Harmonic equiangular tight frames comprised of regular simplices

An equiangular tight frame (ETF) is a sequence of unit-norm vectors in a Euclidean space whose coherence achieves equality in the Welch bound, and thus yields an optimal packing in a projective space. A regular simplex is a simple type of ETF in which the number of vectors is one more than the dimension of the underlying space. More sophisticated examples include harmonic ETFs which equate to difference sets in finite abelian groups. Recently, it was shown that some harmonic ETFs are comprised of regular simplices. In this paper, we continue the investigation into these special harmonic ETFs. We begin by characterizing when the subspaces that are spanned by the ETF's regular simplices form an equi-isoclinic tight fusion frame (EITFF), which is a type of optimal packing in a Grassmannian space. We shall see that every difference set that produces an EITFF in this way also yields a complex circulant conference matrix. Next, we consider a subclass of these difference sets that can be factored in terms of a smaller difference set and a relative difference set. It turns out that these relative difference sets lend themselves to a second, related and yet distinct, construction of complex circulant conference matrices. Finally, we provide explicit infinite families of ETFs to which this theory applies

Acoustic properties of fine‐grained sediments from Emerald Basin: Toward an inversion for physical properties using the Biot–Stoll model

Acoustic data from two long cores, comprising marine clays and silts taken from Emerald Basin off Nova Scotia, are presented. High‐resolution measurements of compressional wavevelocity,attenuation, and power law exponent are made using ultrasonic frequencies between 100 to 1000 kHz. The observed values of the frequency dependence of attenuation suggest that a nonconstant Q mechanism is needed to explain these data, and Biot–Stoll theory is used to model the experimental results. An inversion scheme is used to constrain physical parameters in the Biot–Stoll dispersion relation. The inversion shows that there is a restricted range of permeability and grain size. By assigning reasonable values for grain size in the inversion, the Biot–Stoll model predicts unique values for the permeability and frame bulk modulus that agree well with estimates made by other means

Calculation of acoustic parameters by a filter-correlation method

This paper presents the filter correlation method, a technique for extracting consistent and accurate estimates of attenuation parameters from acoustic waveform data. The method minimizes problems associated with short time windows and multipath secondary arrivals. The method comprises two stages: a causal passband filter stage followed by a cross-correlation step. The results of the filter-correlation estimator are compared to those of the spectral difference approach for short time series with and without a secondary multipath arrival. Preliminary analyses of acoustic data collected on cored marine silts and clays show the attenuation properties of these materials cannot be described by a constant Q mechanism. The filter correlation method refines estimates of frequency-dependent velocity, revealing a small but systematic anisotropy between measurements made parallel and transverse to the sediments\u27 bedding plane. The observed velocity anisotropy can be modeled by assuming layered porosity variations in the cored sediments. No systematic anisotropy in attenuation was observed

Radiation heating in selected NERVA engine components

The role of heating from nuclear radiation in design of the NERVA engine is treated. Some components are subjected to very high gamma heating rates in excess of 0.5 Btu/cubic inch/sec in steel in the primary nozzle or 0.25 Btu/cubic inch/sec in aluminum in the pressure vessel. These components must be cooled by a fraction of the liquid hydrogen propellant before it is passed through the core, heated, and expanded out the nozzle as a gas. Other components that are subjected to lower heating rates such as the thrust structure and the disk shield are designed so that they would not require liquid hydrogen cooling. Typical gamma and neutron heating rates, resulting temperatures, and their design consequences are discussed. Calculational techniques used in the nuclear and thermal analyses of the NERVA engine are briefly treated

Spillovers from the Gridiron: Evidence from Women’s Collegiate Basketball

This paper empirically investigates whether schools with an intercollegiate football team experience greater attendance at women’s basketball games. The empirical question is important because if football increases attendance and hence revenue to other sports then these benefits should be included when considering the net benefits of football. Using a cross-section of 329 Division IA women’s basketball programs from 2005-2006, we find that having a football program corresponds with an increase in per-game attendance of approximately 500 people. This spill-over benefit of having a football team should be credited against the costs of starting and maintaining a football team.NCAA, college sports, positive externalities

Prevalence and Use of Fitness Tracking Devices within a College Community

Purpose: Wearable devices for tracking health and fitness related activities are thought to motivate individuals to participate in regular exercise. The purpose of this study was to examine the frequency of these wearable fitness tracking devices in a college setting. Methods: Students, faculty, administration, and staff of Linfield College were asked to complete a survey that examined the types of fitness tracking devices owned, frequency of use, and application of the device. Results: Of 217 participants surveyed (67 males, 150 females), 29.49% own a fitness tracker, with the most common types being a phone app (46.2% of faculty, staff, and administration) and a specific wearable wrist device (44.7% of students). Step count tracking was the most popularly used feature among all participants (86.8% of students and 96.2% of faculty, staff, and administration). 84% of all participants reported that the device encouraged their participation in physical activity. For those not owning a device (70.51% of participants), lack of interest was the most prevalent reason reported against purchasing a device, followed by expense. Conclusion: Our results suggest that a small percentage of individuals across a college community own fitness tracking devices, despite the fact that they are perceived to encourage physical activity