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    Abundance conjecture

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    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

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    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

    Ion-retarding lens improves the abundance sensitivity of tandem mass spectrometers

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    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

    The primordial lithium abundance

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    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
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