A note on the weighted norm inequality for the one-sided maximal operator

Let be the one-sided maximal function. In this note we obtain some necessary and sufficient conditions in order that the weighted weak type inequality holds for . Meanwhile, some necessary or sufficient conditions for the weighted inequality for are given.

     

Divisors on Generic Complete Intersections in Projective Space

Let be a generic complete intersection of hypersurfaces of degree in -dimensional projective space. We study the question when a divisor on is nonrational or of general type, and give an alternative proof of a result of Ein. We also give some improvement of Ein's result in the case .

     

Polarographic Studies of Dithiodiacetic Acid and the Uranyl-Dithiodiacetic Acid Complex

The polarographic behaviour of dithiodiacetic acid and that of U(VI) in a solution containing dithiodiacetic acid as complexing agent have been investigated. For the dithiodiacetic acid system, two waves appear over the pH range studied. The prewave is kinetic in nature and the mainwave is diffusion-controlled. However, as U(VI) is added into the dithiodiacetic acid system, the polarogram changes due to the existence of a complex. The current-potential curve of the first wave is not the normal S shape. This is due to the superposition of the first wave of the ligand and the wave due to the reduction of the U(VI) in the complex to U(V). The second wave is due to the reduction of the complex The first wave is an adsorption-controlled current and the second wave is partly diffusion-controlled and partly adsorption-controlled. We propose an electrode reaction mechanism for both systems and the complex species. The dissociation constant of the complex HASSAUO⁺₂ is found to be of the order of 10^?4.