3,724 research outputs found
Some complete intersection symplectic quotients in positive characteristic: invariants of a vector and a covector
Given a linear action of a group on a -vector space , we consider
the invariant ring , where is the dual space. We are
particularly interested in the case where V =\gfq^n and is the group
of all upper unipotent matrices or the group of all upper
triangular matrices in \GL_n(\gfq). In fact, we determine \gfq[V \oplus
V^*]^G for and . The result is a complete intersection for
all values of and . We present explicit lists of generating invariants
and their relations. This makes an addition to the rather short list of "doubly
parametrized" series of group actions whose invariant rings are known to have a
uniform description.Comment: 16 page
An Algorithm to Calculate Optimal Homogeneous Systems of Parameters
AbstractWhen a homogeneous system of parametersf1,...,fnis chosen for a graded algebraA, it is important for subsequent computations that the degrees, deg(fi), are as small as possible. More precisely, one would like the product or the sum of the degrees to be minimal, depending on the application.This article investigates which degree vectors can occur as the degrees of a homogeneous system of parameters. From this, an algorithm is derived which constructs an optimal homogeneous system of parameters. Here the notion of what is considered asoptimalis part of the input. An important application is the case whereAis the invariant ring of a finite linear group. There is an implementation of the algorithm in Magma which applies to this case
Crystallinity versus mass-loss rate in Asymptotic Giant Branch stars
Infrared Space Observatory (ISO) observations have shown that O-rich
Asymptotic Giant Branch (AGB) stars exhibit crystalline silicate features in
their spectra only if their mass-loss rate is higher than a certain threshold
value. Usually, this is interpreted as evidence that crystalline silicates are
not present in the dust shells of low mass-loss rate objects. In this study,
radiative transfer calculations have been performed to search for an
alternative explanation to the lack of crystalline silicate features in the
spectrum of low mass-loss rate AGB stars. It is shown that due to a temperature
difference between amorphous and crystalline silicates it is possible to
include up to 40% of crystalline silicate material in the circumstellar dust
shell, without the spectra showing the characteristic spectral features. Since
this implies that low mass-loss rate AGB stars might also form crystalline
silicates and deposit them into the Interstellar Medium (ISM), the described
observational selection effect may put the process of dust formation around AGB
stars and the composition of the predominantly amorphous dust in the
Interstellar Medium in a different light. Our model calculations result in a
diagnostic tool to determine the crystallinity of an AGB star with a known
mass-loss rate.Comment: accepted by A&A, 10 pages, 11 figure
Modelling the alumina abundance of oxygen-rich evolved stars in the Large Magellanic Cloud
In order to determine the composition of the dust in the circumstellar
envelopes of oxygen-rich asymptotic giant branch (AGB) stars we have computed a
grid of modust radiative-transfer models for a range of dust compositions,
mass-loss rates, dust shell inner radii and stellar parameters. We compare the
resulting colours with the observed oxygen-rich AGB stars from the SAGE-Spec
Large Magellanic Cloud (LMC) sample, finding good overall agreement for stars
with a mid-infrared excess. We use these models to fit a sample of 37 O-rich
AGB stars in the LMC with optically thin circumstellar envelopes, for which
535-m Spitzer infrared spectrograph (IRS) spectra and broadband
photometry from the optical to the mid-infrared are available. From the
modelling, we find mass-loss rates in the range to
M, and we show that a grain
mixture consisting primarily of amorphous silicates, with contributions from
amorphous alumina and metallic iron provides a good fit to the observed
spectra. Furthermore, we show from dust models that the AKARI [11][15]
versus [3.2][7] colour-colour diagram, is able to determine the fractional
abundance of alumina in O-rich AGB stars.Comment: 22 pages, 17 figures, accepted MNRA
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