Definition 3 (Polygonal Triangulation). Let K be a two-dimensional simplicial complex (i.e., a collection of triangles). If K is homeomorphic to a disk, then it is called a triangulation of a disk. Furthermore, if K is a k-gon divided by diagonals into k − 2 triangles, then K will be called a polygonal triangulation. See Figure 1. A k-gon dissected into k − 2 triangles will be called a k-triang...

We present a short proof of Descartes Circle Theorem on the “curvaturecenters” of four mutually tangent circles. Key to the proof is associating an octahedral configuration of spheres to four mutually tangent circles. We also prove an analogue for spheres. It can be traced back to at least Descartes that four mutually tangent circles have curvatures (reciprocals of radii) satisfying the relatio...

ture of U.S. public policy discussions for at least the last 20 years. One trigger of these debates is the statistical evidence on the rising cost of health care. For example, according to a survey conducted by the Kaiser Family Foundation (2004), health insurance premiums for employer-sponsored plans increased by 11.2% between the spring of 2003 and the spring of 2004, the fourth consecutive y...

T he 9th International ACM/IEEE Conference on Pervasive Computing Technologies for Healthcare (Pervasive Health 2015) was held from 20–23 May at the scenic Boğaziçi University in Istanbul, Turkey. It had a total of 106 registrations, with 25 full papers and five short papers from around the world (see Figure 1). The conference showcased a wide variety of technology applications, methods, and st...

For this, we obtained a fractal dimension of the proximal convoluted tubuli in the dog kidney by mean box-counting method. The fractal value we obtained is a flat dimension, and it is different than the line fractal dimension of the dog kidney arterial pattern, which was previously calculated by us (Gil et al., 2006). Thus, from optical microscopy images, we are able to obtain a single quantita...

where H > 0 is a given constant, y : dR + R3 is a given function and r c R3 is a given oriented Jordan curve. If u is a solution of (H)-(P), then u ( a ) represents a “soap bubble”, that is, a surface with mean curvature H (at all points x c R where V u ( x ) # O ) spanning r. Let us assume that y(aR) (respectively r) is contained in a closed ball of radius R. It was proved by S. Hildebrandt [8...

Define twist as anticlockwise rotation about the origin, of each point on a graph, by t(r) radians, where t(r) is a function of the point’s distance r from the origin. Transformations of this nature are widely used in computer graphics and engineering (see e.g., Krishnamurthy, 2002). How should an equation f(x, y) = 0 be changed so that its graph is twisted? Since twist involves rotation, the p...

theory and formal model, the other validates the link between the model and the phenomenal world. McKelvey’s distinction is depicted in Figure 1. -------------------------------------------------------Please See Figure 1--Place about here -------------------------------------------------------The first of these activities involves the coevolution of a theory and its formal model which is an ide...

By now, there can be little doubt that most, if not all, "drug-related murders" are the result of drug prohibition. The same type of violence came with the Eighteenth Amendment's ban of alcohol in 1920. The murder rate rose with the start of Prohibition, remained high during Prohibition, and then declined for 11 consecutive years when Prohibition ended.[2] The rate of assaults with a firearm ro...

Given a strictly convex plane curve γ and a point x in its exterior, there are two tangent segments to γ from x. The equitangent locus of γ is the set of points x for which the two tangent segments have equal lengths. An equitangent n-gon of γ is a circumscribed n-gon such that the tangent segments to γ from the vertices have equal lengths, see Figure 1. For example, if γ is a circle, the equit...