Variation of Hilbert Coefficients

For a Noetherian local ring (\RR, \m), the first two Hilbert coefficients, $e_0$ and $e_1$, of the $I$-adic filtration of an \m-primary ideal $I$ are known to code for properties of \RR, of the blowup of \spec(\RR) along $V(I)$, and even of their normalizations. We give estimations for these coefficients when $I$ is enlarged (in the case of $e_1$ in the same integral closure class) for general Noetherian local rings

Variation of the first Hilbert coefficients of parameters with a common integral closure

A problem posed by Wolmer V. Vasconcelos on the variation of the first Hilbert coefficients of parameter ideals with a common integral closure in a local ring is studied. Affirmative answers are given and counterexamples are explored as well

Abundances of Stars with Planets: Trends with Condensation Temperature

Precise abundances of 18 elements have been derived for ten stars known to host giant planets from high signal-to-noise ratio, high-resolution echelle spectroscopy. Internal uncertainties in the derived abundances are typically <=0.05 dex. The stars in our sample have all been previously shown to have abundances that correlate with the condensation temperature (T_c) of the elements in the sense of increasing abundances with increasing T_c; these trends have been interpreted as evidence that the stars may have accreted H-depleted planetary material. Our newly derived abundances also correlate positively with T_c, although slopes of linear least-square fits to the [m/H]-T_c relations for all but two stars are smaller here than in previous studies. When considering the refractory elements (T_c > 900 K) only, which may be more sensitive to planet formation processes, the sample can be separated into a group with positive slopes (four stars) and a group with flat or negative slopes (six stars). The four stars with positive slopes have very close-in giant planets (three at 0.05 AU) and slopes that fall above the general Galactic chemical evolution trend. We suggest that these stars have accreted refractory-rich planet material but not to the extent that would increase significantly the overall stellar metallicity. The flat or negative slopes of the remaining six stars are consistent with recent suggestions of a planet formation signature, although we show that the trends may be the result of Galactic chemical evolution.Comment: 64 pages (single column), 5 figures, 10 tables. Accepted by Ap

Metallicities of Planet Hosting Stars: A Sample of Giants and Subgiants

This work presents a homogeneous derivation of atmospheric parameters and iron abundances for a sample of giant and subgiant stars which host giant planets, as well as a control sample of subgiant stars not known to host giant planets. The analysis is done using the same technique as for our previous analysis of a large sample of planet-hosting and control sample dwarf stars. A comparison between the distributions of [Fe/H] in planet-hosting main-sequence stars, subgiants, and giants within these samples finds that the main-sequence stars and subgiants have the same mean metallicity of \simeq +0.11 dex, while the giant sample is typically more metal poor, having an average metallicity of = -0.06 dex. The fact that the subgiants have the same average metallicities as the dwarfs indicates that significant accretion of solid metal-rich material onto the planet-hosting stars has not taken place, as such material would be diluted in the evolution from dwarf to subgiant. The lower metallicity found for the planet-hosting giant stars in comparison with the planet-hosting dwarfs and subgiants is interpreted as being related to the underlying stellar mass, with giants having larger masses and thus, on average larger-mass protoplanetary disks. In core accretion models of planet formation, larger disk masses can contain the critical amount of metals necessary to form giant planets even at lower metallicities.Comment: 38 pages, 7 figures, 4 tables, accepted for publication in Ap

MORPH: A Reference Architecture for Configuration and Behaviour Self-Adaptation

An architectural approach to self-adaptive systems involves runtime change of system configuration (i.e., the system's components, their bindings and operational parameters) and behaviour update (i.e., component orchestration). Thus, dynamic reconfiguration and discrete event control theory are at the heart of architectural adaptation. Although controlling configuration and behaviour at runtime has been discussed and applied to architectural adaptation, architectures for self-adaptive systems often compound these two aspects reducing the potential for adaptability. In this paper we propose a reference architecture that allows for coordinated yet transparent and independent adaptation of system configuration and behaviour