On the Sequence of Pedal Triangles

Although geometers have studied the properties of triangles for over two thousand years, there still remain problems of interest involving operations performed infinitely often. A given triangle T_0 generates a sequence of triangles T_n where T_(n+1) is the pedal triangle of T_n. This sequence was discussed by Hobson (1897, 1925) but, while his formulae for the transition from T_n to T_(n+1) are correct, those for T_n in terms of T_0 are not. Lacking correct formulae, we experimented numerically, taking the angles of T_0 to be integers in degrees. To our surprise the angles in the pedal sequence became periodic with periods of 12 steps. The explanation of this curious fact led to a general investigation of pedal sequences, revealing that (a) the sequence may stop by degeneration of the triangle to a straight segment, (b) the angles may develop any periodicity, or (c) the sequence may proceed to infinity without any periodicity. We give necessary and sufficient conditions on the angles of T_0 corresponding to these options, and discuss the periodic case in some detail

Anomalously small wave tails in higher dimensions

We consider the late-time tails of spherical waves propagating on even-dimensional Minkowski spacetime under the influence of a long range radial potential. We show that in six and higher even dimensions there exist exceptional potentials for which the tail has an anomalously small amplitude and fast decay. Along the way we clarify and amend some confounding arguments and statements in the literature of the subject.Comment: 13 page

Use of island and mainland shorelines by woodland caribou during the nursery period in two northern Ontario parks

Predation is considered a primary limiting factor of woodland caribou (Rangifer tarandus caribou) populations across North America. Caribou are especially vulnerable to predation during their first few weeks of life and have evolved space-use strategies to reduce predation risk through habitat selection during the critical calving and nursery period. We assessed landscape-scale physical characteristics and landcover types associated with caribou nursery sites in Wabakimi and Woodland Caribou Provincial Parks in northern Ontario to better understand nursery site selection in relatively undisturbed landscapes. Although free from industrial activity, these protected areas may subject caribou to human recreational disturbance, so our secondary objective was to evaluate female caribou nursery site selection relative to human recreational activities. We determined that parturient caribou selected landscape characteristics at multiple spatial scales that may reduce predation risk during the calving and nursery period. Generally, female caribou in both parks selected larger lakes with larger than average sized islands configured within shorter than average distances to other islands or landforms that might facilitate escape from predators. The majority of caribou nursery areas in both parks occurred on islands rather than the mainland shoreline of lakes that were surveyed. The nearest landform for escape from these nursery sites on islands was typically another island, and most often 2-3 islands, suggesting parturient caribou may choose islands clustered together as part of their escape strategy. In Woodland Caribou Provincial Park, caribou nursery sites occurred more often in coniferous landcover than expected from availability, while in Wabakimi Provincial Park caribou used sparse, mixed and coniferous forests for nursery activity. Caribou cow-calf pairs typically used areas for nursery activity that were 9.1 km (± 1.0 km, range 2.3-20.6 km) in Wabakimi Provincial Park and 10.2 km (± 0.7 km, range 0.7-32.6 km) in Woodland Caribou Provincial Park from any human recreational disturbance. These landscape-scale physical characteristics and landcover types associated with caribou nursery sites may be used to predict locations of potential caribou nursery areas both outside and within protected areas for the provision of adequate protection and to ensure the persistence of this valued species

Infrared Instrumentation and Astronomy

Contains research objectives and summary of research on four research projects.Joint Services Electronics Program (Contract DAAB07-75-C-1346)National Aeronautics and Space Administration (Grant NGR 22-009-526)National Aeronautics and Space Administration (Contract NAS5-22828

Gravitation Research

Contains research objectives and summary of research.National Aeronautics and Space Administration (Grant NGR 22-009-526)Joint Services Electronics Program (Contract DAAB07-71-C-0300

Covariation Among Vowel Height Effects on Acoustic Measures

Covariation among vowel height effects on vowel intrinsic fundamental frequency (IF0), voice onset time (VOT), and voiceless interval duration (VID) is analyzed to assess the plausibility of a common physiological mechanism underlying variation in these measures. Phrases spoken by 20 young adults, containing words composed of initial voiceless stops or /s/ and high or low vowels, were produced in habitual and voluntarily increased F0 conditions. High vowels were associated with increased IF0 and longer VIDs. VOT and VID exhibited significant covariation with IF0 only for males at habitua

‘It’s better than daytime television’: questioning the socio-spatial impacts of massage parlours on residential communities

It has been shown that street sex work is problematic for some communities, but there is less evidence of the effects of brothels. Emerging research also suggests that impact discourses outlined by residential communities and in regulatory policies should be critiqued, because they are often based on minority community voices, and limited tangible evidence is used to masquerade wider moral viewpoints about the place of sex work. Using a study of residents living in close proximity to brothels in Blackpool, this paper argues that impact is socially and spatially fluid. Impact needs to be evaluated in a more nuanced manner, which is considerate of the heterogeneity of (even one type of) sex work, and the community in question. Brothels in Blackpool had a variety of roles in the everyday socio-spatial fabric; thus also questioning the common assumption that sex work only impacts negatively on residential communities