Results and estimates on pseudopowers

Let be a positive integer. We say looks like a power of 2 modulo a prime if there exists an integer such that . First, we provide a simple proof of the fact that a positive integer which looks like a power of modulo all but finitely many primes is in fact a power of . Next, we define an -pseudopower of the base to be a positive integer that is not a power of , but looks like a power of modulo all primes . Let denote the least such . We give an unconditional upper bound on , a conditional result (on ERH) that gives a lower bound, and a heuristic argument suggesting that is about for a certain constant . We compare our heuristic model with numerical data obtained by a sieve. Some results for bases other than are also given.

     

Probing the structure of the pomeron

We suggest that the pseudo-rapidity cut dependence of diffractive deep-inelastic scattering events at HERA may provide a sensitive test of models of diffraction. A comparison with the experimental cross section shows that the Donnachie-Landshoff model and a simple two-gluon exchange model of the pomeron model are disfavoured. However a model with a direct coupling of the pomeron to quarks is viable for a harder quark–pomeron form factor, as is a model based on the leading-twist operator contribution. We also consider a direct-coupling scalar pomeron model. We comment on the implications of these results for the determination of the partonic structure of the pomeron. Received: 5 March 1999 / Published online: 3 August 1999     

Mechanical properties of sisal fibre-reinforced polymer composites: a review

There has been a growing interest in the utilization of sisal fibres as reinforcement in the production of polymeric composite materials. Natural fibres have gained recognition as reinforcements in fibre polymer–matrix composites because of their mechanical properties and environmental friendliness. The mechanical properties of sisal fibre-reinforced polymer composites have been studied by many researchers and a few of them are discussed in this article. Various fibre treatments, which are carried out in order to improve adhesion, leading to improved mechanical properties, are also discussed in this review paper. This review also focuses on the influence of fibre content and fabrication methods, which can significantly affect the mechanical properties of sisal fibre-reinforced polymer composites.     

Performance studies of a full-length prototype for the CASTOR forward calorimeter at the CMS experiment

The Time-Of-Flight detector (TOF) of the ALICE experiment at the CERN LHC is based on Multi-gap Resistive Plate Chambers (MRPCs). The TOF detector consists of 152928 readout channels covering a total area of 141 m². In this paper the results of the calibration with cosmic-ray data collected during 2009 are presented.