Proof of the Log-Convex Density Conjecture

We completely characterize isoperimetric regions in R^n with density e^h, where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric regions of any given volume, proving the Log-Convex Density Conjecture due to Kenneth Brakke.Comment: 40 pages, 7 figure

Post Flight Dynamic Analysis Simulation

Digital six-degrees-of-freedom, open loop Saturn 5 first stage flight evaluation simulation program obtains post flight simulation of the launch vehicle using actual flight data as input. Results are compared with measured data. For preflight analysis, the program uses predicted flight data as input

On substitution tilings of the plane with n-fold rotational symmetry

A method is described for constructing, with computer assistance, planar substitution tilings that have n-fold rotational symmetry. This method uses as prototiles the set of rhombs with angles that are integer multiples of pi/n, and includes various special cases that have already been constructed by hand for low values of n. An example constructed by this method for n = 11 is exhibited; this is the first substitution tiling with 11-fold symmetry appearing in the literature.Comment: 17 pages, 10 figure