584 research outputs found

    Diffraction from visible lattice points and k-th power free integers

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    We prove that the set of visible points of any lattice of dimension at least 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settles previous speculation on the exact nature of the diffraction in this situation, see math-ph/9903046 and references therein. Using similar methods we show the same result for the 1-dimensional set of k-th power free integers with k at least 2. Of special interest is the fact that neither of these sets is a Delone set --- each has holes of unbounded inradius. We provide a careful formulation of the mathematical ideas underlying the study of diffraction from infinite point sets.Comment: 45 pages, with minor corrections and improvements; dedicated to Ludwig Danzer on the occasion of his 70th birthda

    Using Videoconferencing to Establish and Maintain a Social Presence in Online Learning Environments

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    For 30 years, the educational administration program faculty at Fort Hays State University (FHSU) followed a traditional face-to-face (F2F) on campus approach to course delivery

    Escape tactics used by bluegills and fathead minnows to avoid predation by tiger muskellunge

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    To explain why esocids prefer cylindrical, soft-rayed prey over compressed, spiny-rayed prey, we quantified behavioral interaction between tiger muskellunge (F1 hybrid of male northern pike Esox lucius and female muskellunge E. masquinongy) and fathead minnows (Pimephales promelas) and bluegills (Lepomis macrochirus). Tiger muskellunge required four times as many strikes and longer pursuits to capture bluegills than fathead minnows. Tiger muskellunge attacked each prey species differently; fathead minnows were grasped at midbody and bluegills were attacked in the caudal area. Each prey species exhibited different escape tactics. Fathead minnows remained in open water and consistently schooled; bluegills dispersed throughout the tank and sought cover by moving to corners and edges. Due to their antipredatory behavior (dispersing, cover seeking, and remaining motionless) and morphology (deep body and spines), bluegills were less susceptible to capture by tiger muskellunge than were fathead minnows.Funding for this project was provided by the Federal Aid in Fish Restoration Act under Dingell-Johnson Project F-57-R

    How model sets can be determined by their two-point and three-point correlations

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    We show that real model sets with real internal spaces are determined, up to translation and changes of density zero by their two- and three-point correlations. We also show that there exist pairs of real (even one dimensional) aperiodic model sets with internal spaces that are products of real spaces and finite cyclic groups whose two- and three-point correlations are identical but which are not related by either translation or inversion of their windows. All these examples are pure point diffractive. Placed in the context of ergodic uniformly discrete point processes, the result is that real point processes of model sets based on real internal windows are determined by their second and third moments.Comment: 19 page

    Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces

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    Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead spaces with p-adic topologies or even with mixed Euclidean/p-adic topologies. We show that a number of well known tilings precisely fit this form, including the chair tiling and the Robinson square tilings. Thus the scope of the cut and project formalism is considerably larger than is usually supposed. Applying the powerful consequences of model sets we derive the diffractive nature of these tilings.Comment: 11 pages, 2 figures; dedicated to Peter Kramer on the occasion of his 65th birthda

    Weighted Dirac combs with pure point diffraction

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    A class of translation bounded complex measures, which have the form of weighted Dirac combs, on locally compact Abelian groups is investigated. Given such a Dirac comb, we are interested in its diffraction spectrum which emerges as the Fourier transform of the autocorrelation measure. We present a sufficient set of conditions to ensure that the diffraction measure is a pure point measure. Simultaneously, we establish a natural link to the theory of the cut and project formalism and to the theory of almost periodic measures. Our conditions are general enough to cover the known theory of model sets, but also to include examples such as the visible lattice points.Comment: 44 pages; several corrections and improvement

    Functional Movement Screentm Scores in Collegiate Track and Field Athletes in Relation to Injury Risk and Performance

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    Purpose: The purpose of this study was to examine the relationship between Functional Movement Screentm (FMS) scores, injury rate, and performance in collegiate track and field athletes. Methods: Forty seven male (n=17) and female (n=30) competitive track and field athletes at an NCAA Division I university volunteered for this study. As part of their regular team assessment, the athletes were evaluated on three separate occasions using the FMS tool: in August, one week prior to the start of university organized practice for the fall (T1); in December, one week prior to the end of the fall academic semester (T2); and in March, the week following the conclusion of the indoor competition season (T3). The FMS consists of the performance of seven fundamental movement patterns that are evaluated and scored by a trained professional. For each time point, athletes were divided into two categories based on total FMS score (≤14 and ≥15). Throughout the competitive season, injuries were tracked and categorized as either mild (no loss of practice or competition time) or moderate/severe (loss of practice or competition time). As part of an ongoing injury prevention program, athletes performed generalized corrective exercises for 15 min 2-3 times per week. The performance in the last event of the season (conference meet) was also recorded. Results: Average FMS scores significantly (p\u3c0.05) decreased across the three time points (Mean ± SD, T1: 15.5 ± 2.2, T2: 14.9 ± 1.8, T3: 14.7 ± 1.6) despite that generalized corrective exercises were performed. Analyses of results found no association between FMS scores and likelihood to sustain a moderate/severe injury. Athletes with a score of ≤14 on the FMS at T1 were 3.1 times more likely not to place in the top 8 at the conference meet. 53% of the athletes who had a score of ≥15 at T1 placed in the top 8 at the meet while only 27% of athletes with a score of ≤14 at T1 placed in the top 8 at the meet. Conclusion: FMS scores ≤14 indicate reduced performance ability but not increased likelihood of injury in track and field athletes

    Extinctions and Correlations for Uniformly Discrete Point Processes with Pure Point Dynamical Spectra

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    The paper investigates how correlations can completely specify a uniformly discrete point process. The setting is that of uniformly discrete point sets in real space for which the corresponding dynamical hull is ergodic. The first result is that all of the essential physical information in such a system is derivable from its nn-point correlations, n=2,3,>...n= 2, 3, >.... If the system is pure point diffractive an upper bound on the number of correlations required can be derived from the cycle structure of a graph formed from the dynamical and Bragg spectra. In particular, if the diffraction has no extinctions, then the 2 and 3 point correlations contain all the relevant information.Comment: 16 page

    Diffractive point sets with entropy

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    After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of lattice gases. We show that taking the site occupation of a model set stochastically results, with probabilistic certainty, in well-defined diffractive properties augmented by a constant diffuse background. We discuss both the case of independent, but identically distributed (i.i.d.) random variables and that of independent, but different (i.e., site dependent) random variables. Several examples are shown.Comment: 25 pages; dedicated to Hans-Ude Nissen on the occasion of his 65th birthday; final version, some minor addition
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