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Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are non-zero using classical multivariate statistics evaluated at each point. The problem is to find the P-value of the maximum of such a(More)
We postulate that almost any motion of an interface between two crystals can produce a coupled tangential motion of the two crystals relative to each other which is proportional to the normal motion of the interface. Such translations can produce grain rotations ; the special case of the rotations of shrinking included circular cylindrical grains which(More)
We use an expanded variational approach based on dissipation to study the motion of the boundary of a non-circular cylindrical, and thus essentially 2-dimensional, crystalline grain of arbitrary cross-section enclosed in another grain of the same material under conditions where the normal grain boundary motion is coupled to relative tangential motion of the(More)
The Burlington Mathfest in August 1995 included an AMS Special Session on Soap Bubble Geometry, organized by Frank Morgan. At the end of the session, participants were asked to pose open problems related to bubble geometry. We have collected those problems here, adding a few introductory comments. Participants in the special session included the following:(More)
OBJECT The DIAM is a polyester-encased silicone interspinous dynamic stabilization device that can unload the anterior column and reestablish the functional integrity of the posterior column. METHODS The DIAM was implanted in 104 patients between May 1, 2001 and October 30, 2001. A retrospective evaluation was performed based on chart review and patient(More)
Mathematical models for various types of crystal surface motions have been made. They all reduce some energy which includes a given (usually crystalline) anisotropic surface free energy and perhaps a bulk free energy. The mechanisms which govern the motions are attachment/detachment kinetics, diiusion of atoms over surfaces, and perhaps diiusion within the(More)
The sphere is the shape which minimizes the surface tension of a drop of fluid. On the atomic scale a fluid – gas or liquid – consists of an isotropic, disorderly configuration of particles. The Wulff shape plays the same minimum-surface-tension role, but for the orderly, nonisotropic particle configurations of solids. For an intuitive picture consider(More)