8,380 research outputs found
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
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
Structural Phases of Bounded Three-Dimensional Screened Coulomb Clusters (Finite Yukawa System)
The formation of three-dimensional (3D) dust clusters within a complex plasma
modeled as a spatially confined Yukawa system is simulated using the box_tree
code. Similar to unscreened Coulomb clusters, the occurrence of concentric
shells with characteristic occupation numbers was observed. Both the occupation
numbers and radii were found to depend on the Debye length. Ground and low
energy meta-stable states of the shielded 3D Coulomb clusters were determined
for 4<N<20. The structure and energy of the clusters in different states was
analyzed for various Debye lengths. Structural phase transitions, including
inter-shell structural phase transitions and intra-shell structural phase
transitions, were observed for varying Debye length and the critical value for
transitions calculated
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Research Reports from the Programme for Belize Archaeological Project, Volume Seven
Table of Contents : Background and Introduction to the 2012 Season of the Programme for Belize Archaeological Project / by Fred Valdez, Jr. and Grant Aylesworth (p.1-6) -- The Architecture and Environs of Structure 3: 2012 Season / by Debora Trein (p.7-34) -- Report of the 2012 Excavations at the South Ballcourt of La Milpa, Operation A6 / by David Chatelain (p.35-38) -- Overview of the 2012 La Milpa Archaeological Field Season / by Brandon s. Lewis, Yoav Me-Bar, Scott Guzman, and Leon de Santillan (p.39-54) -- Several Burials from La Milpa, LM4 in NW Belize / by Stacy Drake (p.55-58) -- Report in the 2012 Excavations at Hun Tun: Operation 5 / by Robyn L. Dodge (p.59-68) -- Research Results of the 2012 Field Season: Excavations at the Tapir Group of the Medicinal Trail Site / by David M. Hyde (p.67-90) -- Mapping Medicinal Trail: A Summary from 2004 to 2012 / by Jeff Brewer, David M. Hyde, and Michael Stowe (p.91-112) -- The 2012 Season of Survey and Excavation at La Milpa North / by Eric J. Heller (p.113-130) -- Preliminary Investigations at RB 71: The 2012 Field Season / by Nicole DeFrancisco and Cory Stevenson (p.131-140) -- Preliminary Report on the 2012 Field Season at Maax Na and Bolsa Verde, Belize / by Eleanor M. King and Leslie C. Shaw (p.141-154) -- Summary Report of Field Investigations at the Site of Dos Hombres, Summer 2012 Season / by Rissa M. Trachman and Jacob A. Canterbury (p.155-164) -- Field Investigations at Chawak But’o’ob: Preliminary Overview of the 2012 Season / Stan Walling (p.165-178) -- Ancient Maya Land Use and Today’s Environment: A Multidisciplinary Research Program / by Nicholas Brokaw (p.179-186) -- Summary Report of the 2012 Obsidian Provenance Project for PfBAP / by Walter Beckwith (p.187-188) -- Application of Low-Field Magnetic Susceptibility to Plaster Floors in Excavation Profiles at Maya Sites in the Three Rivers Region, Belize / by Michael Brennan (p.189)Texas Archeological Research Laborator
Recommended from our members
Research Reports from the Programme for Belize Archaeological Project, Volume Six
Table of Contents : Background and Introduction to the 2011 Season of the Programme for Belize Archaeological Project / by Fred Valdez, Jr. and Marisol Cortes-Rincon (p.1-4) -- Investigations at Structure 3, La Milpa: The 2011 Field Season / by Debora Trein (p.5-32) -- Report of the 2011 Excavations at the South Ballcourt of La Milpa, Op A6 / by David Chatelain (p.33-44) -- Summary of the 2011 Activities of the La Milpa Core Project / by Brett A. Houk and Gregory Zaro (p.45-54) -- Summary of 2011 Field Season: Examination of Extended Lineages Associated with Courtyards 135 & 149 at La Milpa, Belize / by Brandon S. Lewis (p.55-58) -- Report on a Northern Residential Complex at La Milpa, Belize: Operation LM4 / by Deanna M. Riddick (p.59-62) -- Preliminary Notes on a Chultun Burial at La Milpa – LM-4 / by Stacy Drake (p.63-68) -- Excavations at Groups B and C, Say Kah, Belize, 2011 / by Sarah E. Jackson and Linda A. Brown (p.69-102) -- Hun Tun Archaeology: Report on the 2011 Field Season / by Robyn L. Dodge (p.103-114) -- Aguada Lagunita Elusiva (RB Lagunita), La Milpa East (RB LME) and Results of the 2011 Explorations along the LaMap East Transect Extension / by Estella Weiss-Krejci and Michael Brandl (p.115-126) -- Towards a Biography Of Place: The 2011 Season of Survey and Excavation at La Milpa North / by Eric J. Heller (p.127-144) -- Phase 2 Research at Wari Camp (RB-56): Summer 2011 / by Laura Levi (p.145-152) -- Summary Report of Investigations at the Site of Dos Hombres: Summer 2011 / by Rissa M. Trachman and Katherine MacDonald (p.153-158) -- Preliminary Report on the 2011 Activities of the Mount Allison University Archaeological Field School in Belize / by Grant R. Aylesworth (p.159-162) -- Tree Species Composition at Medicinal Trail Group A / by Nicholas Brokaw and Sheila Ward (p.163-164) -- Report on Some Stone Tools from RB 18, Northwest Belize: Guijarral and the Chispas Group / by David M. Hyde (p.165)Texas Archeological Research Laborator
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