PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees

In this article we complete the proof---for a broad class of four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear combination of the Euler characteristic and signature of the four-manifold. This article is a revision of sections 4--7 of an earlier version, while a revision of sections 1--3 of that earlier version now appear in a separate companion article (math.DG/0007190). Here, we use our computations of Chern classes for the virtual normal bundles for the Seiberg-Witten strata from the companion article (math.DG/0007190), a comparison of all the orientations, and the PU(2) monopole cobordism to compute pairings with the links of level-zero Seiberg-Witten moduli subspaces of the moduli space of PU(2) monopoles. These calculations then allow us to compute low-degree Donaldson invariants in terms of Seiberg-Witten invariants and provide a partial verification of Witten's conjecture.Comment: Journal fur die Reine und Angewandte Mathematik, to appear; 65 pages. Revision of sections 4-7 of version v1 (December 1997

Euler number of the compactified Jacobian and multiplicity of rational curves

In this paper we show that the Euler number of the compactified Jacobian J\u304C of a rational curve C with locally planar singularities is equal to the multiplicity of the (\u3b4-constant stratum in the base of a semi-universal deformation of C. The number e(J\u304C) is the multiplicity assigned by Beauville to C in his proof of the formula, proposed by Yau and Zaslow, for the number of rational curves on a K3 surface X. We prove that e(J\u304C) also coincides with the multiplicity of the normalisation map of C in the moduli space of stable maps to X

Validation of satellite land surface temperature products using ground-based measurements and heritage satellite data – Protocol, limitations and results

National audienc

Validation of satellite land surface temperature products using ground-based measurements and heritage satellite data – Protocol, limitations and results

National audienc

Zinc–Acetate–Amine Complexes as Precursors to ZnO and the Effect of the Amine on Nanoparticle Morphology, Size, and Photocatalytic Activity

Zinc oxide is an environmentally friendly and readily synthesized semiconductor with many industrial applications. ZnO powders were prepared by alkali precipitation using different [Zn(acetate)2(amine)x] compounds to alter the particle size and aspect ratio. Slow precipitations from 95 °C solutions produced micron-scale particles with morphologies of hexagonal plates, rods, and needles, depending on the precursor used. Powders prepared at 65 °C with rapid precipitation yielded particles with minimal morphology differences, but particle size was dependent on the precursor used. The smallest particles were produced using precursors that yielded crystals with low aspect ratios during high-temperature synthesis. Particles produced during rapid synthesis had sizes ranging from 21–45 nm. The materials were characterized by scanning electron microscopy, transmission electron microscopy, X-ray diffraction, thermogravimetric analysis, BET, and diffuse reflectance. The materials prepared using precursors with less-volatile amines were found to retain more organic material than ZnO produced using precursors with more volatile amines. The amount of organic material associated with the nanoparticles influenced the photocatalytic activity of the ZnO, with powders containing less organic material producing faster rate constants for the decolorizing of malachite green solutions under ultraviolet illumination, independent of particle size. [Zn(acetate)2(hydrazine)2] produced ZnO with the fastest rate constant and was recycled five times for dye degradation studies that revealed minimal to no reduction in catalytic efficiency