We establish the L p pR 3 q boundedness of the helical maximal function for the sharp range p ą 3. Our results improve the previous known bounds for p ą 4. The key ingredient is a new microlocal smoothing estimate for averages along dilates of the helix, which is established via a square function analysis.
In-furnace desulfurization has been widely used in circulating fluidized bed boilers. SO 2 is removed by reacting with limestone during the process of sulfation after calcination in air combustion. Although CaCO 3 is the main component of limestone, there are also other impurities such as CaMg(CO 3 ) 2 and SiO 2 which can influence the desulfurization. The porous CaO produced by calcination plays an important role in sulfation, and water vapor in the furnace influences the calcination. This work aims to understand the impacts of impurities and water vapor on limestone calcination. Two kinds of China limestone were used to investigate the issues in a rotatable fluidized bed reactor. Mercury injection apparatus (MIP), scanning electron microscope−energy dispersive spectrometer (SEM-EDS), and X-ray diffraction (XRD) techniques were employed to analyze the pore structure, micromorphology, and crystal structure of the CaO calcined, respectively. The results show that the water vapor improves the calcination rate and shortens the reaction time, and those influences are stronger for higher impurity limestone possibly because of more defects in the crystal structure. Water vapor can directly influence the chemical reaction of calcination without affecting the diffusion property of CO 2 . Higher water vapor content results in slightly lower ultimate degree of conversion of limestone, but for different kinds of limestone the difference is not obvious. The results of SEM and MIP also mean that the existence of water vapor improves sintering and growth of grains. The results of XRD give further evidence to the previous conclusion. These tests and analysis give rise to the mechanisms behind the impacts of water vapor on limestone calcination: the binding ability of H 2 O to active site O* in Ca−O is stronger than that of CO 2 . H 2 O tends to replace CO 2 on the active site to increase the release of CO 2 in calcination. Water vapor also accelerates sintering, most possibly in the initial stage when the sintering neck is formed. There exist two possibilities: H 2 O molecules are absorbed on the active site of Ca−O* to promote the formation of the sintering neck of CaO by interaction between H 2 O molecules (such as hydrogen bond). Water vapor can also act as a solvent to improve the solid state diffusion from surface to sintering neck which also benefits the fusion and growth of minicrystals.
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