New upper bounds on sphere packings II

We continue the study of the linear programming bounds for sphere packing introduced by Cohn and Elkies. We use theta series to give another proof of the principal theorem, and present some related results and conjectures.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper10.abs.htm

Analysis and use of VAS satellite data

Four interrelated investigations have examined the analysis and use of VAS satellite data. A case study of VAS-derived mesoscale stability parameters suggested that they would have been a useful supplement to conventional data in the forecasting of thunderstorms on the day of interest. A second investigation examined the roles of first guess and VAS radiometric data in producing sounding retrievals. Broad-scale patterns of the first guess, radiances, and retrievals frequently were similar, whereas small-scale retrieval features, especially in the dew points, were often of uncertain origin. Two research tasks considered 6.7 micron middle tropospheric water vapor imagery. The first utilized radiosonde data to examine causes for two areas of warm brightness temperature. Subsidence associated with a translating jet streak was important. The second task involving water vapor imagery investigated simulated imagery created from LAMPS output and a radiative transfer algorithm. Simulated image patterns were found to compare favorably with those actually observed by VAS. Furthermore, the mass/momentum fields from LAMPS were powerful tools for understanding causes for the image configurations

Optimality and uniqueness of the Leech lattice among lattices

We prove that the Leech lattice is the unique densest lattice in R^24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in R^24 can exceed the Leech lattice's density by a factor of more than 1+1.65*10^(-30), and we give a new proof that E_8 is the unique densest lattice in R^8.Comment: 39 page

Analysis and use of VAS satellite data

A series of interrelated investigations has examined the analysis and use of VAS (VISSR Atmospheric Sounder) satellite data. A case study of VAS-derived mesoscale stability parameters suggested that they would have been a useful supplement to conventional data in the forecasting of thunderstorms on the day of interest. However, the meteorological significance of small or short lived stability features was uncertain. A second investigation examined the roles of first guess and VAS radiometric data in producing sounding retrievals. The radiance data often did not have a decisive influence on the final satellite soundings. Broad-scale patterns of the first guess, radiances, and retrievals frequently were similar, whereas small scale retrieval features, especially in the dew points, were often of uncertain origin