A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

Distributed Transmission Line Phase Shifter with Loaded BST Capacitors using Thick Film Technology

A thick-film phase shifter fabricated from screenprinted ferroelectric capacitors and metallization is described. At 30 GHz a phase shift of 4º/dB at 1kV mm-1 was achieved. The phase shift less dependent on frequency than conventional transmission-line phase design

Applications of p-deficiency and p-largeness

We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large, which implies that Schlage-Puchta's infinite finitely generated p-groups are not finitely presented. We also show that for all primes p at least 7, any group having a presentation of p-deficiency greater than 1 is Golod-Shafarevich, and has a finite index subgroup which is Golod-Shafarevich for the remaining primes. We also generalise a result of Grigorchuk on Coxeter groups to odd primes.Comment: 23 page

Effects of truck traffic on top-down fatigue cracking performance of flexible pavements using a new mechanics-based analysis framework

The mechanics-based analysis framework predicts top-down fatigue cracking initiation time in asphalt concrete pavements by utilising fracture mechanics and mixture morphology-based property. To reduce the level of complexity involved, traffic data were characterised and incorporated into the framework using the equivalent single axle load (ESAL) approach. There is a concern that this kind of simplistic traffic characterisation might result in erroneous performance predictions and pavement structural designs. This paper integrates axle load spectra and other traffic characterisation parameters into the mechanics-based analysis framework and studies the impact these traffic characterisation parameters have on predicted fatigue cracking performance. The traffic characterisation inputs studied are traffic growth rate, axle load spectra, lateral wheel wander and volume adjustment factors. For this purpose, a traffic integration approach which incorporates Monte Carlo simulation and representative traffic characterisation inputs was developed. The significance of these traffic characterisation parameters was established by evaluating a number of field pavement sections. It is evident from the results that all the traffic characterisation parameters except truck wheel wander have been observed to have significant influence on predicted top-down fatigue cracking performance

Maximal Voluntary Activation of the Elbow Flexors Is under Predicted by Transcranial Magnetic Stimulation Compared to Motor Point Stimulation Prior to and Following Muscle Fatigue

Transcranial magnetic (TMS) and motor point stimulation have been used to determine voluntary activation (VA). However, very few studies have directly compared the two stimulation techniques for assessing VA of the elbow flexors. The purpose of this study was to compare TMS and motor point stimulation for assessing VA in non-fatigued and fatigued elbow flexors. Participants performed a fatigue protocol that included twelve, 15 s isometric elbow flexor contractions. Participants completed a set of isometric elbow flexion contractions at 100, 75, 50, and 25% of maximum voluntary contraction (MVC) prior to and following fatigue contractions 3, 6, 9, and 12 and 5 and 10 min post-fatigue. Force and EMG of the bicep and triceps brachii were measured for each contraction. Force responses to TMS and motor point stimulation and EMG responses to TMS (motor evoked potentials, MEPs) and Erb's point stimulation (maximal M-waves, Mmax) were also recorded. VA was estimated using the equation: VA% = (1−SITforce/PTforce) × 100. The resting twitch was measured directly for motor point stimulation and estimated for both motor point stimulation and TMS by extrapolation of the linear regression between the superimposed twitch force and voluntary force. MVC force, potentiated twitch force and VA significantly (p < 0.05) decreased throughout the elbow flexor fatigue protocol and partially recovered 10 min post fatigue. VA was significantly (p < 0.05) underestimated when using TMS compared to motor point stimulation in non-fatigued and fatigued elbow flexors. Motor point stimulation compared to TMS superimposed twitch forces were significantly (p < 0.05) higher at 50% MVC but similar at 75 and 100% MVC. The linear relationship between TMS superimposed twitch force and voluntary force significantly (p < 0.05) decreased with fatigue. There was no change in triceps/biceps electromyography, biceps/triceps MEP amplitudes, or bicep MEP amplitudes throughout the fatigue protocol at 100% MVC. In conclusion, motor point stimulation as opposed to TMS led to a higher estimation of VA in non-fatigued and fatigued elbow flexors. The decreased linear relationship between TMS superimposed twitch force and voluntary force led to an underestimation of the estimated resting twitch force and thus, a reduced VA

Models and metaphors: complexity theory and through-life management in the built environment

Complexity thinking may have both modelling and metaphorical applications in the through-life management of the built environment. These two distinct approaches are examined and compared. In the first instance, some of the sources of complexity in the design, construction and maintenance of the built environment are identified. The metaphorical use of complexity in management thinking and its application in the built environment are briefly examined. This is followed by an exploration of modelling techniques relevant to built environment concerns. Non-linear and complex mathematical techniques such as fuzzy logic, cellular automata and attractors, may be applicable to their analysis. Existing software tools are identified and examples of successful built environment applications of complexity modelling are given. Some issues that arise include the definition of phenomena in a mathematically usable way, the functionality of available software and the possibility of going beyond representational modelling. Further questions arising from the application of complexity thinking are discussed, including the possibilities for confusion that arise from the use of metaphor. The metaphor of a 'commentary machine' is suggested as a possible way forward and it is suggested that an appropriate linguistic analysis can in certain situations reduce perceived complexity

Elastic and inelastic scattering of 240-MeV (6)Li ions from (40)Ca and (48)Ca and tests of a systematic optical potential

Journals published by the American Physical Society can be found at http://publish.aps.org/Elastic and inelastic scattering of 240-MeV (6)Li particles from (40)Ca and (48)Ca were measured with the multipole-dipole-multipole spectrometer from 4 degrees <= theta(c.m.) <= 40 degrees. Optical potential parameters were obtained by fitting the elastic-scattering data with the double-folding model using the density-dependent M3Y NN effective interaction and B(E2) and B(E3) values obtained for low-lying 2(+) and 3(-) states agreed with the adopted values. The results are compared with those obtained using potentials derived from the systematics of potentials previously obtained for (24)Mg, (28)Si, (58)Ni, and (90)Zr. Cross sections for excitation of giant resonances were also calculated with the potentials obtained

Assessment of New Hub-and-spoke and Point-to-point Airline Network Configurations

This paper aims to provide new measures of airline network configuration with a view to analyse effectively the complexity of modern carriers' network design. It studies network configurations in the airline sector by taking into account both spatial and temporal dimensions. The spatial dimension is measured by using both the Gini index and the Freeman index, which originate from social science research. The temporal dimension is measured by the connectivity ratio, i.e. the share of indirect connections over the total number of connections. According to these indicators, the configuration of the largest full-service carriers and the largest low-cost carriers in Europe is investigated. The results show that the temporal dimension provides a clear distinction between full-service carriers and low-cost carriers; while the spatial dimension appears useful when identifying the peculiarities within groups