An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.Comment: LaTex, 22 page

Stochastic Gross-Pitaevsky Equation for BEC via Coarse-Grained Effective Action

We sketch the major steps in a functional integral derivation of a new set of Stochastic Gross-Pitaevsky equations (GPE) for a Bose-Einstein condensate (BEC) confined to a trap at zero temperature with the averaged effects of non-condensate modes incorporated as stochastic sources. The closed-time-path (CTP) coarse-grained effective action (CGEA) or the equivalent influence functional method is particularly suitable because it can account for the full back-reaction of the noncondensate modes on the condensate dynamics self-consistently. The Langevin equations derived here containing nonlocal dissipation together with colored and multiplicative noises are useful for a stochastic (as distinguished from say, a kinetic) description of the nonequilibrium dynamics of a BEC. This short paper contains original research results not yet published anywhere.Comment: 6 page

Urban structure and growth

Most economic activity occurs in cities. This creates a tension between local increasing returns, implied by the existence of cities, and aggregate constant returns, implied by balanced growth. To address this tension, we develop a theory of economic growth in an urban environment. We show how the urban structure is the margin that eliminates local increasing returns to yield constant returns to scale in the aggregate, thereby implying a city size distribution that is well described by a power distribution with coefficient one: Zipf's Law. Under strong assumptions our theory produces Zipf's Law exactly. More generally, it produces the systematic deviations from Zipf's Law observed in the data, namely, the underrepresentation of small cities and the absence of very large ones. In these cases, the model identifies the standard deviation of industry productivity shocks as the key element determining dispersion in the city size distribution. We present evidence that the dispersion of city sizes is consistent with the dispersion of productivity shocks in the data.

The radial abundance gradient of oxygen towards the Galactic anticentre

We present deep optical spectroscopy of eight HII regions located in the anticentre of the Milky Way. The spectra were obtained at the 10.4m GTC and 8.2m VLT. We determined Te([NII]) for all objects and Te([OIII]) for six of them. We also included in our analysis an additional sample of 13 inner-disc Galactic Hii regions from the literature that have excellent T_e determinations. We adopted the same methodology and atomic dataset to determine the physical conditions and ionic abundances for both samples. We also detected the CII and OII optical recombination lines in Sh 2-100, which enables determination of the abundance discrepancy factor for this object. We found that the slopes of the radial oxygen gradients defined by the HII regions from R_25 (= 11.5 kpc) to 17 kpc and those within R_25 are similar within the uncertainties, indicating the absence of flattening in the radial oxygen gradient in the outer Milky Way. In general, we found that the scatter of the O/H ratios of Hii regions is not substantially larger than the observational uncertainties. The largest possible local inhomogeneities of the oxygen abundances are of the order of 0.1 dex. We also found positive radial gradients in Te([O III]) and Te([N II]) across the Galactic disc. The shapes of these temperature gradients are similar and also consistent with the absence of flattening of the metallicity distribution in the outer Galactic disc.Comment: 20 pages, 11 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Societ

A new survey for high velocity HI detections in the southern hemisphere

A new high-sensitivity HI survey of the southern sky was made south of Declination , at the Instituto Argentino de Radioastronomía (IAR), on a half-degree grid in galactic coordinates. A total of 50980 positions were observed. One of the goals of this survey was to search for high velocity clouds (HVCs). The HI profiles have been smoothed to a velocity resolution of 8 km s-1. The resulting rms noise falls in the range 0.015 to 0.020 K. We have detected 6848 high velocity (HV) components.Fil: Morras, Ricardo. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Bajaja, Esteban. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Arnal, Edmundo Marcelo. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Poppel, W. G. L.. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; Argentin