The higher grading structure of the WKI hierarchy and the two-component short pulse equation

A higher grading affine algebraic construction of integrable hierarchies, containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is proposed. We show that a two-component generalization of the Sch\" afer-Wayne short pulse equation arises quite naturally from the first negative flow of the WKI hierarchy. Some novel integrable nonautonomous models are also proposed. The conserved charges, both local and nonlocal, are obtained from the Riccati form of the spectral problem. The loop-soliton solutions of the WKI hierarchy are systematically constructed through gauge followed by reciprocal B\" acklund transformation, establishing the precise connection between the whole WKI and AKNS hierarchies. The connection between the short pulse equation with the sine-Gordon model is extended to a correspondence between the two-component short pulse equation and the Lund-Regge model

The algebraic structure behind the derivative nonlinear Schroedinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schr\" odinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of a $\hat{s\ell}_2$ Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows, respectively. The equivalence between the latter and the massive Thirring model is explicitly demonstrated also. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation.Comment: references adde

On the AGN radio luminosity distribution and the black hole fundamental plane

We have studied the dependence of the AGN nuclear radio (1.4 GHz) luminosity on both the AGN 2-10 keV X-ray and the host-galaxy K-band luminosity. A complete sample of 1268 X-ray selected AGN (both type 1 and type 2) has been used, which is the largest catalogue of AGN belonging to statistically well defined samples where radio, X and K band information exists. At variance with previous studies, radio upper limits have been statistically taken into account using a Bayesian Maximum Likelihood fitting method. It resulted that a good fit is obtained assuming a plane in the 3D L_R-L_X-L_K space, namely logL_R= xi_X logL_X + xi_K logL_K + xi_0, having a ~1 dex wide (1 sigma) spread in radio luminosity. As already shown, no evidence of bimodality in the radio luminosity distribution was found and therefore any definition of radio loudness in AGN is arbitrary. Using scaling relations between the BH mass and the host galaxy K-band luminosity, we have also derived a new estimate of the BH fundamental plane (in the L_5GHz -L_X-M_BH space). Our analysis shows that previous measures of the BH fundamental plane are biased by ~0.8 dex in favor of the most luminous radio sources. Therefore, many AGN studies, where the BH fundamental plane is used to investigate how AGN regulate their radiative and mechanical luminosity as a function of the accretion rate, or many AGN/galaxy co-evolution models, where radio-feedback is computed using the AGN fundamental plane, should revise their conclusions.Comment: Submitted to MNRAS. Revised version after minor referee comments. 12 pages, 12 figure

The BeppoSAX High Energy Large Area Survey (HELLAS) - VI. The radio properties

We present results of a complete radio follow-up obtained with the VLA and ATCA radio telescopes down to a 6 cm flux limit of about 0.3 mJy of all the 147 X-ray sources detected in the BeppoSAX HELLAS survey. We found 53 X-ray/radio likely associations, corresponding to about one third of the X-ray sample. Using the two point spectral index alpha_ro=0.35 we divided all the HELLAS X-ray sources in radio quiet and radio loud. We have 26 sources classified as radio-loud objects, corresponding to about 18% of the HELLAS sample. In agreement with previous results, the identified radio-loud sources are associated mainly with Type 1 AGNs with L(5-10 keV) > 10^44 erg/s, while all the identified Type 2 AGNs and Emission Line Galaxies are radio quiet objects with L(5-10 keV) < 10^44 erg/s. The analysis of the radio spectral index suggests that Type 1 AGNs have a mean radio spectral index flatter than Type 2 AGNs and Emission Line Galaxies.Comment: 12 pages, 5 figures, MNRAS, accepte

The contribution of faint AGN to the hard X-ray background

Hard X-ray selection is the most efficient way to discriminate between accretion-powered sources, such as AGN, from sources dominated by starlight. Hard X-rays are also less affected than other bands by obscuration. We have then carried out the BeppoSAX High Energy Large Area Survey (HELLAS) in the largely unexplored 5-10 keV band, finding 180 sources in ~50 deg^2 of sky with flux >5E-14 erg cm-2 s-1. After correction for the non uniform sky coverage this corresponds to resolving about 30 % of the hard Cosmic X-ray Background (XRB). Here we report on a first optical spectroscopic identification campaign, finding 12 AGN out of 14 X-ray error-boxes studied. Seven AGN show evidence for obscuration in X-ray and optical bands, a fraction higher than in previous ROSAT or ASCA-ROSAT surveys (at a 95-99 % and 90 % confidence level respectively), thus supporting the scenario in which a significant fraction of the XRB is made by obscured AGN.Comment: MNRAS, revised version after minor referee comment

Uso de SIG´S no delineamento de zonas de manejo para uso agrícola.

Este trabalho trata da utilização do sistema de informação geográfica (SIG) e aplicativos geoestatísticos para definição de sub-áreas homogêneas em um sítio específico, tendo como referência um pivot central de 38 ha instalado na Embrapa Milho e Sorgo em LEd, fase cerrado, 19"28 '03" latitude S, 44°10'37" longitude W, com declive de cerca de 5%, aqui denominado pivot 3. Foi utilizada a base cartográfica da Embrapa Milho e Sorgo, na escala de 1:10.000, e coleta direta de dados, com o Global Positioning System (GPS). Foram utilizados na análise, dados de produtividade de milho dos anos agrícola 1999/00 e 2000/01 (metade do pivot) e soja do ano agrícola 2000/01 (metade do pivot), fertilidade de solos, condutividade elétrica, altitude. O processo de análise incluiu tratamento geoestatístico, tratamento espacial e interpretação visual de imagem de satélite Landsat5, como balizador dos resultados aferídos. Pode -se concluir que o Modelo FuzMe mostrou ser eficiente na definição das quatro zonas de manejo pois é um método de resposta rápida aos agrupamentos similares. O refinamento das informações poderá oferecer subsídios ao incremento de eficiência no manejo agrícola

The BeppoSAX HELLAS survey: on the nature of faint hard X-ray selected sources

The BeppoSAX 4.5-10 keV High Energy Large Area Survey has covered about 80 square degrees of sky down to a flux of F(5-10keV)~5E-14 cgs. Optical spectroscopic identification of about half of the sources in the sample (62) shows that many (~50%) are highly obscured AGN, in line with the predictions of AGN synthesis models for the hard X-ray background (XRB, see e.g. Comastri et al. 1995). The X-ray data, complemented by optical, near-IR and radio follow-up, indicate that the majority of these AGN are ``intermediate'' objects, i.e. type 1.8-1.9 AGN,`red' quasars, and even a few broad line, blue continuum quasars, obscured in X-rays by columns of the order of logNH=22.5-23.5 cm-2, but showing a wide dispersion in optical extinction. The optical and near-IR photometry of the obscured objects are dominated by galaxy starlight, indicating that a sizeable fraction of the accretion power in the Universe may actually have been missed in optical color surveys. This also implies that multicolor photometry techniques may be efficiently used to assess the redshift of the hard X-ray selected sources.Comment: 9 pages, Invited talk to appear in the Proceedings of the Conference X-ray Astronomy '999: Stellar Endpoints, AGNs and the Diffuse X-ray Background. (September 6-10 - 1999