Pointed order polytopes: Studying geometrical aspects of the polytope of bi-capacities

Geometrical Aspects on Bi-Material Microtensile Tests

Recently the bond strength of composite resin to tooth has received attention from researchers of dental materials. Limitations imposed by the biological substrate, such as the size of the specimen, fostered the development of a tensile test with small dimensions. Due to the reduced size of the specimens, the test is called microtensile test. The specialized literature has not presented standar...

Geometrical aspects of first-order optical systems

We reconsider the basic properties of ray-transfer matrices for firstorder optical systems from a geometrical viewpoint. In the paraxial regime of scalar wave optics, there is a wide family of beams for which the action of a raytransfer matrix can be fully represented as a bilinear transformation on the upper complex half-plane, which is the hyperbolic plane. Alternatively, this action can be a...

2 Expansive Motions and the Polytope of Pointed Pseudo

Entropy of bi-capacities

In the context of multicriteria decision making whose aggregation process is based on the Choquet integral, bi-capacities can be regarded as a natural extension of capacities when the underlying evaluation scale is bipolar. The notion of entropy, recently generalized to capacities to measure their uniformity, is now extended to bi-capacities. We show that the resulting entropy measure has a ver...

Expansive Motions and the Polytope of Pointed Pseudo-Triangulations

We introduce the polytope of pointed pseudo-triangulations of a point set in the plane, defined as the polytope of infinitesimal expansive motions of the points subject to certain constraints on the increase of their distances. Its 1-skeleton is the graph whose vertices are the pointed pseudo-triangulations of the point set and whose edges are flips of interior pseudo-triangulation edges. For p...