16,176 research outputs found
Zariski Closures and Subgroup Separability
The main result of this article is a refinement of the well-known subgroup
separability results of Hall and Scott for free and surface groups. We show
that for any finitely generated subgroup, there is a finite dimensional
representation of the free or surface group that separates the subgroup in the
induced Zariski topology. As a corollary, we establish a polynomial upper bound
on the size of the quotients used to separate a finitely generated subgroup in
a free or surface group.Comment: Final version. To appear in Selecta Mat
Structural Refinement for the Modal nu-Calculus
We introduce a new notion of structural refinement, a sound abstraction of
logical implication, for the modal nu-calculus. Using new translations between
the modal nu-calculus and disjunctive modal transition systems, we show that
these two specification formalisms are structurally equivalent.
Using our translations, we also transfer the structural operations of
composition and quotient from disjunctive modal transition systems to the modal
nu-calculus. This shows that the modal nu-calculus supports composition and
decomposition of specifications.Comment: Accepted at ICTAC 201
Spectroscopic Constraints on the Form of the Stellar Cluster Mass Function
This contribution addresses the question of whether the initial cluster mass
function (ICMF) has a fundamental limit (or truncation) at high masses. The
shape of the ICMF at high masses can be studied using the most massive young
(<10 Myr) clusters, however this has proven difficult due to low-number
statistics. In this contribution we use an alternative method based on the
luminosities of the brightest clusters, combined with their ages. If a
truncation is present, a generic prediction (nearly independent of the cluster
disruption law adopted) is that the median age of bright clusters should be
younger than that of fainter clusters. In the case of an non-truncated ICMF,
the median age should be independent of cluster luminosity. Here, we present
optical spectroscopy of twelve young stellar clusters in the face-on spiral
galaxy NGC 2997. The spectra are used to estimate the age of each cluster, and
the brightness of the clusters is taken from the literature. The observations
are compared with the model expectations of Larsen (2009) for various ICMF
forms and both mass dependent and mass independent cluster disruption. While
there exists some degeneracy between the truncation mass and the amount of mass
independent disruption, the observations favour a truncated ICMF. For low or
modest amounts of mass independent disruption, a truncation mass of 5-6*10^5
Msun is estimated, consistent with previous determinations. Additionally, we
investigate possible truncations in the ICMF in the spiral galaxy M83, the
interacting Antennae galaxies, and the collection of spiral and dwarf galaxies
present in Larsen (2009) based on photometric catalogues taken from the
literature, and find that all catalogues are consistent with having a
(environmentally dependent) truncation in the cluster mass functions.Comment: 6 pages, 5 figures, in press, A&A Research Note
Strings in Kerr-Newmann Black Holes
We study the evolution of strings in the equatorial plane of a Kerr-Newmann
black hole. Writting the equations of motion and the constraints resulting from
Hamilton's principle, three classes of exact solutions are presented, for a
closed string, encircling the black hole. They all depend on two arbitrary
integration functions and two constants. A process of extracting energy is
examined for the case of one of the three families of solutions. This is the
analog of the Penrose process for the case of a particle.Comment: 14 pages, no figures, LaTeX. To appear in Gen. Rel. Gra
Second Order Perturbations of a Macroscopic String; Covariant Approach
Using a world-sheet covariant formalism, we derive the equations of motion
for second order perturbations of a generic macroscopic string, thus
generalizing previous results for first order perturbations. We give the
explicit results for the first and second order perturbations of a contracting
near-circular string; these results are relevant for the understanding of the
possible outcome when a cosmic string contracts under its own tension, as
discussed in a series of papers by Vilenkin and Garriga. In particular, second
order perturbations are necessaary for a consistent computation of the energy.
We also quantize the perturbations and derive the mass-formula up to second
order in perturbations for an observer using world-sheet time . The high
frequency modes give the standard Minkowski result while, interestingly enough,
the Hamiltonian turns out to be non-diagonal in oscillators for low-frequency
modes. Using an alternative definition of the vacuum, it is possible to
diagonalize the Hamiltonian, and the standard string mass-spectrum appears for
all frequencies. We finally discuss how our results are also relevant for the
problems concerning string-spreading near a black hole horizon, as originally
discussed by Susskind.Comment: New discussion about the quantum mass-spectrum in chapter
Extraction efficiency of drifting electrons in a two-phase xenon time projection chamber
We present a measurement of the extraction efficiency of quasi-free electrons
from the liquid into the gas phase in a two-phase xenon time-projection
chamber. The measurements span a range of electric fields from 2.4 to 7.1 kV/cm
in the liquid xenon, corresponding to 4.5 to 13.1 kV/cm in the gaseous xenon.
Extraction efficiency continues to increase at the highest extraction fields,
implying that additional charge signal may be attained in two-phase xenon
detectors through careful high-voltage engineering of the gate-anode region
Damp Mergers: Recent Gaseous Mergers without Significant Globular Cluster Formation?
Here we test the idea that new globular clusters (GCs) are formed in the same
gaseous ("wet") mergers or interactions that give rise to the young stellar
populations seen in the central regions of many early-type galaxies. We compare
mean GC colors with the age of the central galaxy starburst. The red GC
subpopulation reveals remarkably constant mean colors independent of galaxy
age. A scenario in which the red GC subpopulation is a combination of old and
new GCs (formed in the same event as the central galaxy starburst) can not be
ruled out; although this would require an age-metallicity relation for the
newly formed GCs that is steeper than the Galactic relation. However, the data
are also well described by a scenario in which most red GCs are old, and few,
if any, are formed in recent gaseous mergers. This is consistent with the old
ages inferred from some spectroscopic studies of GCs in external systems. The
event that induced the central galaxy starburst may have therefore involved
insufficient gas mass for significant GC formation. We term such gas-poor
events "damp" mergers.Comment: 17 pages, 5 figures, ApJ accepte
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