On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev\'e equation

Using a simple operator-norm estimate we show that the solution to the second Painlev\'e equation within the Ablowitz-Segur family is pole-free in a well defined region of the complex plane of the independent variable. The result is illustrated with several numerical examples.Comment: 8 pages, to appear in Nonlinearit

Szeg\"o kernel and symplectic aspects of spectral transform for extended spaces of rational matrices

We revisit the sympectic aspects of the spectral transform for matrix-valued rational functions with simple poles. We construct eigenvectors of such matrices in terms of the Szeg\"o kernel on the spectral curve. Using variational formulas for the Szeg\"o kernel we construct a new system of action-angle variables for the canonical symplectic form on the space of such functions. Comparison with previously known action-angle variables shows that the vector of Riemann constants is the gradient of some function on the moduli space of spectral curves; this function is found in the case of matrix dimension 2, when the spectral curve is hyperelliptic.Comment: 19 page

Color--Luminosity Relations for the Resolved Hot Stellar Populations in the Centers of M 31 and M 32

We present Faint Object Camera (FOC) ultraviolet images of the central 14x14'' of Messier 31 and Messier 32. The hot stellar population detected in the composite UV spectra of these nearby galaxies is partially resolved into individual stars, and their individual colors and apparent magnitudes are measured. We detect 433 stars in M 31 and 138 stars in M 32, down to detection limits of m_F275W = 25.5 mag and m_F175W = 24.5 mag. We investigate the luminosity functions of the sources, their spatial distribution, their color-magnitude diagrams, and their total integrated far-UV flux. Although M 32 has a weaker UV upturn than M 31, the luminosity functions and color-magnitude diagrams of M 31 and M 32 are surprisingly similar, and are inconsistent with a majority contribution from any of the following: PAGB stars more massive than 0.56 Msun, main sequence stars, or blue stragglers. Both the the luminosity functions and color-magnitude diagrams are consistent with a dominant population of stars that have evolved from the extreme horizontal branch (EHB) along tracks with masses between 0.47 and 0.53 Msun. These stars are well below the detection limits of our images while on the zero-age EHB, but become detectable while in the more luminous (but shorter) AGB-Manque' and post-early asymptotic giant branch (PEAGB) phases. The FOC observations require that only a only a very small fraction of the main sequence population (2% in M 31 and 0.5% in M 32) in these two galaxies evolve though the EHB and post-EHB phases, with the remainder evolving through bright PAGB evolution that is so rapid that few if any stars are expected in the small field of view covered by the FOC.Comment: 35 pages, Latex. 19 figures. To appear in ApJ. Uses emulateapj.sty and apjfonts.sty (included). Color plates distributed seperatedly: fig1.jpg and fig2.jp

The Nature of SN 1961V

The nature of SN 1961V has been uncertain. Its peculiar optical light curve and slow expansion velocity are similar to those of super-outbursts of luminous blue variables (LBVs), but its nonthermal radio spectral index and declining radio luminosity are consistent with decades-old supernovae (SNe). We have obtained Hubble Space Telescope STIS images and spectra of the stars in the vicinity of SN 1961V, and find Object 7 identified by Filippenko et al. to be the closest to the optical and radio positions of SN 1961V. Object 7 is the only point source detected in our STIS spectra and only its H-alpha emission is detected; it cannot be the SN or its remnant because of the absence of forbidden lines. While the H-alpha line profile of Object 7 is remarkably similar to that of eta Car, the blue color (similar to an A2Ib supergiant) and lack of appreciable variability are unlike known post-outburst LBVs. We have also obtained Very Long Baseline Array (VLBA) observations of SN 1961V at 18 cm. The non-detection of SN 1961V places a lower limit on the size of the radio-emitting region, 7.6 mas or 0.34 pc, which implies an average expansion velocity in excess of 4,400 km/s, much higher than the optical expansion velocity measured in 1961. We conclude the following: (1) A SN occurred in the vicinity of SN 1961V a few decades ago. (2) If the SN 1961V light maximum originates from a giant eruption of a massive star, Object 7 is the most probable candidate for the survivor, but its blue color and lack of significant variability are different from a post-outburst eta Car. (3) The radio SN and Object 7 could be physically associated with each other through a binary system. (4) Object 7 needs to be monitored to determine its nature and relationship to SN 1961V.Comment: 16 pages, 3 figures, accepted by the Astronomical Journal for the 2004 May issu

Absolute-Magnitude Distributions and Light Curves of Stripped-Envelope Supernovae

The absolute visual magnitudes of three Type IIb, 11 Type Ib and 13 Type Ic supernovae (collectively known as stripped-envelope supernovae) are studied by collecting data on the apparent magnitude, distance, and interstellar extinction of each event. Weighted and unweighted mean absolute magnitudes of the combined sample as well as various subsets of the sample are reported. The limited sample size and the considerable uncertainties, especially those associated with extinction in the host galaxies, prevent firm conclusions regarding differences between the absolute magnitudes of supernovae of Type Ib and Ic, and regarding the existence of separate groups of overluminous and normal-luminosity stripped-envelope supernovae. The spectroscopic characteristics of the events of the sample are considered. Three of the four overluminous events are known to have had unusual spectra. Most but not all of the normal luminosity events had typical spectra. Light curves of stripped-envelope supernovae are collected and compared. Because SN 1994I in M51 was very well observed it often is regarded as the prototypical Type Ic supernova, but it has the fastest light curve in the sample. Light curves are modeled by means of a simple analytical technique that, combined with a constraint on E/M from spectroscopy, yields internally consistent values of ejected mass, kinetic energy, and nickel mass.Comment: 39 pages, 14 figures, 7 tables; Accepted to A

Wightman Functions' Behaviour on the Event Horizon of an Extremal Reissner-Nordstr\"om Black Hole

A weaker Haag, Narnhofer and Stein prescription as well as a weaker Hessling Quantum Equivalence Principle for the behaviour of thermal Wightman functions on an event horizon are analysed in the case of an extremal Reissner-Nordstr\"{o}m black hole in the limit of a large mass. In order to avoid the degeneracy of the metric in the stationary coordinates on the horizon, a method is introduced which employs the invariant length of geodesics which pass the horizon. First the method is checked for a massless scalar field on the event horizon of the Rindler wedge, extending the original procedure of Haag, Narnhofer and Stein onto the {\em whole horizon} and recovering the same results found by Hessling. Afterwards the HNS prescription and Hessling's prescription for a massless scalar field are analysed on the whole horizon of an extremal Reissner-Nordstr\"{o}m black hole in the limit of a large mass. It is proved that the weak form of the HNS prescription is satisfyed for all the finite values of the temperature of the KMS states, i.e., this principle does not determine any Hawking temperature. It is found that the Reissner-Nordstr\"{o}m vacuum, i.e., $T=0$ does satisfy the weak HNS prescription and it is the only state which satisfies weak Hessling's prescription, too. Finally, it is suggested that all the previously obtained results should be valid dropping the requirements of a massless field and of a large mass black hole.Comment: 27 pages, standard LaTex, no figures, final version containing the results following from Hessling's principle as they appeared in the other paper gr-qc/9510016, minor changes in the text and in references, it will appear on Class. Quant. Gra

A SAURON study of stars and gas in Sa bulges

We present results from our ongoing effort to understand the morphological and kinematical properties of early-type galaxies using the integral-field spectrograph SAURON. We discuss the relation between the stellar and gas morphology and kinematics in our sub-sample of 24 representative Sa spiral bulges. We focus on the frequency of kinematically decoupled components and on the presence of star formation in circumnuclear rings.Comment: 6 pages, 3 figures; To appear in the proceedings of the "Island Universes: Structure and Evolution of Disk Galaxies" conference held in Terschelling, Netherlands, July 2005, ed. R. de Jong. A high resolution version is available at http://www.strw.leidenuniv.nl/~jfalcon/JFB_terschelling.pdf.g

Programa computacional de simulação da produtividade para suporte a decisão no plantio de milho.

O objetivo deste trabalho foi desenvolver um programa computacional que simule a produção do milho, sendo utilizado como um suporte a decisão para o produtor. O algoritmo utilizado consta de modelos de regressão obtidos a partir de resultados de uma pesquisa de campo realizada na Embrapa Milho e Sorgo, sob condições de plantio direto e com modelos de estimativas de produção obtidos em tabelas e resultados de outros trabalhos constantes na literatura. O pacote computacional resultante é completo o suficiente para a simulação da produtividade em um determinado solo e implantação e uso por produtores (usuários) como uma ferramenta de Agricultura de Precisão, capaz de auxiliar à tomada de decisão. O programa é de fácil manuseio, onde o usuário pode optar em digitar os valores que representam as condições do solo de plantio, ou resgatar valores de um banco de dados histórico que pode ser implementado pelo próprio usuário, ou obtido através da Embrapa que disponibilizará, através da rede mundial de computadores, condições de solo de todo o país. A saída do programa é de simples interpretação e fornece, entre outros resultados, a produtividade máxima de um solo sob as condições de simulação, auxiliando o produtor na tomada de decisão quanto a aplicação de insumos

Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I

The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the analysis on the real axis without any additional transformation to a "string" type boundary value problem known from prior works