The square root function has a unique positive ¿xed point. This function has the following properties: it is strictly increasing and strictly concave, with sEf ' f, sE@ : @ for @ , and sEK K for K : . It is shown that any function from U to U satisfying these properties has a unique positive ¿xed point.

We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel’skii (1964) and Krasnosel’skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone conc...

This paper aims to recognize and extract deformed Asterias amurensis through the use of the concave and convex feature points, central moment, and short lines and long lines. Another purpose of this paper is to restore Asterias amurensis using the radial symmetry. Marked by the characteristics that include pentaradiality and the ability to vary in outward shapes according to circumstances, Aste...

In this paper, by introducing the concept of a generalized concave operator and the properties of cone and monotone iterative technique in ordered Banach spaces, some new existence and uniqueness theorems of fixed points for the operator under more extensive conditions are obtained. Finally, as applications, we apply the results obtained in this paper to study the existence and uniqueness of po...

This paper 1 presents a new approach to detect and localise contact between concave deformable polyhedra. In this case there are many contact points between two polyhedra, the proposed algorithm detect and localise the contact in linear time O(n). It returns also the direction of this contact and the value of the maximum inter-penetration between the two convex-hulls of these two polyhedra.

We develop a model of multi-candidate electoral competition in a multi-dimensional policy space with strategic voters. We show that when the distribution of voter ideal points is log-concave, there exist pure-strategy subgame perfect equilibria in weakly undominated strategies in which platforms are located in the minmax set. Analytical and numerical results suggest that the size of the minmax ...

The property that an optimal solution to the problem of minimizing a continuous concave function over a compact convex set in IRn is attained at an extreme point is generalized by the Bauer Minimum Principle to the infinite dimensional context. The problem of approximating and characterizing infinite dimensional extreme points thus becomes an important problem. Consider now an infinite dimensio...

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.

The n-interior point variant of the Erdős-Szekeres problem is the following: for any n, n ≥ 1, does there exist a g(n) such that every point set in the plane with at least g(n) interior points has a convex polygon containing exactly n-interior points. The existence of g(n) has been proved only for n ≤ 3. In this paper, we show that, for point sets having at most logarithmic number of convex lay...

Using copper thin-walled tubular specimens, the subsequent yield surfaces under pre-tension, pre-torsion and pre-combined tension-torsion are measured, where the single-sample and multi-sample methods are applied respectively to determine the yield stresses at specified offset strain. The rule and characteristics of the evolution of the subsequent yield surface are investigated. Under the condi...