The geodesic center of a simple polygon is a point inside the polygon which minimizes the maximum internal distance to any point in the polygon. We present an algorithm which calculates the geodesic center of a simple polygon with n vertices in time O(n log n).

This paper constructs a class of complete Kähler metrics of positive holomorphic sectional curvature on C and finds that the constructed metrics satisfy the following properties: As the geodesic distance ρ → ∞, the volume of geodesic balls grows like O(ρ 2(β+1)n β+2 ) and the Riemannian scalar curvature decays like O(ρ − 2(β+1) β+2 ), where β ≥ 0.

Since density is considered as one of the most important numerical indices to explain quantitative values of a plant community by affecting on many aspects and activity of ecosystem, on the other hand, awareness about plants distribution pattern in environment is an essential preparation for measurement and study of vegetative cover, therefore, in this research determination of density and dist...

We introduce the heat method for computing the shortest geodesic distance to an arbitrary subset of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting algorithm represents a significant breakthrough in the practical computation of distance on a wide variety of geometric domains, si...

The mechanisms underlying responses of invertebrates to forest edges remain poorly understood. Here, we use an experimental approach to investigate the predation rates on butterflies in two neotropical forest fragments. Neither distance from forest edge nor degree of forest openness affected predation rates on artificial caterpillars. The mean predation rate of artificial caterpillars on Barro ...