We develop a fast algorithm to construct the robustness degradation function, which describes quantitatively the relationship between the proportion of systems guaranteeing the robustness requirement and the radius of the uncertainty set. This function can be applied to predict whether a controller design based on an inexact mathematical model will perform satisfactorily when implemented on the...

Distal radius fractures account for the most commonly treated fracture of the upper extremity and are especially common in the elderly population. Despite new treatment strategies many questions remain regarding the optimal treatment regime. Controversies include the treatment modalities and the expected outcome as well as economical considerations. It is the goal of this presentation to discus...

We develop a fast algorithm to construct the robustness degradation function, which describes quantitatively the relationship between the proportion of systems guaranteeing the robustness requirement and the radius of the uncertainty set. This function can be applied to predict whether a controller design based on an inexact mathematical model will perform satisfactorily when implemented on the...

The global radius of curvature of a space curve is introduced. This function is related to, but distinct from, the standard local radius of curvature and is connected to various physically appealing properties of a curve. In particular, the global radius of curvature function provides a concise characterization of the thickness of a curve, and of certain ideal shapes of knots as have been inves...

It is proved that the Green’s function of the simple random walk on a surface group of large genus decays exponentially in distance at the (inverse) spectral radius. It is also shown that Ancona’s inequalities extend to the spectral radius R, and therefore that the Martin boundary for R−potentials coincides with the natural geometric boundary S. This implies that the Green’s function obeys a po...

Introduction: The commercial 252Cf sources are too large in size and clinical applications of neutron brachytherapy (NBT) are limited to a small number of intracavitary treatments of cervical cancers. Recently, under the Cooperative Research and Development Agreement (CRADA) with Isotron Inc., the Oak Ridge National Laboratory (ORNL) encapsulated a new medical 252Cf sources, c...

We prove that given a fixed radius r, the maximum density achieved by packings of the hyperbolic plane by radius r circles is the supremum of densities of “periodic packings” (those packings with cofinite symmetry). We also show that the maximal density function is continuous as a function of radius. Our investigations lead us to consider more general questions regarding the density of periodic...