Optimal-Partitioning Inequalities for Nonatomic Probability Measures

Suppose μ1,...,μn are nonatomic probability measures on the same measurable space (S, B). Then there exists a measurable partition {Si}ni=1 of S such that μi(Si) ≥ (n + 1 - M)-1 for all i = 1,...,n, where M is the total mass of Vni=1μ1 (the smallest measure majorizing each μi). This inequality is the best possible for the functional M, and sharpens and quantifies a well-known cake-cutting theorem of Urbanik and of Dubins and Spanier. Applications are made to L1-functions, discrete allocation problems, statistical decision theory, and a dual problem

Design and fabrication of highly efficient non-linear optical devices for implementing high-speed optical processing

We present the design and fabrication of micro-cavity semiconductor devices for enhanced Two-Photon-Absorption response, and demonstrate the use of these devices for implementing sensitive autocorrelation measurements on pico-second optical pulses

High-sensitivity two-photon absorption microcavity autocorrelator

A GaAs-AlAs microcavity device has been used as a photodetector in an autocorrelator for measuring the temporal pulsewidth of 1.5-/spl mu/m optical pulses. Enhancement of the two-photon absorption photocurrent due to the microcavity structure results in an autocorrelation (average power times peak power) sensitivity of 9.3/spl times/10/sup -4/ (mW)/sup 2/, which represents two orders of magnitude improvement when compared with conventional autocorrelators

Two-photon absorption in microcavities for optical autocorrelation and sampling

We have designed novel semiconductor microcavity structures for the enhancement of the two-photon absorption (TPA) photocurrent. We report a TPA autocorrelation technique for short optical pulses that uses the microcavity structure instead of a second harmonic generation crystal. Knowledge of these characteristics is important for implementation in applications such as optical switching and sampling in optical time division multiplexed (OTDM) communications systems

A novel approach towards two-photon absorption based detectors

Summary: We have demonstrated that the inherent inefficiency of the TPA process in semiconductors can be overcome by incorporating the semiconductor in a microcavity structure. Proof of concept devices with a 0.27μm Ga0.7Al0.3As active region and two Bragg reflectors with the cavity resonance of 890 nm were fabricated. We measured the TPA photocurrent of these devices and have demonstrated a factor of 12000 enhancement over a nonmicrocavity device at 890 nm. Our active length of 0.27 nm is as efficient as 5.4 mm without a microcavity, overcoming the very long detector lengths limiting the use of TPA in practical autocorrelators, optical switches and sampling devices for real telecommunication systems. The effect of the cavity is to enhance the intra-cavity optical intensity, which leads to an increase in the nonlinear response of the active region. We studied, theoretically and experimentally, the impact of the cavity on the temporal response and the sensitivity of the device, which are critical considerations for commercial applications. This cavity design has a 3 pico-second response time and the autocorrelation trace is comparable with the BBO crystal response for an input 1.6 ps pulse. Devices designed for 1550 nm have also been realised and our measurements indicate these two-photon absorption based detectors are potential candidates for optical autocorrelation of short optical pulses, and for optical switching and sampling in optical time division multiplexed (OTDM) communications systems

‘He’s Got Growth’: Coaches Understanding and Management of the Growth Spurt in Male Academy Football

The majority of studies investigating maturation in football have focused on the impact of maturity status or timing upon athletic performance. There is comparatively little research investigating the impact of the adolescent growth spurt, and few research articles that have focussed on injury incidence and burden rather than performance. The aim of this study was to explore and better understand how the adolescent growth spurt impacts youth football players within professional academies. This longitudinal mixed-methods study aimed to understand youth football coaches’ perceptions, experiences, and management of male adolescent football players. Players’ maturity status, growth velocities, and match performance were measured and interviews with coaches were conducted in parallel. The qualitative and quantitative data were combined to generate a deeper contextualised understanding. This study revealed that academy football coaches describe adolescent growth as a ‘condition’; players are diagnosed with growth through perceived signs and symptoms, which coaches must manage and treat. Growth was also seen to impact coaches’ perceptions and therefore had implications for selection and release decisions. The findings from this study emphasise the complexities of experiencing and managing adolescent growth and maturation in the context of elite youth football

A Comprehensive Radio and Optical Study of Abell 2256: Activity from an Infalling Group

Abell 2256 is a nearby (z~0.06), rich cluster of galaxies with fascinating observed properties across a range of wavelengths. Long believed to represent a cluster merger, recent X-ray and optical results have suggested that in addition to the primary cluster and subcluster there is evidence for a third, poorer system. We present wide-field, high sensitivity 1.4 GHz VLA radio observations of Abell 2256 in conjunction with optical imaging and additional spectroscopy. Over 40 cluster radio galaxies are identified, with optical spectroscopy indicating the emission source (star formation or AGN) for most of them. While the overall fraction of galaxies exhibiting radio emission is consistent with a large sample of other nearby clusters, we find an increase in the activity level of galaxies belonging to the third system (hereafter, the ``Group''). Specifically, the Group has relatively more star formation than both the primary cluster and main subcluster. The position of the Group is also coincident with the observed cluster radio relic. We suggest that the Group recently (~0.3 Gyr) merged with the primary cluster and that this merger, not the ongoing merger of the primary and the main subcluster, might be responsible for many of the unusual radio properties of Abell 2256. Furthermore, the greater star formation activity of the Group suggests that the infall of groups is an important driver of galaxy evolution in clusters.Comment: 21 pages plus 13 JPEG figures; to appear in the Astronomical Journa