Unimodular integer circulants associated with trinomials

The n � n circulant matrix associated with the polynomial [image removed] (with d < n) is the one with first row (a0 ? ad 0 ? 0). The problem as to when such circulants are unimodular arises in the theory of cyclically presented groups and leads to the following question, previously studied by Odoni and Cremona: when is Res(f(t), tn-1) = �1? We give a complete answer to this question for trinomials f(t) = tm � tk � 1. Our main result was conjectured by the author in an earlier paper and (with two exceptions) implies the classification of the finite Cavicchioli?Hegenbarth?Repov? generalized Fibonacci groups, thus giving an almost complete answer to a question of Bardakov and Vesnin

The mass of (1) Ceres from perturbations on (348) May

The most promising ground-based technique for determining the mass of a minor planet is the observation of the perturbations it induces in the motion of another minor planet. This method requires careful observation of both minor planets over extended periods of time. The mass of (1) Ceres has been determined from the perturbations on (348) May, which made three close approaches to Ceres at intervals of 46 years between 1891 and 1984. The motion of May is clearly influenced by Ceres, and by using different test masses for Ceres, a search was made to determine the mass of Ceres that minimizes the residuals in the observations of May

Nordic Himalaya Research Network (NHRN) First Inaugural Meeting

On May 7, 2018, the inaugural meeting for the newly established Nordic Himalaya Research Network was held at the Department of Cross-Cultural and Regional Studies at the University of Copenhagen

It is always on your mind: Experiences and perceptions of falling of older people and their carers and the potential of a mobile falls detection device

Copyright © 2013 Veronika Williams et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background. Falls and fear of falling present a major risk to older people as both can affect their quality of life and independence. Mobile assistive technologies (AT) fall detection devices may maximise the potential for older people to live independently for as long as possible within their own homes by facilitating early detection of falls. Aims. To explore the experiences and perceptions of older people and their carers as to the potential of a mobile falls detection AT device. Methods. Nine focus groups with 47 participants including both older people with a range of health conditions and their carers. Interviews were audio recorded, transcribed verbatim, and thematically analysed. Results. Four key themes were identified relating to participants’ experiences and perceptions of falling and the potential impact of a mobile falls detector: cause of falling, falling as everyday vulnerability, the environmental context of falling, and regaining confidence and independence by having a mobile falls detector. Conclusion. The perceived benefits of a mobile falls detector may differ between older people and their carers. The experience of falling has to be taken into account when designing mobile assistive technology devices as these may influence perceptions of such devices and how older people utilise them.European Commissio

How terrestrial planets traverse spin-orbit resonances: A camel goes through a needle's eye

The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into account the frequency-dependent quality factors and Love numbers. The torque equations are integrated numerically with a small step in time, includng the oscillating triaxial torque components but neglecting the layered structure of the planet and assuming a zero obliquity. We find that a Mercury-like planet with its current value of orbital eccentricity (0.2056) is always captured in the 3:2 resonance. The probability of capture in the higher 2:1 resonance is approximately 0.23. These results are confirmed by a semi-analytical estimation of capture probabilities as functions of eccentricity for both prograde and retrograde evolution of spin rate. As follows from analysis of equilibrium torques, entrapment in the 3:2 resonance is inevitable at eccentricities between 0.2 and 0.41. Considering the phase space parameters at the times of periastron, the range of spin rates and phase angles, for which an immediate resonance passage is triggered, is very narrow, and yet, a planet like Mercury rarely fails to align itself into this state of unstable equilibrium before it traverses the 2:1 resonance.Comment: 10 figures. Fig. 8 may be corrupted when printed on some printers but shows fine in the PDF file. Submitted in ApJ v. 2: the probabilities of capture of Mercury in 2:1 resonance are re-evaluated; a general formula for capture probability derived. v3: accepted in ApJ under a different title: Conditions of passage and entrapment of terrestrial planets in spin-orbit resonance

Development of an ultra-low-shock separation nut

The technical problems encountered in the development of an advanced separation nut design are described. The nut is capable of sustaining a large preload and releasing that load with a low level of induced pyrotechnic shock, while demonstrating a tolerance for extremely high shock imposed by other pyrotechnic devices. The analysis of the separation nut was performed to acquire additional understanding of the phenomena affecting operation of the nut and to provide quantitative evaluation of design modification for aerospace applications

Notched and Unnotched Fatigue Behavior of Angle-Ply Graphite/Epoxy Composites

The axial fatigue behavior of both notched and unnotched graphite/epoxy composites was studied. In unnotched studies, conducted on a 0/+ or - 30 3S AS/3501 laminate, S-N curves were determined for various stress ratios R using simply supported test specimens. Apparent fatigue limits in tension-tension (T-T) and compression-compression (C-C) cycling occurred at about 60% of the respective static strengths. The overall results were expressed in the form of a constant life diagram showing the relationship between mean stress and stress amplitude. The diagram illustrates a skew-symmetry in fatigue life caused by the relatively low compressive strength of the unrestrained test specimens used. In effect, a maximum in fatigue properties occurs at a positive value of mean stress. Results are of significance in situations where structural members are buckling or crippling critical in design