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Abundance conjecture
We sketch a proof of the abundance conjecture that the Kodaira dimension of a
compact complex algebraic manifold equals its numerical Kodaira dimension. The
proof consists of the following three parts: (i) the case of numerical Kodaira
dimension zero, (ii) the general case under the assumption of the coincidence
of the numerically trivial foliation and fibration for the canonical bundle,
and (iii) the verification of the coincidence of the numerically trivial
foliation and fibration for the canonical bundle. Besides the use of standard
techniques such as the L2 estimates of d-bar, the first part uses Simpson's
method of replacing the flat line bundle in a nontrivial flatly twisted
canonical section by a torsion flat line bundle. Simpson's method relies on the
technique of Gelfond-Schneider for the solution of the seventh problem of
Hilbert. The second part uses the semi-positivity of the direct image of a
relative pluricanonical bundle. The third part uses the technique of the First
Main Theorem of Nevanlinna theory and its use is related to the technique of
Gelfond-Schneider in the first part
Nebular Abundance Errors
The errors inherent to the use of the standard "ionization correction factor"
("i_CF") method of calculating nebular conditions and relative abundances of H,
He, N, O, Ne, S, and Ar in emission line nebulae have been investigated under
conditions typical for planetary nebulae. The photoionization code CLOUDY was
used to construct a series of model nebulae with properties spanning the range
typical of PNe. Its radial "profiles" of bright, frequently observed optical
emission lines were then summed over a variety of "apertures" to generate sets
of emission line measurements. These resulting line ratios were processed using
the i_CF method to "derive" nebular conditions and abundances. We find that for
lines which are summed over the entire nebula the i_CF-derived abundances
differ from the input abundances by less than 5% for He and O up to 25% or more
for Ne, S, and Ar. For resolved observations, however, the discrepancies are
often much larger and are systematically variable with radius. This effect is
especially pronounced in low-ionization zones where nitrogen and oxygen are
neutral or once-ionized such as in FLIERs, ansae and ionization fronts. We
argue that the reports of stellar-enriched N in the FLIERs of several PNe are
probably specious.Comment: 22 pages, 4 tables, and 1 figure. Accepted for publication in the
Astronomical Journal. Replaced to correct a referenc
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A pedagogy of abundance
The digitisation of content combined with a global network for delivery and an open system for sharing has seen radical changes in many industries. The economic model which has underpinned many content based industries has been based on an assumption of scarcity. With a digital, open, networked approach we are witnessing a shift to abundance of content, and subsequently new economic models are being developed which have this as an assumption. In this article the role of scarcity in developing higher education practice and pedagogy is explored. The shift to abundant content has as profound implications for education as it has for content industries. The possible contenders for a ‘pedagogy of abundance’ are examined and the necessary requirements for such a pedagogy outlined
The primordial lithium abundance
Lithium abundances in a selected sample of halo stars have been revised by
using the new accurate IRFM effective temperatures by Alonso, Arribas &
Martinez-Roger (1996a). From 41 plateau stars (Teff > 5700 and [Fe/H] <= -1.5)
we found no evidence for intrinsic dispersion, a tiny trend with Teff and no
trend with [Fe/H]. The trend with the Teff is fully consistent with the
standard Li isochrones of Deliyannis, Demarque & Kawaler (1990) implying a
primordial value for Li of A(Li) = 2.238 +/- 0.012 {1 sigma} +/- 0.05{sys}. The
present results argue against any kind of depletion predicted by diffusion,
rotational mixing or stellar winds. Therefore the Li observed in Pop II stars
provides a direct and reliable estimate of the baryonic density that can rival
other baryonic indicators such as the deuterium in high redshift systems. The
present upwards revision of primordial Li in the framework of SBBN gives at 1
sigma two solutions for the baryonic density: Omega_{B}h^2 = 0.0062
{+0.0018,-0.0011} or Omega_{B}h^2 = 0.0146 {+0.0029,-0.0033} .Comment: Tex, uses MN.tex, 18 .ps figures; accepted MNRA
Ion-retarding lens improves the abundance sensitivity of tandem mass spectrometers
Ion-retarding lens which increases the abundance sensitivity of tandem magnetic-analyzer mass spectrometers measures isotopes of low abundance in mass positions adjacent to isotopes of high abundance. The lens increases the abundance sensitivity for isotopes lying farther from high abundance isotopes than the energy cutoff of the lens
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