The diameter of the commuting graph of a finite group with trivial centre

The commuting graph of a finite group with trivial centre is examined. It is shown that the connected components of the commuting graph have diameter at most 10

Theory of the cold collision frequency shift in 1S--2S spectroscopy of Bose-Einstein-condensed and non-condensed hydrogen

We show that a correct formulation of the cold collision frequency shift for two photon spectroscopy of Bose-condensed and cold non-Bose-condensed hydrogen is consistent with experimental data. Our treatment includes transport and inhomogeneity into the theory of a non-condensed gas, which causes substantial changes in the cold collision frequency shift for the ordinary thermal gas, as a result of the very high frequency (3.9kHz) of transverse trap mode. For the condensed gas, we find substantial corrections arise from the inclusion of quasiparticles, whose number is very large because of the very low frequency (10.2Hz) of the longitudinal trap mode. These two effects together account for the apparent absence of a "factor of two" between the two possibilities. Our treatment considers only the Doppler-free measurements, but could be extended to Doppler-sensitive measurements. For Bose-condensed hydrogen, we predict a characteristic "foot" extending into higher detunings than can arise from the condensate alone, as a result of a correct treatment of the statistics of thermal quasiparticles.Comment: 16 page J Phys B format plus 6 postscript figure

Thin-walled pressure vessel Patent

Thin walled pressure test vessel using low-melting alloy-filled joint to attach shell to head

Radioisotope thermal photovoltaic application of the GaSb solar cell

An examination of a RTVP (radioisotopic thermophotovoltaic) conceptual design has shown a high potential for power densities well above those achievable with radioisotopic thermoelectric generator (RTG) systems. An efficiency of 14.4 percent and system specific power of 9.25 watts/kg were predicted for a system with sixteen GPHS (general purpose heat source) sources operating at 1100 C. The models also showed a 500 watt system power by the strontium-90 isotope at 1200 C at an efficiency of 17.0 percent and a system specific power of 11.8 watts/kg. The key to this level of performance is a high-quality photovoltaic cell with narrow bandgap and a reflective rear contact. Recent work at Boeing on GaSb cells and transparent back GaAs cells indicate that such a cell is well within reach

Feeding Systems for Layers

Numerous reports show there are many feeding systems for layers that the poultryman will find satisfactory. The important factor for good results is proper management of the feeding system. Essentially the most common feeding systems recommended and in use today are ( 1) all-mash, ( 2) 18-20 percent protein mash with limited or free-choice grain, and (3) 25-27 percent protein concentrate with free-choice grain. Some poultrymen have reported successful use of a 32 percent protein concentrate fed free-choice with grains. The laying hen has a remarkable ability to balance her own ration, but it has generally been felt that more concentrate is consumed than necessary •when a 32 percent protein concentrate is used. Before poultrymen started to use high energy feeds, all-mash rations were considered somewhat low in energy for maximum egg production-particularly during the winter. High energy all-mash diets should supply the extra energy needed for maintenance under cold weather conditions and therefore support production equal to that of the other systems. Many field reports indicate that some all-mash diets today are giving better results than the various mash and grain feeding systems. Here are some of the reasons poultrymen have again become interested in all-mash diets. 1) Bulk handling of feed has greater application where all-mash diets are used. Bulk handling of feed, in itself, appeals to many because of price discounts and the economy of handling costs. 2) All-mash feeds are more adaptable for use in mechanical feeders and cage-feeding operations. 3) Use of fats and oils in feeds to increase energy content finds greater application in all-mash feeds. The data in this circular were obtained from three experiments with heavy-type hens in which three feeding systems were compared. Also data obtained from use of a 20 percent protein mash and free-choice grain feeding system with various groups of layers are presented

Substituted phenylarsonic acids; structures and spectroscopy

Full NMR and ESI-MS spectra, and differential scanning calorimeter data are presented for 15 substituted phenylarsonic acids, including two new fluoro-substituted examples. X-ray crystal structure determinations of five examples (phenylarsonic acid and the 4-fluoro-, 4-fluoro-3-nitro-, 3-amino-4-hydroxy- and 3-amino-4-methoxy-substituted derivatives) were determined and the H-bonding crystal-packing patterns analysed

Buyer power in U.K. food retailing: a 'first-pass' test

Habtu Weldegebriel, University of Warwick Abstract The potential existence of buyer power in U.K. food retailing has attracted the scrutiny of the U.K.'s anti-trust authorities, culminating in the second of two comprehensive regulatory inquiries in recent years. Such inquiries are authoritative but correspondingly time-consuming and costly. Moreover, detection of buyer power has been dogged by the paucity of reliable evidence of its existence. In this paper, we present a simple theoretical model of oligopsony which delivers quasi-reduced form retailer-producer pricing equations with which the null of perfect competition can be tested using readily available market data. Using a cointegrated vector autoregression, we find empirical results that show the null of perfect competition can be rejected in seven of the nine food products investigated. Though not conclusive on the existence of buyer power, the proposed test offers a means via which the behaviour of the retail-producer price spread is consistent with it. At the very least, it can corroborate the concerns of the anti-trust authorities as to whether buyer power is potentially one source of concern