27,058 research outputs found
Symmetrization in Geometry
The concept of an -symmetrization is introduced, which provides a
convenient framework for most of the familiar symmetrization processes on
convex sets. Various properties of -symmetrizations are introduced and the
relations between them investigated. New expressions are provided for the
Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual
relationship between them. Characterizations of Steiner, Minkowski and central
symmetrization, in terms of natural properties that they enjoy, are given and
examples are provided to show that none of the assumptions made can be dropped
or significantly weakened. Other familiar symmetrizations, such as Schwarz
symmetrization, are discussed and several new ones introduced.Comment: A chacterization of central symmetrization has been added and several
typos have been corrected. This version has been accepted for publication on
Advances in Mathematic
On the reconstruction of planar lattice-convex sets from the covariogram
A finite subset of is said to be lattice-convex if is
the intersection of with a convex set. The covariogram of
is the function associating to each u \in
\integer^d the cardinality of . Daurat, G\'erard, and Nivat and
independently Gardner, Gronchi, and Zong raised the problem on the
reconstruction of lattice-convex sets from . We provide a partial
positive answer to this problem by showing that for and under mild extra
assumptions, determines up to translations and reflections. As a
complement to the theorem on reconstruction we also extend the known
counterexamples (i.e., planar lattice-convex sets which are not
reconstructible, up to translations and reflections) to an infinite family of
counterexamples.Comment: accepted in Discrete and Computational Geometr
Galaxy Morphology from NICMOS Parallel Imaging
We present high resolution NICMOS images of random fields obtained in
parallel to other HST observations. We present galaxy number counts reaching
H=24. The H-band galaxy counts show good agreement with the deepest I- and
K-band counts obtained from ground-based data. We present the distribution of
galaxies with morphological type to H<23. We find relatively fewer irregular
galaxies compared to an I-band sample from the Hubble Deep Field, which we
attribute to their blue color, rather than to morphological K-corrections. We
conclude that the irregulars are intrinsically faint blue galaxies at z<1.Comment: 13 pages, including 4 figures. Accepted for publication in ApJ
Letter
Counts and Sizes of Galaxies in the Hubble Deep Field - South: Implications for the Next Generation Space Telescope
Science objectives for the Next Generation Space Telescope (NGST) include a
large component of galaxy surveys, both imaging and spectroscopy. The Hubble
Deep Field datasets include the deepest observations ever made in the
ultraviolet, optical and near infrared, reaching depths comparable to that
expected for NGST spectroscopy. We present the source counts, galaxy sizes and
isophotal filling factors of the HDF-South images. The observed integrated
galaxy counts reach >500 galaxies per square arcminute at AB<30. We extend
these counts to faint levels in the infrared using models. The trend previously
seen that fainter galaxies are smaller, continues to AB=29 in the high
resolution HDF-S STIS image, where galaxies have a typical half-light radius of
0.1 arcseconds. Extensive Monte Carlo simulations show that the small measured
sizes are not due to selection effects until >29mag. Using the HDF-S NICMOS
image, we show that galaxies are smaller in the near infrared than they are in
the optical. We analyze the isophotal filling factor of the HDF-S STIS image,
and show that this image is mostly empty sky even at the limits of galaxy
detection, a conclusion we expect to hold true for NGST spectroscopy. At the
surface brightness limits expected for NGST imaging, however, about a quarter
of the sky is occupied by the outer isophotes of AB<30 galaxies. We discuss the
implications of these data on several design concepts of the NGST near-infrared
spectrograph. We compare the effects of resolution and the confusion limit of
various designs, as well as the multiplexing advantages of either multi-object
or full-field spectroscopy. We argue that the optimal choice for NGST
spectroscopy of high redshift galaxies is a multi-object spectrograph (MOS)
with target selection by a micro electro mechanical system (MEMS) device.Comment: 27 pages including 10 figures, accepted for publication in the
Astronomical Journal, June 2000, abridged abstrac
Multifractal analysis of perceptron learning with errors
Random input patterns induce a partition of the coupling space of a
perceptron into cells labeled by their output sequences. Learning some data
with a maximal error rate leads to clusters of neighboring cells. By analyzing
the internal structure of these clusters with the formalism of multifractals,
we can handle different storage and generalization tasks for lazy students and
absent-minded teachers within one unified approach. The results also allow some
conclusions on the spatial distribution of cells.Comment: 11 pages, RevTex, 3 eps figures, version to be published in Phys.
Rev. E 01Jan9
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Tafassasset: The Saga Continues
In this study, we compare data for two separate Tafassasset stones and supply new oxygen isotope data for our sample. We include a discussion of the debate surrounding the classification of Tafassasset and offer a hypothesis for its origin based upon new information
Statistical mechanics of the multi-constraint continuous knapsack problem
We apply the replica analysis established by Gardner to the multi-constraint
continuous knapsack problem,which is one of the linear programming problems and
a most fundamental problem in the field of operations research (OR). For a
large problem size, we analyse the space of solution and its volume, and
estimate the optimal number of items to go into the knapsack as a function of
the number of constraints. We study the stability of the replica symmetric (RS)
solution and find that the RS calculation cannot estimate the optimal number of
items in knapsack correctly if many constraints are required.In order to obtain
a consistent solution in the RS region,we try the zero entropy approximation
for this continuous solution space and get a stable solution within the RS
ansatz.On the other hand, in replica symmetry breaking (RSB) region, the one
step RSB solution is found by Parisi's scheme. It turns out that this problem
is closely related to the problem of optimal storage capacity and of
generalization by maximum stability rule of a spherical perceptron.Comment: Latex 13 pages using IOP style file, 5 figure
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