Non-degenerate solutions of universal Whitham hierarchy

The notion of non-degenerate solutions for the dispersionless Toda hierarchy is generalized to the universal Whitham hierarchy of genus zero with $M+1$ marked points. These solutions are characterized by a Riemann-Hilbert problem (generalized string equations) with respect to two-dimensional canonical transformations, and may be thought of as a kind of general solutions of the hierarchy. The Riemann-Hilbert problem contains $M$ arbitrary functions $H_a(z_0,z_a)$, $a = 1,...,M$, which play the role of generating functions of two-dimensional canonical transformations. The solution of the Riemann-Hilbert problem is described by period maps on the space of $(M+1)$-tuples $(z_\alpha(p) : \alpha = 0,1,...,M)$ of conformal maps from $M$ disks of the Riemann sphere and their complements to the Riemann sphere. The period maps are defined by an infinite number of contour integrals that generalize the notion of harmonic moments. The $F$-function (free energy) of these solutions is also shown to have a contour integral representation.Comment: latex2e, using amsmath, amssym and amsthm packages, 32 pages, no figur

A class of chiral fermion models

We study the relation between the Roma and Zaragoza proposals for chiral fermions on the lattice. The fermion action in the Roma approach is shown to be equivalent to one of the Zaragoza type. This result is used to perform a mean-field study of the phase diagram for chiral Yukawa models based on the Roma action. The phase diagram is compared with the one based on the Zaragoza model with the most local choice for the fermion interactions.Comment: Version to appear in Nucl. Phys. B. Some general discussion added to the Introduction and Conclusion sections. Now 33 pages Latex; style files and (unchanged) PostScript figures again attached in uufiles forma

The OPTX Project I: The Flux and Redshift Catalogs for the CLANS, CLASXS, and CDF-N fields

We present the redshift catalogs for the X-ray sources detected in the Chandra Deep Field North (CDF-N), the Chandra Large Area Synoptic X-ray Survey (CLASXS), and the Chandra Lockman Area North Survey (CLANS). The catalogs for the CDF-N and CLASXS fields include redshifts from previous work, while the redshifts for the CLANS field are all new. For fluxes above 10^-14 ergs cm^-2 s^-1 (2-8 keV) we have redshifts for 76% of the sources. We extend the redshift information for the full sample using photometric redshifts. The goal of the OPTX Project is to use these three surveys, which are among the most spectroscopically complete surveys to date, to analyze the effect of spectral type on the shape and evolution of the X-ray luminosity functions and to compare the optical spectral types with the X-ray spectral properties. We also present the CLANS X-ray catalog. The nine ACIS-I fields cover a solid angle of ~0.6 square degrees and reach fluxes of 7x10^-16 ergs cm^-2 s^-1 (0.5-2 keV) and 3.5x10^-15 ergs cm^-2 s^-1 (2-8 keV). We find a total of 761 X-ray point sources. Additionally, we present the optical and infrared photometric catalog for the CLANS X-ray sources, as well as updated optical and infrared photometric catalogs for the X-ray sources in the CLASXS and CDF-N fields. The CLANS and CLASXS surveys bridge the gap between the ultradeep pencil-beam surveys, such as the CDFs, and the shallower, very large-area surveys. As a result, they probe the X-ray sources that contribute the bulk of the 2-8 keV X-ray background and cover the flux range of the observed break in the logN-logS distribution. We construct differential number counts for each individual field and for the full sample.Comment: Published in The Astrophysical Journal Supplement. 18 pages, 16 figures, 14 table

Quicksort with unreliable comparisons: a probabilistic analysis

We provide a probabilistic analysis of the output of Quicksort when comparisons can err.Comment: 29 pages, 3 figure

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

Infrared Observations of AGN

We present results from an imaging and spectroscopic study of the dust properties of Seyfert galaxies in the 1-10um range. The data are compared to state of the art models of torus emission to constrain geometrical and physical properties of the obscuring medium.Comment: 2 pages, to appear in the IAU Symp.No.222 proceedings:"The Interplay among Black Holes, Stars and ISM in Galactic Nuclei", Gramado, Brazil, March 1-5, 200