PlanetMath Redux: Web 2.0 infrastructure for mathematical problem solving

This demo shows work in progress on a Web 2.0 infrastructure for mathematical problem solving. Our aim is to make undergraduate-level mathematics easier to learn: our strategy is to link problems and solved examples to prerequisite material drawn from an existing free/open mathematical knowledge repository, the encyclopedia at PlanetMath.org

Dissecting the Power Sources of Low-Luminosity Emission-Line Galaxy Nuclei via Comparison of HST-STIS and Ground-Based Spectra

Using a sample of ~100 nearby line-emitting galaxy nuclei, we have built the currently definitive atlas of spectroscopic measurements of H_alpha and neighboring emission lines at subarcsecond scales. We employ these data in a quantitative comparison of the nebular emission in Hubble Space Telescope (HST) and ground-based apertures, which offer an order-of-magnitude difference in contrast, and provide new statistical constraints on the degree to which Transition Objects and low-ionization nuclear emission-line regions (LINERs) are powered by an accreting black hole at <10 pc. We show that while the small-aperture observations clearly resolve the nebular emission, the aperture dependence in the line ratios is generally weak, and this can be explained by gradients in the density of the line-emitting gas: the higher densities in the more nuclear regions potentially flatten the excitation gradients, suppressing the forbidden emission. The Transition Objects show a threefold increase in the incidence of broad H_alpha emission in the high-resolution data, as well as the strongest density gradients, supporting the composite model for these systems as accreting sources surrounded by star-forming activity. The narrow-line LINERs appear to be the weaker counterparts of the Type 1 LINERs, where the low accretion rates cause the disappearance of the broad-line component. The enhanced sensitivity of the HST observations reveals a 30% increase in the incidence of accretion-powered systems at z~0. A comparison of the strength of the broad-line emission detected at different epochs implies potential broad-line variability on a decade-long timescale, with at least a factor of three in amplitude.Comment: 27 pages, 13 figures, 4 tables, accepted for publication in Ap

Improved variational principle for bounds on energy dissipation in turbulent shear flow

We extend the Doering-Constantin approach to upper bounds on energy dissipation in turbulent flows by introducing a balance parameter into the variational principle. This parameter governs the relative weight of different contributions to the dissipation rate. Its optimization leads to improved bounds without entailing additional technical difficulties. For plane Couette flow, the high-Re-bounds obtainable with one-dimensional background flows are methodically lowered by a factor of 27/32.Comment: 15 pages, RevTeX, 3 postscript figure

L\u27amour de l\u27or : pour voix de basse

Un Vieillard tout creusé de rides,le front courbé,l\u27oeil scintillant,plongeait ses regards avides sur un trésor richeet brilliant:oh! disait il, que mon âme est ravie! c\u27est là mon sang,c\u27est là ma vie,c\u27est mon bonheur!c\u27est plus encor c\u27est mon amour c\u27est mon amour l\u27amour de l\u27or!de l\u27or de l\u27or de l\u27or de l\u27or toujour, de l\u27or! sans richesse, sans richesse,oh! mieux vaut mieux vaut la mort de l\u27or! de l\u27or! de l\u27or!toujours de l\u27or! de l\u27or! de l\u27or! de l\u27or! jusqu\u27a la mort! Loin de moi fuyez, jeunes femmes!non, vous neme seduirez pas!vous poète aux ardentes flammes, a mon coeur vous parlez trop bas:laissez moi contempler encore ces ducats au bruit plus sonore;ce langage parle plus fort:c\u27est mon amour!l\u27amour de l\u27or! Mais bientôt le vieillard cupide,la main brulante et l\u27oeil éteint,mourant sur un grabat humide,maudissait encor le destin.oh! lui diton, quittant la terre, l\u27amour du Ciel c\u27est la prière!non, non! le Ciel c\u27est ce trésor,et mon amour et mon amour, l\u27amour de l\u27or

The Metallicity of the Redshift 4.16 Quasar BR2248-1242

We estimate the metallicity in the broad emission-line region of the redshift z=4.16 quasar, BR2248-1242, by comparing line ratios involving nitrogen to theoretical predictions. BR2248-1242 has unusually narrow emission lines with large equivalent widths, thus providing a rare opportunity to measure several line-ratio abundance diagnostics. The combined diagnostics indicate a metallicity of ~2 times solar. This result suggests that an episode of vigorous star formation occurred near BR2248-1242 prior to the observed z=4.16 epoch. The time available for this enrichment episode is only ~1.5 Gyr at z=4.16 (for H_{0}=65 km s^-1 Mpc^-1, Omega_{m}=0.3 and Omega_Lambda ~< 1). This evidence for high metallicities and rapid star formation is consistent with the expected early-epoch evolution of dense galactic nuclei.Comment: 8 pages, 3 figures. Prepared in AAStex. Submitted to the Astrophysical Journal Revised version: added 1 referenc

Emission-Line Properties of z > 4 Quasars

We present results of a program of high signal-to-noise spectroscopy for 44 QSOs at redshifts > 4 using the MMT and Keck observatories. The quasar spectra cover 1100 -- 1700 A in the rest frame for sources spanning a luminosity range of approximately 2 orders of magnitude. Comparisons between these data and spectra of lower redshift quasars reveal a high degree of similarity, although differences are present in the profiles and the strengths of some emission features. An examination of the luminosity dependence of the emission lines reveals evidence for a weak or absent Baldwin effect among z > 4 QSOs. We compare measurements for objects in our sample with results from other high redshift surveys characterized by different selection techniques. Distributions of equivalent widths for these different ensembles are consistent with a common parent population, suggesting that our sample is not strongly biased, or in any case, subject to selection effects that are not significantly different from other surveys, including the Sloan Digital Sky Survey. Based on this comparison, we tentatively conclude that the trends identified here are representative of high z QSOs. In particular, the data bolster indications of supersolar metallicities in these luminous, high-z sources, which support scenarios that assume substantial star formation at epochs preceding or concurrent with the QSO phenomena.Comment: 26 pages (incl. 9 figures), AASTeX v5.0, to appear in The Astrophysical Journa