Geometry of canonical self-similar tilings

We give several different geometric characterizations of the situation in which the parallel set $F_\epsilon$ of a self-similar set $F$ can be described by the inner $\epsilon$-parallel set $T_{-\epsilon}$ of the associated canonical tiling $\mathcal T$, in the sense of \cite{SST}. For example, $F_\epsilon=T_{-\epsilon} \cup C_\epsilon$ if and only if the boundary of the convex hull $C$ of $F$ is a subset of $F$, or if the boundary of $E$, the unbounded portion of the complement of $F$, is the boundary of a convex set. In the characterized situation, the tiling allows one to obtain a tube formula for $F$, i.e., an expression for the volume of $F_\epsilon$ as a function of $\epsilon$. On the way, we clarify some geometric properties of canonical tilings. Motivated by the search for tube formulas, we give a generalization of the tiling construction which applies to all self-affine sets $F$ having empty interior and satisfying the open set condition. We also characterize the relation between the parallel sets of $F$ and these tilings.Comment: 20 pages, 6 figure

Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable

A long-standing conjecture of Lapidus claims that under certain conditions, self-similar fractal sets fail to be Minkowski measurable if and only if they are of lattice type. The theorem was established for fractal subsets of $\mathbb{R}$ by Falconer, Lapidus and v.~Frankenhuijsen, and the forward direction was shown for fractal subsets of $\mathbb{R}^d$, $d \geq 2$, by Gatzouras. Since then, much effort has been made to prove the converse. In this paper, we prove a partial converse by means of renewal theory. Our proof allows us to recover several previous results in this regard, but is much shorter and extends to a more general setting; several technical conditions appearing in previous versions of this result have now been removed.Comment: 20 pages, 6 figure

Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators

In a previous paper by the first two authors, a tube formula for fractal sprays was obtained which also applies to a certain class of self-similar fractals. The proof of this formula uses distributional techniques and requires fairly strong conditions on the geometry of the tiling (specifically, the inner tube formula for each generator of the fractal spray is required to be polynomial). Now we extend and strengthen the tube formula by removing the conditions on the geometry of the generators, and also by giving a proof which holds pointwise, rather than distributionally. Hence, our results for fractal sprays extend to higher dimensions the pointwise tube formula for (1-dimensional) fractal strings obtained earlier by Lapidus and van Frankenhuijsen. Our pointwise tube formulas are expressed as a sum of the residues of the "tubular zeta function" of the fractal spray in $\mathbb{R}^d$. This sum ranges over the complex dimensions of the spray, that is, over the poles of the geometric zeta function of the underlying fractal string and the integers $0,1,...,d$. The resulting "fractal tube formulas" are applied to the important special case of self-similar tilings, but are also illustrated in other geometrically natural situations. Our tube formulas may also be seen as fractal analogues of the classical Steiner formula.Comment: 43 pages, 13 figures. To appear: Advances in Mathematic

Minkowski measurability results for self-similar tilings and fractals with monophase generators

In a previous paper [arXiv:1006.3807], the authors obtained tube formulas for certain fractals under rather general conditions. Based on these formulas, we give here a characterization of Minkowski measurability of a certain class of self-similar tilings and self-similar sets. Under appropriate hypotheses, self-similar tilings with simple generators (more precisely, monophase generators) are shown to be Minkowski measurable if and only if the associated scaling zeta function is of nonlattice type. Under a natural geometric condition on the tiling, the result is transferred to the associated self-similar set (i.e., the fractal itself). Also, the latter is shown to be Minkowski measurable if and only if the associated scaling zeta function is of nonlattice type.Comment: 18 pages, 1 figur

Early English Books Online and the Text Creation Partnership: Applications, Innovations, and Alternatives

Early English Books Online or EEBO is a database of more than 140,000 images of rare and early books used by scholars of history and literature for decades. EEBO is a longstanding microfilm product turned image database with established use patterns. EEBO-TCP, a set of 60,000 manually transcribed documents from EEBO, has enabled unprecedented opportunities for large-scale analysis of surviving English print. In this exploratory study, I examine the practices of teaching and research with EEBO and EEBO-TCP in American universities through findings derived from the qualitative coded insights of a focus group of professors and librarians. The focus group discussed teaching methodologies, alternative digital archives, and organizational techniques scholars and librarians have utilized in working with a EEBO and EEBO-TCP. This study is intended to provoke further research into the complex technical mediations underpinning digitization of early printed books and identify areas where academic libraries can facilitate the research process.Master of Science in Information Scienc

Family Perception of Quality in Nursing Home Care: Impact of Gender, Level of Involvement, and Utilization of Empowered CNA Teams

As the United States' baby boom generation ages, the future of nursing home care becomes increasingly important. Through this study the researcher seeks to understand quality in nursing home care from the family's perspective. Surveys were collected at one North Texas nursing home, and data were analyzed to determine how gender and level of family involvement impact their concept of quality. Further, the information in this study is aimed at clarifying if interventions, specifically empowered CNA teams, have an impact on how family members view quality. Findings are identified and recommendations for future study are made

Able Flight at Purdue: Opportunities in Technology

Developing aircraft piloting skills takes years of training with experts to meet flight certification requirements. Not everyone can reach those standards, and the challenge is even greater for those with physical disabilities. There are opportunities to modify aircraft and train physically impaired students to be pilots; however, due to the high cost, few are able to do so. Able Flight seeks to change that by providing scholarship opportunities for people with disabilities to learn to fly and opening up new educational and career opportunities. Over 30 individuals with various disabilities have received scholarships since Able Flights inception, and all have successfully completed the requirements for a sport pilots’ license

USEPA Education and Outreach Projects: Outcomes from the Great Lakes Regional Collaboration

Describes three EPA initiatives: Learn Not To Burn (Backyard Burning Reduction); Medicines in the Environment (establishing community pharmaceutical collection programs); and the Green Electronics Management Toolkit.Ope

Complainant behavioral tone, ambivalent sexism, and perceptions of sexual harassment

Previous research has examined the impact of the law on decisions made about social sexual interactions in the workplace in the context of a variety of individual difference variables including gender of the observer and sexist attitudes, as well as situational factors including legal standard and prior exposure to aggressive and submissive complainants. The current study continued this line of inquiry by testing whether hostile or benevolent sexist attitudes behaved differently under manipulated exposure to aggressive and submissive complainants. Full-time workers watched 1 videotape in which aggressive, submissive, or neutral (i.e., businesslike) women complained that male coworkers sexually harassed them; then, participants viewed a second complainant who always acted in a neutral behavioral tone. In the first case, participants high in hostile sexism who took a reasonable person perspective (but not those with a reasonable woman point of view) and all men who viewed an aggressive complainant found less evidence of harassment. With the second set of allegations, female workers who were exposed to a submissive complainant in the first case found less evidence of harassment against the neutral complainant, suggesting that exposure to a submissive complainant triggered some type of victim blaming in female workers. Policy and training implications are discussed