In the class of Carnot groups we study fine properties of sets of finite perimeter. Improving a recent result by Ambrosio-Kleiner-Le Donne, we show that the perimeter measure is local, i.e., that given any pair of sets of finite perimeter their perimeter measures coincide on the intersection of their essential boundaries. This solves a question left open in [4]. As a consequence we prove a gene...

Candidates to the least perimeter partition of a disk into N planar connected regions are calculated for N ≤ 43. A Voronoi construction is used to randomly create the candidates and then the perimeter of each is found with the Surface Evolver. Formulae for the perimeter and number of peripheral regions are given, and the candidates classified according to their topology. The simulation techniqu...

Web services security is becoming a critical concern for any organization adopting the XML-based Web services approach to application integration. While many access control techniques for Web services are becoming available, several issues still need to be solved in order to correctly split the burden of securing Web services between the perimetral and the service level. In this paper, a techni...

The square decomposition problem has applications in a number of areas such as bin packing of flexible objects of fixed area and circuit layout with minimum communication requirements. Our interest in the square decomposition problem arises from the following problem in parallel computation [1]. One wishes to compute a table of all values of a binary function f on the Cartesian product S x T, w...