8,321 research outputs found
Term Graph Representations for Cyclic Lambda-Terms
We study various representations for cyclic lambda-terms as higher-order or
as first-order term graphs. We focus on the relation between
`lambda-higher-order term graphs' (lambda-ho-term-graphs), which are
first-order term graphs endowed with a well-behaved scope function, and their
representations as `lambda-term-graphs', which are plain first-order term
graphs with scope-delimiter vertices that meet certain scoping requirements.
Specifically we tackle the question: Which class of first-order term graphs
admits a faithful embedding of lambda-ho-term-graphs in the sense that: (i) the
homomorphism-based sharing-order on lambda-ho-term-graphs is preserved and
reflected, and (ii) the image of the embedding corresponds closely to a natural
class (of lambda-term-graphs) that is closed under homomorphism?
We systematically examine whether a number of classes of lambda-term-graphs
have this property, and we find a particular class of lambda-term-graphs that
satisfies this criterion. Term graphs of this class are built from application,
abstraction, variable, and scope-delimiter vertices, and have the
characteristic feature that the latter two kinds of vertices have back-links to
the corresponding abstraction.
This result puts a handle on the concept of subterm sharing for higher-order
term graphs, both theoretically and algorithmically: We obtain an easily
implementable method for obtaining the maximally shared form of
lambda-ho-term-graphs. Also, we open up the possibility to pull back properties
from first-order term graphs to lambda-ho-term-graphs. In fact we prove this
for the property of the sharing-order successors of a given term graph to be a
complete lattice with respect to the sharing order.
This report extends the paper with the same title
(http://arxiv.org/abs/1302.6338v1) in the proceedings of the workshop TERMGRAPH
2013.Comment: 35 pages. report extending proceedings article on arXiv:1302.6338
(changes with respect to version v2: added section 8, modified Proposition
2.4, added Remark 2.5, added Corollary 7.11, modified figures in the
conclusion
Surface motion in the pulsating DA white dwarf G 29-38
We present time-resolved spectrophotometry of the pulsating DA white dwarf G
29-38. As in previous broad-band photometry, the light curve shows the presence
of a large number of periodicities. Many of these are combination frequencies,
i.e., periodicities occurring at frequencies that are sums or differences of
frequencies of stronger, real modes. We identify at least six real modes, and
at least five combination frequencies. We measure line-of-sight velocities for
our spectra and detect periodic variations at the frequencies of five of the
six real modes, with amplitudes of up to 5 km/s. We argue that these variations
reflect the horizontal surface motion associated with the g-mode pulsations. No
velocity signals are detected at any of the combination frequencies, confirming
that the flux variations at these frequencies do not reflect physical
pulsation, but rather mixing of frequencies due to a non-linear transformation
in the outer layers of the star. We discuss the amplitude ratios and phase
differences found for the velocity and light variations, as well as those found
for the real modes and their combination frequencies, both in a
model-independent way and in the context of models based on the
convective-driving mechanism. In a companion paper, we use the wavelength
dependence of the amplitudes of the modes to infer their spherical degree.Comment: 12 pages, 5 figures, mn.sty. Accepted for publication in MNRA
Mode identification from time-resolved spectroscopy of the pulsating white dwarf G 29-38
We have used time-resolved spectroscopy to measure the colour dependence of
pulsation amplitudes in the DAV white dwarf G 29-38. Model atmospheres predict
that mode amplitudes should change with wavelength in a manner that depends on
the spherical harmonic degree l of the mode. This dependence arises from the
convolution of mode geometry with wavelength-dependent limb darkening. Our
analysis of the six largest normal modes detected in Keck observations of G
29-38 reveals one mode with a colour dependence different from the other five,
permitting us to identify the l value of all six modes and to test the model
predictions. The Keck observations also show pulsation amplitudes that are
unexpectedly asymmetric within absorption lines. We show that these asymmetries
arise from surface motions associated with the non-radial pulsations (which are
discussed in detail in a companion paper). By incorporating surface velocity
fields into line profile calculations, we are able to produce models that more
closely resemble the observations.Comment: 10 pages, 9 figures, mn.sty. Accepted for publication in MNRA
A Quantitative Non-radial Oscillation Model for the Subpulses in PSR B0943+10
In this paper, we analyze time series measurements of PSR B0943+10 and fit
them with a non-radial oscillation model. The model we apply was first
developed for total intensity measurements in an earlier paper, and expanded to
encompass linear polarization in a companion paper to this one. We use PSR
B0943+10 for the initial tests of our model because it has a simple geometry,
it has been exhaustively studied in the literature, and its behavior is
well-documented. As prelude to quantitative fitting, we have reanalyzed
previously published archival data of PSR B0943+10 and uncovered subtle but
significant behavior that is difficult to explain in the framework of the
drifting spark model. Our fits of a non-radial oscillation model are able to
successfully reproduce the observed behavior in this pulsar.Comment: 45 pages, 16 figures, accepted Ap
Molecular Feshbach dissociation as a source for motionally entangled atoms
We describe the dissociation of a diatomic Feshbach molecule due to a
time-varying external magnetic field in a realistic trap and guide setting. An
analytic expression for the asymptotic state of the two ultracold atoms is
derived, which can serve as a basis for the analysis of dissociation protocols
to generate motionally entangled states. For instance, the gradual dissociation
by sequences of magnetic field pulses may delocalize the atoms into
macroscopically distinct wave packets, whose motional entanglement can be
addressed interferometrically. The established relation between the applied
magnetic field pulse and the generated dissociation state reveals that
square-shaped magnetic field pulses minimize the momentum spread of the atoms.
This is required to control the detrimental influence of dispersion in a
recently proposed experiment to perform a Bell test in the motion of the two
atoms [C. Gneiting and K. Hornberger, Phys. Rev. Lett. 101, 260503 (2008)].Comment: 12 pages, 3 figures; corresponds to published versio
Quartic double solids with ordinary singularities
We study the mixed Hodge structure on the third homology group of a threefold
which is the double cover of projective three-space ramified over a quartic
surface with a double conic. We deal with the Torelli problem for such
threefolds.Comment: 14 pages, presented at the Conference Arnol'd 7
Time-resolved optical spectroscopy of the pulsating DA white dwarf HS 0507+0434B: New constraints on mode identification and pulsation properties
We present a detailed analysis of time-resolved optical spectra of the ZZ
Ceti white dwarf, HS 0507+0434B. Using the wavelength dependence of observed
mode amplitudes, we deduce the spherical degree, l, of the modes, most of which
have l=1. The presence of a large number of combination frequencies (linear
sums or differences of the real modes) enabled us not only to test theoretical
predictions but also to indirectly infer spherical and azimuthal degrees of
real modes that had no observed splittings. In addition to the above, we
measure line-of-sight velocities from our spectra. We find only marginal
evidence for periodic modulation associated with the pulsation modes: at the
frequency of the strongest mode in the lightcurve, we measure an amplitude of
2.6+/-1.0 km/s, which has a probability of 2% of being due to chance; for the
other modes, we find lower values. Our velocity amplitudes and upper limits are
smaller by a factor of two compared to the amplitudes found in ZZ Psc. We find
that this is consistent with expectations based on the position of HS
0507+0434B in the instability strip. Combining all the available information
from data such as ours is a first step towards constraining atmospheric
properties in a convectionally unstable environment from an observational
perspective.Comment: 16 pages, 12 figs.; accepted for publication in A&
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