4,564 research outputs found
Splitting Proofs for Interpolation
We study interpolant extraction from local first-order refutations. We
present a new theoretical perspective on interpolation based on clearly
separating the condition on logical strength of the formula from the
requirement on the com- mon signature. This allows us to highlight the space of
all interpolants that can be extracted from a refutation as a space of simple
choices on how to split the refuta- tion into two parts. We use this new
insight to develop an algorithm for extracting interpolants which are linear in
the size of the input refutation and can be further optimized using metrics
such as number of non-logical symbols or quantifiers. We implemented the new
algorithm in first-order theorem prover VAMPIRE and evaluated it on a large
number of examples coming from the first-order proving community. Our
experiments give practical evidence that our work improves the state-of-the-art
in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201
The Gap Function Phi(k,w) for a Two-leg t-J Ladder and the Pairing Interaction
The gap function phi(k,omega), determined from a Lanczos calculation for a
doped 2-leg t-J ladder, is used to provide insight into the spatial and
temporal structure of the pairing interaction. It implies that this interaction
is a local near-neighbor coupling which is retarded. The onset frequency of the
interaction is set by the energy of an S=1 magnon-hole-pair and it is spread
out over a frequency region of order the bandwith
Star cluster ecology IVa: Dissection of an open star cluster---photometry
The evolution of star clusters is studied using N-body simulations in which
the evolution of single stars and binaries are taken self-consistently into
account. Initial conditions are chosen to represent relatively young Galactic
open clusters, such as the Pleiades, Praesepe and the Hyades. The calculations
include a realistic mass function, primordial binaries and the external
potential of the parent Galaxy. Our model clusters are generally significantly
flattened in the Galactic tidal field, and dissolve before deep core collapse
occurs. The binary fraction decreases initially due to the destruction of soft
binaries, but increases later because lower mass single stars escape more
easily than the more massive binaries. At late times, the cluster core is quite
rich in giants and white dwarfs. There is no evidence for preferential
evaporation of old white dwarfs, on the contrary the formed white dwarfs are
likely to remain in the cluster. Stars tend to escape from the cluster through
the first and second Lagrange points, in the direction of and away from the
Galactic center. Mass segregation manifests itself in our models well within an
initial relaxation time. As expected, giants and white dwarfs are much more
strongly affected by mass segregation than main-sequence stars. Open clusters
are dynamically rather inactive. However, the combined effect of stellar mass
loss and evaporation of stars from the cluster potential drives its dissolution
on a much shorter timescale than if these effects are neglected. The often-used
argument that a star cluster is barely older than its relaxation time and
therefore cannot be dynamically evolved is clearly in error for the majority of
star clusters.Comment: reduced abstract, 33 pages (three separate color .jpg figures),
submitted to MNRA
Evolution of Binary Stars in Multiple-Population Globular Clusters - II. Compact Binaries
We present the results of a survey of N-body simulations aimed at exploring
the evolution of compact binaries in multiple-population globular clusters.We
show that as a consequence of the initial differences in the structural
properties of the first-generation (FG) and the second-generation (SG)
populations and the effects of dynamical processes on binary stars, the SG
binary fraction decreases more rapidly than that of the FG population. The
difference between the FG and SG binary fraction is qualitatively similar to
but quantitatively smaller than that found for wider binaries in our previous
investigations.The evolution of the radial variation of the binary fraction is
driven by the interplay between binary segregation, ionization and ejection.
Ionization and ejection counteract in part the effects of mass segregation but
for compact binaries the effects of segregation dominate and the inner binary
fraction increases during the cluster evolution. We explore the variation of
the difference between the FG and the SG binary fraction with the distance from
the cluster centre and its dependence on the binary binding energy and cluster
structural parameters. The difference between the binary fraction in the FG and
the SG populations found in our simulations is consistent with the results of
observational studies finding a smaller binary fraction in the SG population.Comment: 9 pages, 12 figures. Accepted for publication in MNRA
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