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...

We give the first polynomial-time algorithm for the problem of finding a minimumperimeter k-gon that encloses a given n-gon. Our algorithm is based on a simple structural result, that an optimal k-gon has at least one “flush” edge with the ngon. This allows one to reduce the problem to computing the shortest k-link path in a simple polygon. As a by-product we observe that the minimum-perimeter ...

Gap-scale disturbances drive successional and structural development patterns in most forest ecosystems. Although fire-maintained Pinus palustris woodlands are less light limited than closed canopy forests, gap-scale disturbance processes may still influence developmental pathways. We quantified biophysical characteristics of 50 gaps a montane woodland to analyze processes. found (64%) were cau...

In this article, we study the regularity of the boundary of sets minimizing a quasi perimeter T (E) = P (E,Ω) + G (E) with a volume constraint. Here Ω is any open subset of Rn with n ≥ 2, G is a lower semicontinuous function on sets of finite perimeter satisfying a condition that G (E) ≤ G (F ) + C |E∆F | among all sets of finite perimeter with equal volume. We show that under the condition β >...

1. INTRODUCTION. Physics often provides mathematics not only with a problem, but also with the idea of a solution. Physical reasoning has traditionally been a fruitful source of mathematical invention, having played a key role in some of the main discoveries of Archimedes, Bernoulli, and Riemann, among many others. In this article we give a much more modest example of a mathematical result that...

We derive formulas for the number of polycubes of size n and perimeter t that are proper in n − 1 and n − 2 dimensions. These formulas complement computer based enumerations of perimeter polynomials in percolation problems. We demonstrate this by computing the perimeter polynomial for n = 12 in arbitrary dimension d.

carpal tunnel syndrome (cts) is the most common entrapment neuropathy. it accounts 90% of all entrapment neuropathies all over the world. ultrasound is a non-invasive, cost effective and available para-clinical method which could be applied for cts diagnosis. cross-sectional area of the median nerve at the level of the inlet is considered as a diagnostic criterion in cts cases. in this study, t...

The XML port scanning technique described in this paper allows an attacker to utilise an XML parser to execute port scanning of systems behind a restrictive perimeter firewall. While the technique relies on some reasonably specific implementation details in order to be exploitable remotely, it is potentially applicable to any application that accepts XML document inputs. Several workarounds exi...