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

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 $[0,1]^d$ for $d \in \mathbb{N}$ 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