156 research outputs found

    Principal forms X^2 + nY^2 representing many integers

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    In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X^2+nY^2. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n=2. In this paper, we prove that in fact this constant is unbounded as n runs through positive integers with a fixed number of prime divisors.Comment: 10 pages, title has been changed, Sections 2 and 3 are new, to appear in Abh. Math. Sem. Univ. Hambur

    The Nature of the Halo Population of NGC 5128 Resolved with NICMOS on the Hubble Space Telescope

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    We present the first infrared color-magnitude diagram (CMD) for the halo of a giant elliptical galaxy. The CMD for the stars in the halo of NGC 5128 (Centaurus A) was constructed from HST NICMOS observations of the WFPC2 CHIP-3 field of Soria et al. (1996) to a 50% completeness magnitude limit of [F160W]=23.8. This field is located at a distance of 08'50" (~9 kpc) south of the center of the galaxy. The luminosity function (LF) shows a marked discontinuity at [F160W]=20.0. This is 1-2 mag above the tip of the red giant branch (TRGB) expected for an old population (~12 Gyr) at the distance modulus of NGC 5128. We propose that the majority of stars above the TRGB have intermediate ages (~2 Gyr), in agreement with the WFPC2 observations of Soria et al. (1996). Five stars with magnitudes brighter than the LF discontinuity are most probably due to Galactic contamination. The weighted average of the mean giant branch color above our 50% completeness limit is [F110W]-[F160W]=1.22+-0.08 with a dispersion of 0.19 mag. From our artificial-star experiments we determine that the observed spread in color is real, suggesting a real spread in metallicity. We estimate the lower and upper bounds of the stellar metallicity range by comparisons with observations of Galactic star clusters and theoretical isochrones. Assuming an old population, we find that, in the halo field of NGC 5128 we surveyed, stars have metallicities ranging from roughly 1% of solar at the blue end of the color spread to roughly solar at the red end, with a mean of [Fe/H]=-0.76 and a dispersion of 0.44 dex.Comment: Accepted for publication in AJ, 23 pages of text, 13 figures, uses aastex v5.

    The Velocity Function of Galaxies

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    We present a galaxy circular velocity function, Psi(log v), derived from existing luminosity functions and luminosity-velocity relations. Such a velocity function is desirable for several reasons. First, it enables an objective comparison of luminosity functions obtained in different bands and for different galaxy morphologies, with a statistical correction for dust extinction. In addition, the velocity function simplifies comparison of observations with predictions from high-resolution cosmological N-body simulations. We derive velocity functions from five different data sets and find rough agreement among them, but about a factor of 2 variation in amplitude. These velocity functions are then compared with N-body simulations of a LCDM model (corrected for baryonic infall) in order to demonstrate both the utility and current limitations of this approach. The number density of dark matter halos and the slope of the velocity function near v_*, the circular velocity corresponding to an ~L_* spiral galaxy, are found to be comparable to that of observed galaxies. The primary sources of uncertainty in construction of Psi(log v) from observations and N-body simulations are discussed and explanations are suggected to account for these discrepancies.Comment: Latex. 28 pages, 4 figures. Accepted by Ap

    Proceedings, Pot Chrysanthemum School, 1971

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    Space management / Robert W. Langhans -- Soils / D. C. Kiplinger -- Nutrition / George L. Staby -- Temperature and photoperiod / Joseph W. Love -- Automated short day control -- R. A. Aldrich -- Growth regulators / James B. Shanks -- Programming for insect-free pot mums / Richard K. Lindquist -- Programming for disease-free pot mums / Lester P. Nichols and Paul E. Nelson -- Where you go wrong / Harry K. Tayam

    Binary Quasars in the Sloan Digital Sky Survey: Evidence for Excess Clustering on Small Scales

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    We present a sample of 218 new quasar pairs with proper transverse separations R_prop < 1 Mpc/h over the redshift range 0.5 < z < 3.0, discovered from an extensive follow up campaign to find companions around the Sloan Digital Sky Survey and 2dF Quasar Redshift Survey quasars. This sample includes 26 new binary quasars with separations R_prop < 50 kpc/h (theta < 10 arcseconds), more than doubling the number of such systems known. We define a statistical sample of binaries selected with homogeneous criteria and compute its selection function, taking into account sources of incompleteness. The first measurement of the quasar correlation function on scales 10 kpc/h < R_prop < 400 kpc/h is presented. For R_prop < 40 kpc/h, we detect an order of magnitude excess clustering over the expectation from the large scale R_prop > 3 Mpc/h quasar correlation function, extrapolated down as a power law to the separations probed by our binaries. The excess grows to ~ 30 at R_prop ~ 10 kpc/h, and provides compelling evidence that the quasar autocorrelation function gets progressively steeper on sub-Mpc scales. This small scale excess can likely be attributed to dissipative interaction events which trigger quasar activity in rich environments. Recent small scale measurements of galaxy clustering and quasar-galaxy clustering are reviewed and discussed in relation to our measurement of small scale quasar clustering.Comment: 25 pages, 12 figures, 9 tables. Submitted to the Astronomical Journa

    Picturing the nation : The Celtic periphery as discursive other in the archaeological displays of the museum of Scotland

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    Using the archaeological displays at the Museum of Scotland in Edinburgh, this paper examines the exhibition as a site of identity creation through the negotiations between categories of same and Other. Through an analysis of the poetics of display, the paper argues that the exhibition constructs a particular relationship between the Celtic Fringe and Scottish National identity that draws upon the historical discourses of the Highlands and Islands of Scotland as a place and a time \u27apart\u27. This will be shown to have implications for the display of archaeological material in museums but also for contemporary understandings of Scottish National identity. <br /

    Global Distribution of Human-Associated Fecal Genetic Markers in Reference Samples from Six Continents

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    Numerous bacterial genetic markers are available for the molecular detection of human sources of fecal pollution in environmental waters. However, widespread application is hindered by a lack of knowledge regarding geographical stability, limiting implementation to a small number of well-characterized regions. This study investigates the geographic distribution of five human-associated genetic markers (HF183/BFDrev, HF183/BacR287, BacHum-UCD, BacH, and Lachno2) in municipal wastewaters (raw and treated) from 29 urban and rural wastewater treatment plants (750-4»400»000 population equivalents) from 13 countries spanning six continents. In addition, genetic markers were tested against 280 human and nonhuman fecal samples from domesticated, agricultural and wild animal sources. Findings revealed that all genetic markers are present in consistently high concentrations in raw (median log10 7.2-8.0 marker equivalents (ME) 100 mL-1) and biologically treated wastewater samples (median log10 4.6-6.0 ME 100 mL-1) regardless of location and population. The false positive rates of the various markers in nonhuman fecal samples ranged from 5% to 47%. Results suggest that several genetic markers have considerable potential for measuring human-associated contamination in polluted environmental waters. This will be helpful in water quality monitoring, pollution modeling and health risk assessment (as demonstrated by QMRAcatch) to guide target-oriented water safety management across the globe.Fil: Mayer, René E.. Vienna University of Technology; Austria. Interuniversity Cooperation Centre for Water and Health; AustriaFil: Reischer, Georg. Vienna University of Technology; AustriaFil: Ixenmaier, Simone K.. Vienna University of Technology; Austria. Interuniversity Cooperation Centre for Water and Health; AustriaFil: Derx, Julia. Vienna University of Technology; AustriaFil: Blaschke, Alfred Paul. Vienna University of Technology; AustriaFil: Ebdon, James E.. University of Brighton; Reino UnidoFil: Linke, Rita. Vienna University of Technology; Austria. Interuniversity Cooperation Centre Water And Health; AustriaFil: Egle, Lukas. Vienna University of Technology; AustriaFil: Ahmed, Warish. Csiro Land And Water; AustraliaFil: Blanch, Anicet R.. Universidad de Barcelona; EspañaFil: Byamukama, Denis. Makerere University; UgandaFil: Savill, Marion. Affordable Water Limited;Fil: Mushi, Douglas. Sokoine University Of Agriculture; TanzaniaFil: Cristobal, Hector Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones para la Industria Química; ArgentinaFil: Edge, Thomas A.. Canada Centre for Inland Waters. Environment and Climate Change Canada; CanadåFil: Schade, Margit A.. Bavarian Environment Agency; AlemaniaFil: Aslan, Asli. Georgia Southern University; Estados UnidosFil: Brooks, Yolanda M.. Michigan State University; Estados UnidosFil: Sommer, Regina. Interuniversity Cooperation Centre Water And Health; Austria. Medizinische Universitat Wien; AustriaFil: Masago, Yoshifumi. Tohoku University; JapónFil: Sato, Maria I.. Cia. Ambiental do Estado de Sao Paulo. Departamento de Anålises Ambientais; BrasilFil: Taylor, Huw D.. University of Brighton; Reino UnidoFil: Rose, Joan B.. Michigan State University; Estados UnidosFil: Wuertz, Stefan. Nanyang Technological University. Singapore Centre for Environmental Life Sciences Engineering and School of Civil and Environmental Engineering; SingapurFil: Shanks, Orin. U.S. Environmental Protection Agency; Estados UnidosFil: Piringer, Harald. Vrvis Research Center; AustriaFil: Mach, Robert L.. Vienna University of Technology; AustriaFil: Savio, Domenico. Karl Landsteiner University of Health Sciences; AustriaFil: Zessner, Matthias. Vienna University of Technology; AustriaFil: Farnleitner, Andreas. Vienna University of Technology; Austria. Interuniversity Cooperation Centre Water And Health; Austria. Karl Landsteiner University of Health Sciences; Austri
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