Subresultants in multiple roots: an extremal case

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\alpha)^m and (x-\beta)^n with respect to the set of Bernstein polynomials \{(x-\alpha)^j(x-\beta)^{d-j}, \, 0\le j\le d\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.Comment: 18 pages, uses elsart. Revised version accepted for publication at Linear Algebra and its Application

The IRAC Dark Field; Far- Infrared to X-ray Data

We present 20 band photometry from the far-IR to X-ray in the Spitzer IRAC dark field. The bias for the near-IR camera on Spitzer is calibrated by observing a ~20 arcminute diameter "dark" field near the north ecliptic pole roughly every two-to-three weeks throughout the mission duration of Spitzer. The field is unique for its extreme depth, low background, high quality imaging, time-series information, and accompanying photometry including data taken with Akari, Palomar, MMT, KPNO, Hubble, and Chandra. This serendipitous survey contains the deepest mid-IR data taken to date. This dataset is well suited for studies of intermediate redshift galaxy clusters, high redshift galaxies, the first generation of stars, and the lowest mass brown dwarfs, among others. This paper provides a summary of the data characteristics and catalog generation from all bands collected to date as well as a discussion of photometric redshifts and initial and expected science results and goals. To illustrate the scientific potential of this unique dataset, we also present here IRAC color color diagrams.Comment: 12 pages, ApJS accepte

The Infrared Array Camera Dark Field: Far-Infrared to X-ray Data

We present 20 band photometry from the far-IR to X-ray in the Spitzer Infrared Array Camera (IRAC) dark field. The bias for the near-IR camera on Spitzer is calibrated by observing a ~20' diameter "dark" field near the north ecliptic pole roughly every two-to-three weeks throughout the mission duration of Spitzer. The field is unique for its extreme depth, low background, high quality imaging, time-series information, and accompanying photometry including data taken with Akari, Palomar, MMT, KPNO, Hubble, and Chandra. This serendipitous survey contains the deepest mid-IR data taken to date. This data set is well suited for studies of intermediate-redshift galaxy clusters, high-redshift galaxies, the first generation of stars, and the lowest mass brown dwarfs, among others. This paper provides a summary of the data characteristics and catalog generation from all bands collected to date as well as a discussion of photometric redshifts and initial and expected science results and goals. To illustrate the scientific potential of this unique data set, we also present here IRAC color-color diagrams

Caregiver Criticism, Help-giving and the Burden of Schizophrenia Among Mexican American Families

Objectives—The present study tested an attribution model of help-giving in family caregivers of persons with schizophrenia as it relates to caregivers’ reported burden. We hypothesized (a) that caregivers’ attributions of their ill relatives’ responsibility for their symptoms would be associated with more negative and less positive affective reactions, (b) that affective reactions would be related to perceptions of administered support, and (c) that support would in turn predict greater burden. Methods—We examined 60 family caregivers of Mexican origin living in Southern California. Mexican Americans were chosen because of their high degree of contact with their ill relative thereby facilitating the examination of help-giving and burden. Contrary to past studies, caregivers’ attributions and affective stance were assessed independently, the former based on self-report and the latter based on codes drawn from the Camberwell Family Interview. Caregiver burden was assessed at baseline and one year later. Results—Path analyses showed partial support for the attribution model of help-giving. Specifically, attributions of responsibility negatively predicted caregiver’s warmth, which in turn predicted more administered support. Contrary to hypotheses, attributions were not associated with caregiver criticism, and criticism was positively related to administered support. In addition, caregiver support was not related to burden at either baseline or a year later. Criticism was a significant predictor of burden at follow-up through burden at baseline. Conclusion—The emotional stance of caregivers predicts burden independent of the help they provide. Caregiver criticism not only predicts negative patient outcomes but can predict negative caregiver outcomes as well

A Spitzer IRAC Measure of the Zodiacal Light

The dominant non-instrumental background source for space–based infrared observatories is the zodiacal light (ZL). We present Spitzer Infrared Array Camera (IRAC) measurements of the ZL at 3.6, 4.5, 5.8, and 8.0 μm, taken as part of the instrument calibrations. We measure the changing surface brightness levels in approximately weekly IRAC observations near the north ecliptic pole over the period of roughly 8.5 years. This long time baseline is crucial for measuring the annual sinusoidal variation in the signal levels due to the tilt of the dust disk with respect to the ecliptic, which is the true signal of the ZL. This is compared to both Cosmic Background Explorer Diffuse Infrared Background Experiment data and a ZL model based thereon. Our data show a few percent discrepancy from the Kelsall et al.(1998) model including a potential warping of the interplanetary dust disk and a previously detected overdensity in the dust cloud directly behind the Earth in its orbit. Accurate knowledge of the ZL is important for both extragalactic and Galactic astronomy including measurements of the cosmic infrared background, absolute measures of extended sources, and comparison to extrasolar interplanetary dust models. IRAC data can be used to further inform and test future ZL models

The star pile in Abell 545

Context:Struble (1988) found what appeared to be a cD halo without cD galaxy in the center of the galaxy cluster Abell 545. This remarkable feature has been passed almost unnoticed for nearly twenty years. Aims:Our goal is to review Struble's claim by providing a first (preliminary) photometric and spectroscopic analysis of this ''star pile''. Methods:Based on archival VLT-images and long-slit spectra obtained with Gemini-GMOS, we describe the photometric structure and measure the redshift of the star pile and of the central galaxy. Results:The star pile is indeed associated with Abell 545. Its velocity is higher by about 1300 km/s than that of the central object. The spectra indicate an old, presumably metal-rich population. Its brightness profile is much shallower than that of typical cD-galaxies. Conclusions:The formation history and the dynamical status of the star pile remain elusive, until high S/N spectra and a dynamical analysis of the galaxy cluster itself become available. We suggest that the star pile might provide an interesting test of the Cold Dark Matter paradigm.Comment: 6 pages, 7 figures. Accepted for publication in A&

Diffuse Optical Light in Galaxy Clusters I: Abell 3888

We are undertaking a program to measure the characteristics of the intracluster light (total flux, profile, color, and substructure) in a sample of 10 galaxy clusters with a range of cluster mass, morphology, and redshift. We present here the methods and results for the first cluster in that sample, A3888. We have identified an intracluster light (ICL) component in A3888 in V and r that contains 13\pm5% of the total cluster light and extends to 700h_{70}^{-1}kpc (~0.3 r_{200}) from the center of the cluster. The ICL color in our smallest radial bin is V-r = 0.3 \pm 0.1, similar to the central cluster ellipticals. The ICL is redder than the galaxies at 400 < r < 700h_{70}^{-1}kpc although the uncertainty in any one radial bin is high. Based on a comparison of V-r color with simple stellar models, the ICL contains a component which formed more than 7 Gyr ago (at z > 1), coupled with a high metallicity (1.0Z_{\odot} < Z_{ICL} \la 2.5Z_{\odot}), and a more centralized component which contains stars formed within the past 5 Gyr (at z ~ 1). The profile of the ICL can be roughly fit by a shallow exponential in the outer regions and a steeper exponential in the central region. We also find a concentration of diffuse light around a small group of galaxies 1.4h_{70}^{-1}Mpc from the center of the cluster. In addition, we find 3 low surface brightness features near the cluster center which are blue (V-r = 0.0) and contain a total flux of 0.1M*. Based on these observations and X-ray and galaxy morphology, we suggest that this cluster is entering a phase of significant merging of galaxy groups in the core, whereupon we expect the ICL fraction to grow significantly with the formation of a cD galaxy as well as the in-fall of groups.Comment: 16 pages, 13 figures, 3 tables, AJ accepte

On the complexity of computing real radicals of polynomial systems

International audienceLet f= (f1, ..., fs) be a sequence of polynomials in Q[X1,...,Xn] of maximal degree D and V⊂ Cn be the algebraic set defined by f and r be its dimension. The real radical re associated to f is the largest ideal which defines the real trace of V . When V is smooth, we show that re , has a finite set of generators with degrees bounded by V. Moreover, we present a probabilistic algorithm of complexity (snDn )O(1) to compute the minimal primes of re . When V is not smooth, we give a probabilistic algorithm of complexity sO(1) (nD)O(nr2r) to compute rational parametrizations for all irreducible components of the real algebraic set V ∩ Rn. Experiments are given to show the efficiency of our approaches