericanos de la comunicación, y propone una visión de la movilización centrada en la comunicación

ALMA follows streaming of dense gas down to 40 pc from the supermassive black hole in NGC1097

We present a kinematic analysis of the dense molecular gas in the central 200 parsecs of the nearby galaxy NGC1097, based on Cycle 0 observations with the Atacama Large Millimeter/sub-millimeter Array (ALMA). We use the HCN(4-3) line to trace the densest interstellar molecular gas, and quantify its kinematics, and estimate an inflow rate for the molecular gas. We find a striking similarity between the ALMA kinematic data and the analytic spiral inflow model that we have previously constructed based on ionized gas velocity fields on larger scales. We are able to follow dense gas streaming down to 40 pc distance from the supermassive black hole in this Seyfert 1 galaxy. In order to fulfill marginal stability, we deduce that the dense gas is confined to a very thin disc, and we derive a dense gas inflow rate of 0.09 Msun/yr at 40 pc radius. Combined with previous values from the Ha and CO gas, we calculate a combined molecular and ionized gas inflow rate of 0.2 Msun/yr at 40 pc distance from the central supermassive black hole of NGC1097.Comment: Accepted for Publication in the ApJ Letter

On total reality of meromorphic functions

We show that if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points then it is conjugate to a real meromorphic function after a suitable projective automorphism of the image.Comment: 13 page

Scalelength of disc galaxies

We have derived disk scale lengths for 30374 non-interacting disk galaxies in all five SDSS bands. Virtual Observatory methods and tools were used to define, retrieve, and analyse the images for this unprecedentedly large sample classified as disk/spiral galaxies in the LEDA catalogue. Cross correlation of the SDSS sample with the LEDA catalogue allowed us to investigate the variation of the scale lengths for different types of disk/spiral galaxies. We further investigat asymmetry, concentration, and central velocity dispersion as indicators of morphological type, and are able to assess how the scale length varies with respect to galaxy type. We note however, that the concentration and asymmetry parameters have to be used with caution when investigating type dependence of structural parameters in galaxies. Here, we present the scale length derivation method and numerous tests that we have carried out to investigate the reliability of our results. The average r-band disk scale length is 3.79 kpc, with an RMS dispersion of 2.05 kpc, and this is a typical value irrespective of passband and galaxy morphology, concentration, and asymmetry. The derived scale lengths presented here are representative for a typical galaxy mass of $10^{10.8\pm 0.54} \rm{M}_\odot$, and the RMS dispersion is larger for more massive galaxies. Distributions and typical trends of scale lengths have also been derived in all the other SDSS bands with linear relations that indicate the relation that connect scale lengths in one passband to another. Such transformations could be used to test the results of forthcoming cosmological simulations of galaxy formation and evolution of the Hubble sequence.Comment: Accepter for publication in MNRAS (15 pages, 15 figures, and 3 tables

New Multiplier Sequences via Discriminant Amoebae

In their classic 1914 paper, Polya and Schur introduced and characterized two types of linear operators acting diagonally on the monomial basis of R[x], sending real-rooted polynomials (resp. polynomials with all nonzero roots of the same sign) to real-rooted polynomials. Motivated by fundamental properties of amoebae and discriminants discovered by Gelfand, Kapranov, and Zelevinsky, we introduce two new natural classes of polynomials and describe diagonal operators preserving these new classes. A pleasant circumstance in our description is that these classes have a simple explicit description, one of them coinciding with the class of log-concave sequences.Comment: 11 pages, 6 figures. Submitted for publicatio

Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix

Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the corresponding Lie superalgebra is simple otherwise the quotient of the derived Lie superalgebra modulo center is simple (if its rank is greater than 1). Eleven new exceptional simple modular Lie superalgebras are discovered. Several features of classic notions, or notions themselves, are clarified or introduced, e.g., Cartan matrix, several versions of restrictedness in characteristic 2, Dynkin diagram, Chevalley generators, and even the notion of Lie superalgebra if the characteristic is equal to 2. Interesting phenomena in characteristic 2: (1) all simple Lie superalgebras with Cartan matrix are obtained from simple Lie algebras with Cartan matrix by declaring several (any) of its Chevalley generators odd; (2) there exist simple Lie superalgebras whose even parts are solvable. The Lie superalgebras of fixed points of automorphisms corresponding to the symmetries of Dynkin diagrams are also listed and their simple subquotients described

Assessing lidar-based classification schemes for polar stratospheric clouds based on 16 years of measurements at Esrange, Sweden

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License CC BY-NC-ND 3.0 https://creativecommons.org/licenses/by-nc-nd/3.0/, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.Lidar measurements of polar stratospheric clouds (PSCs) are commonly analyzed in classification schemes that apply the backscatter ratio and the particle depolarization ratio. This similarity of input data suggests comparable results of different classification schemes - despite measurements being performed with a variety of mostly custom-made instruments. Based on a time series of 16 years of lidar measurements at Esrange (68°N, 21°E), Sweden, we show that PSC classification differs substantially depending on the applied scheme. The discrepancies result from varying threshold values of lidar-derived parameters used to define certain PSC types. The resulting inconsistencies could impact the understanding of long-term PSC observations documented in the literature. We identify two out of seven considered classification schemes that are most likely to give reliable results and should be used in future lidar-based studies. Using polarized backscatter ratios gives the advantage of increased contrast for observations of weakly backscattering and weakly depolarizing particles. Improved confidence in PSC classification can be achieved by a more comprehensive consideration of the effect of measurement uncertainties. The particle depolarization ratio is the key to a reliable identification of different PSC types. Hence, detailed information on the calibration of the polarization-sensitive measurement channels should be provided to assess the findings of a study. Presently, most PSC measurements with lidar are performed at 532 nm only. The information from additional polarization-sensitive measurements in the near infrared could lead to an improved PSC classification. Coincident lidar-based temperature measurements at PSC level might provide useful information for an assessment of PSC classification. Key Points Assessment of PSC classification schemes Statistical analysis of PSC observations Recommendations for lidar-based PSC studiesPeer reviewe

Articulation rate in Swedish child-directed speech increases as a function of the age of the child even when surprisal is controlled for

In earlier work, we have shown that articulation rate in Swedish child-directed speech (CDS) increases as a function of the age of the child, even when utterance length and differences in articulation rate between subjects are controlled for. In this paper we show on utterance level in spontaneous Swedish speech that i) for the youngest children, articulation rate in CDS is lower than in adult-directed speech (ADS), ii) there is a significant negative correlation between articulation rate and surprisal (the negative log probability) in ADS, and iii) the increase in articulation rate in Swedish CDS as a function of the age of the child holds, even when surprisal along with utterance length and differences in articulation rate between speakers are controlled for. These results indicate that adults adjust their articulation rate to make it fit the linguistic capacity of the child.Comment: 5 pages, Interspeech 201

The Extremely Young Star Cluster Population In Haro 11

We have performed a deep multi-band photometric analysis of the star cluster population of Haro 11. This starburst galaxy (log L_FUV = 10.3 L_sun) is considered a nearby analogue of Lyman break galaxies (LBGs) at high redshift. The study of the numerous star clusters in the systems is an effective way to investigate the formation and evolution of the starburst phase. In fact, the SED fitting models have revealed a surprisingly young star cluster population, with ages between 0.5 and 40 Myr, and estimated masses between 10^3 and 10^7 solar masses. An independent age estimation has been done with the EW(Halpha) analysis of each cluster. This last analysis has confirmed the young ages of the clusters. We noticed that the clusters with ages between 1 and 10 Myr show a flux excess in H (NIC3/F160W) and/or I (WFPC2/F814W) bands with respect to the evolutionary models. Once more Haro 11 represents a challenge to our understanding.Comment: 4 pages, 3 figures. To appear in the proceedings of "Galaxy Wars: Stellar Populations and Star Formation in Interacting Galaxies" (Tennessee, July 09