In this paper we study the area function of polygons, where vertices are sliding along curves. We give geometric criteria for critical points and determine also Hesse matrix at those points. This is starting point a Morse-theoretic approach, which includes relation with topology configuration spaces. Moreover condition extremal gives rise to new type billiard: inner billiard.

We describe a method for multiresolution deformation of closed planar curves that keeps the enclosed area constant. We use a wavelet based multiresolution representation of the curves that are represented by a finite number of control points at each level of resolution. A deformation can then be applied to the curve by modifying one or more control points at any level of resolution. This proces...

Uncertainty about the past has made it difficult to evaluate the relative roles of ecological and historical processes in generating species diversity. Although diversity is predicted to be higher on larger islands compared with that on smaller islands because of the effect of area on immigration and extinction rates, ecological theories do not fully account for positive species–area relationsh...

We construct unramified central simple algebras representing 2-torsion classes in the Brauer group of a hyperelliptic curve, and show that every 2-torsion class can be constructed this way when the curve has a rational Weierstrass point or when the base field is C1. In general, we show that a large (but in general proper) subgroup of the 2torsion classes are given by the construction. Examples ...

In this brief note, we prove the following two Artin-Schreier curves are supersin-gular.