84,096 research outputs found
A note on the 1-prevalence of continuous images with full Hausdorff dimension
We consider the Banach space consisting of real-valued continuous functions
on an arbitrary compact metric space. It is known that for a prevalent (in the
sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the
image is as large as possible, namely 1. We extend this result by showing that
`prevalent' can be replaced by `1-prevalent', i.e. it is possible to
\emph{witness} this prevalence using a measure supported on a one dimensional
subspace. Such one dimensional measures are called \emph{probes} and their
existence indicates that the structure and nature of the prevalence is simpler
than if a more complicated `infinite dimensional' witnessing measure has to be
used.Comment: 8 page
An empirical investigation of the effect of corporate charter antitakeover amendments on stockholder wealth
The Hausdorff dimension of graphs of prevalent continuous functions
We prove that the Hausdorff dimension of the graph of a prevalent continuous
function is 2. We also indicate how our results can be extended to the space of
continuous functions on for and use this to obtain
results on the `horizon problem' for fractal surfaces. We begin with a survey
of previous results on the dimension of a generic continuous function
Bondi-Sachs Energy-Momentum for the CMC Initial Value Problem
The constraints on the asymptotic behavior of the conformal factor and
conformal extrinsic curvature imposed by the initial value equations of general
relativity on constant mean extrinsic curvature (CMC) hypersurfaces are
analyzed in detail. We derive explicit formulas for the Bondi-Sachs energy and
momentum in terms of coefficients of asymptotic expansions on CMC hypersurfaces
near future null infinity. Precise numerical results for the Bondi-Sachs
energy, momentum, and angular momentum are used to interpret physically
Bowen-York solutions of the initial value equations on conformally flat CMC
hypersurfaces of the type obtained earlier by Buchman et al. [Phys. Rev. D
80:084024 (2009)].Comment: version to be published in Phys. Rev.
Making Photographs Speak
It has often been said that “a picture is worth a thousand words.” Making that picture spit out those mythical thousand words, as we can all attest, is no easy task. Over the course of the first half of the fall semester, the three of us were tasked with developing brief interpretive captions for two Civil War photographs each, with the end goal to display our work at the Civil War Institute’s 2019 Summer Conference. What initially appeared as a simple project quickly revealed itself to be a difficult, yet rewarding, challenge that taught us all important lessons concerning history, photography, and writing that we will not soon forget. Producing the photography exhibit enhanced our skills as historical writers, introduced us to the challenge of writing for a popular audience, and deepened our understanding of Civil War photography. [excerpt
Open/Closed String Topology and Moduli Space Actions via Open/Closed Hochschild Actions
In this paper we extend our correlation functions to the open/closed case.
This gives rise to actions of an open/closed version of the Sullivan PROP as
well as an action of the relevant moduli space. There are several unexpected
structures and conditions that arise in this extension which are forced upon us
by considering the open sector. For string topology type operations, one cannot
just consider graphs, but has to take punctures into account and one has to
restrict the underlying Frobenius algebras. In the moduli space, one first has
to pass to a smaller moduli space which is closed under open/closed duality and
then consider covers in order to account for the punctures
Masers and the Massive Star Formation Process: New Insights Through Infrared Observations
Our mid-infrared and near-infrared surveys over the last five years have
helped to strengthen and clarify the relationships between water, methanol, and
OH masers and the star formation process. Our surveys show that maser emission
seems to be more closely associated with mid-infrared emission than cm radio
continuum emission from UC HII regions. We find that masers of all molecular
species surveyed trace a wide variety of phenomena and show a proclivity for
linear distributions. The vast majority of these linear distributions can be
explained by outflows or shocks, and in general do not appear to trace
circumstellar disks as was previously thought. Some water and methanol masers
that are not associated with radio continuum emission appear to trace
infrared-bright hot cores, the earliest observable stage of massive stellar
life before the onset of a UC HII region.Comment: 6 pages, 3 figures, to appear in the proceedings of IAU Symposium
227: "Massive Star Birth: A Crossroads of Astrophysics", version with
full-resolution images available at http://www.ctio.noao.edu/~debuize
12 and 18 micron images of dust surrounding HD 32297
We present the first subarcsecond-resolution images at multiple mid-IR
wavelengths of the thermally-emitting dust around the A0 star HD 32297. Our
observations with T-ReCS at Gemini South reveal a nearly edge-on resolved disk
at both 11.7 microns and 18.3 microns that extends ~150 AU in radius. The
mid-IR is the third wavelength region in which this disk has been resolved,
following coronagraphic observations by others of the source at optical and
near-IR wavelengths. The global mid-IR colors and detailed consideration of the
radial color-temperature distribution imply that the central part of the disk
out to ~80 AU is relatively deficient in dust.Comment: 4 pages, 3 figures; accepted for publication in ApJ
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