It is well known that antipodal grasps can be achieved on curved objects in the presence of friction. This paper presents an efficient algorithm that finds, up to numerical resolution, all pairs of antipodal points on a closed, simple, and twice continuously differentiable plane curve. Dissecting the curve into segments everywhere convex or everywhere concave, the algorithm marches simultaneous...

In robotics it is well known that antipodal grasps can be achieved on curved objects in the presence of friction. This paper presents an efficient algorithm that computes, up to numerical resolution, all pairs of antipodal points on a simple, closed, and twice continuously differentiable plane curve. Dissecting the curve into segments everywhere convex or everywhere concave, the algorithm perfo...

The c-Balanced Separator problem is a graph-partitioning problem in which given a graph G, one aims to find a cut of minimum size such that both the sides of the cut have at least cn vertices. In this paper, we present new directions of progress in the c-Balanced Separator problem. More specifically, we propose a family of mathematical programs, that depend upon a parameter p > 0, and is an ext...

In this paper the problem of minimum cost communication network design is considered where the costs are piecewise linear concave. Several methods are compared: Simulated Annealing method, a heuristic based on the method proposed by Minoux, and a lagrangian method based on lower bounding procedure.

Purpose: Scoliosis is one of the most common spinal deformities that affect chest wall mechanics. Scoliosis results in ventilator disorders and respiratory muscle weakness. However, the mechanism of these disorders is still unknown. The main objective of this study was to identify the intensity of respiratory muscles activity in patients with idiopathic scoliosis compare with healthy indi...

in the past, rock slope stability analysis were performed either graphically or using a hand-held calculator, but nowadays there are variety of slope stability analysis which can be used according to the field condition and potential failure mode. in 2-d analysis, effect of convex and concave walls are neglected, however concave slopes are believed to be more stable than straight walls due to t...

In this paper we prove the following results concerning the product f1f2 of two concave functions f1and f2 defined in a non empty, compact, convex set K of R. The first result states that necessary and sufficient condition for the product f1f2 of two linear affine functions to be concave is that they are Gonzi. Finally the main result says that a necessary and sufficient condition for the produ...

We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincaré inequalities for such functions. This leads naturally to the concept of f -divergence and, in particular, relative entropy for s-concave and log concave functions. We establish their basic properties, among them the affine invariant valua...

Abstract Mirrors that are convex in some places and concave others can generate images of extended objects (such as the viewer’s face) curiously distorted often topologically disrupted. Understanding these involves caustics family rays emitted by each point object, totality all such families constituting from points object. The general theory is illustrated simplest mirror with an inflection, w...