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We present a number of new results for the combinatorial game Toads and Frogs. We begin by presenting a set of simplification rules, which allow us to split positions into independent components or replace them with easily computable numerical values. Using these simplication rules, we prove that there are Toads and Frogs positions with arbitrary numerical(More)
We construct, for any positive integer n, a family of n congruent convex polyhedra in IR 3 , such that every pair intersects in a common facet. Our polyhedra are Voronoi regions of evenly distributed points on the helix (t, cos t, sin t). The largest previously published example of such a family contains only eight polytopes. With a simple modification, we(More)
The <i>spread</i> of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in IR<sup>3</sup> with spread &#916; has complexity O(&#916;<sup>3</sup>). This bound is tight in the worst case for all &#916; = O(&radic;n). In particular, the Delaunay triangulation(More)
Previous research on enterprise resource planning (ERP) systems has focused mainly on the initial implementations of the solution. However, many companies that installed ERP solutions in the late 1990's are at the point where they need to upgrade their solution to a current release. This paper provides a model that identifies the different types of(More)
This report documents a revised model for estimating emissions savings for nitrogen oxides (NOx), sulfur oxides (SOx), carbon dioxide (CO 2), and mercury (Hg) from Focus on Energy efficiency efforts. The report covers four key areas: 1. Improved yearly emissions factors for calculating emission reduction as a result of Focus on Energy activity. 2. Emission(More)