Wavelet frame bijectivity on Lebesgue and Hardy spaces

We prove a sufficient condition for frame-type wavelet series in $L^p$, the Hardy space $H^1$, and BMO. For example, functions in these spaces are shown to have expansions in terms of the Mexican hat wavelet, thus giving a strong answer to an old question of Meyer. Bijectivity of the wavelet frame operator acting on Hardy space is established with the help of new frequency-domain estimates on the Calder\'on-Zygmund constants of the frame kernel.Comment: 23 pages, 7 figure

Recent work on an RF ion thruster

An experimental investigation of an rf ion thruster using an immersed coupler in an argon discharge is reported. The conical coil, used to couple rf power into the discharge, is placed inside the discharge vessel. The discharge was self-sustained by 100-150 MHz rf power at low environmental pressures. The ion extraction was accomplished by conventional accelerated grid optics from an unoptimized 8 cm diameter ion thruster

The impact of a wave farm on large scale sediment transport

This study investigates the interactions of waves and tides at a wave farm in the southwest of England, in particular their effects on radiation stress, bottom stress, and consequently on the sediment transport and the coast adjacent to the wave-farm (the Wave Hub). In this study, an integrated complex numerical modelling system is setup at the Wave Hub site and is used to compute the wave and current fields by taking into account the wave-current interaction, as well as the sediment transport. Results show that tidal elevation and tidal currents have a significant effect on the wave height and direction predictions; tidal forcing and wind waves have a significant effect on the bed shear-stress, relevant to sediment transport; waves via radiation stresses have an important effect on the longshore and cross-shore velocity components, particularly during the spring tides. Waves can impact on bottom boundary layer and mixing in the water column. The results highlight the importance of the interactions between waves and tides when modelling coastal morphology with presence of wave energy devices

Back reaction, covariant anomaly and effective action

In the presence of back reaction, we first produce the one-loop corrections for the event horizon and Hawking temperature of the Reissner-Nordstr\"om black hole. Then, based on the covariant anomaly cancelation method and the effective action technique, the modified expressions for the fluxes of gauge current and energy momentum tensor, due to the effect of back reaction, are obtained. The results are consistent with the Hawking fluxes of a (1+1)-dimensional blackbody at the temperature with quantum corrections, thus confirming the robustness of the covariant anomaly cancelation method and the effective action technique for black holes with back reaction.Comment: 17 page