Given a set of n points S in the plane, a triangulation T of S is a maximal set of non-crossing segments with endpoints in S. We present an algorithm that computes the number of triangulations on a given set of n points in time n √ , significantly improving the previous best running time of O(2n) by Alvarez and Seidel [SoCG 2013]. Our main tool is identifying separators of size O( √ n) of a tri...

In the oil industry, huge saving may be made if suitable multi-interface level measurement systems are employed for effectively monitoring crude oil separators and efficient control of their operation. A number of techniques, e.g. externally mounted displacers, differential pressure transmitters and capacitance rod devices, have been developed to measure the separation process with gas, oil, wa...

A scheme is presented for mapping the connectivity of a potential magnetic field arising from an arbitrary distribution of discrete sources. The field lines interconnecting the sources are classified into Nd domains, defining the field’s connectivity. The number of domains is shown to depend on the number of sources and on the numbers of nulls and separators according to a simple relation. A cl...

In this paper, we analyze ptolemaic graphs for its properties as chordal graphs. Firstly, two characterizations of ptolemaic graphs are proved. The first one is based on the reduced clique graph, a structure that was defined by Habib and Stacho [8]. In the second one, we simplify the characterization presented by Uehara and Uno [13] with a new proof. Then, known subclasses of ptolemaic graphs a...

The auditory system appears to begin listening to an input with a basis toward hearing the input as a single stream, but it gradually accumulates evidence over a period of seconds which may lead to the input's being split into substreams. Several seconds of silence or of unpatterned noise slowly remove the bias of the mechanism in favor of these streams. The effects were demonstrated in experim...

A potential maximal clique of a graph is a vertex set that induces a maximal clique in some minimal triangulation of that graph. It is known that if these objects can be listed in polynomial time for a class of graphs, the treewidth and the minimum 5ll-in are polynomially tractable for these graphs. We show here that the potential maximal cliques of a graph can be generated in polynomial time i...

Correction for 'Highly lithium-ion conductive battery separators from thermally rearranged polybenzoxazole' by Moon Joo Lee et al., Chem. Commun., 2015, 51, 2068-2071.

Abstract Development of numerical methods for calculating the movement gas-dispersed flows in vortex and inertial separators, creation devices with counter tangential increased dust collection efficiency, determination optimal profile corrugated channels order to minimize release droplet moisture from separators.