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

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

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

Numerical study of the effects of crack location on creep crack growth in weldment

A numerical study on the effects of crack location on creep crack growth, in a P91 weldment, was carried out using a finite element package (ABAQUS). Models of compact tension specimens were used. The obtained results showed that, the creep crack growth in the weld metal are much higher than that in the parent metal. However, the creep crack growth in cross-weld specimens is controlled by the properties of the weakest component of the weld. This highlights the importance of the heat affected zone (HAZ) as the weakest region of the weldment. Effects of the width of HAZ are presented, too