12,454 research outputs found
Discrete Modified Projection Methods for Urysohn Integral Equations with Green's Function Type Kernels
In the present paper we consider discrete versions of the modified projection
methods for solving a Urysohn integral equation with a kernel of the type of
Green's function. For a space of piecewise polynomials of degree
with respect to an uniform partition is chosen to be the
approximating space. We define a discrete orthogonal projection onto this space
and replace the Urysohn integral operator by a Nystr\"{o}m approximation. The
order of convergence which we obtain for the discrete version indicates the
choice of numerical quadrature which preserves the orders of convergence in the
continuous modified projection methods. Numerical results are given for a
specific example.Comment: This is the the same paper with the arXiv identifier 1904.07895, but
the shortened version. A bit change in the title als
Metallicity Evolution of Damped Lyman-Alpha Galaxies
We have reanalyzed the existing data on Zinc abundances in damped Ly-alpha
(DLA) absorbers to investigate whether their mean metallicity evolves with
time. Most models of cosmic chemical evolution predict that the mass- weighted
mean interstellar metallicity of galaxies should rise with time from a low
value ~ 1/30 solar at z ~ 3 to a nearly solar value at z ~ 0. However, several
previous analyses have suggested that there is little or no evolution in the
global metallicity of DLAs. We have used a variety of statistical techniques to
quantify the global metallicity-redshift relation and its uncertainties, taking
into account both measurement and sampling errors. Three new features of our
analysis are: (a) an unbinned N(H I)-weighted nonlinear chi-square fit to an
exponential relation; (b) survival analysis to treat the large number of limits
in the existing data; and (c) a comparison of the data with several models of
cosmic chemical evolution based on an unbinned N(H I)-weighted chi-square. We
find that a wider range of evolutionary rates is allowed by the present data
than claimed in previous studies. The slope of the exponential fit to the N(H
I)-weighted mean Zn metallicity vs. redshift relation is -0.20 plus minus 0.11
counting limits as detections and -0.27 plus minus 0.12 counting limits as
zeros. Similar results are also obtained if the data are binned in redshift,
and if survival analysis is used. These slopes are marginally consistent with
no evolution, but are also consistent with the rates predicted by several
models of cosmic chemical evolution. Finally, we outline some future
measurements necessary to improve the statistics of the global
metallicity-redshift relation.Comment: 25 pages, 1 figure, accepted for publication in the Astrophysical
Journa
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