A generalization of Rader's utility representation theorem

Rader's utility representation theorem guarantees the existence of an upper semicontinuous utility function for any upper semicontinuous total preorder on a second countable topological space. In this paper we present a generalization of Rader's theorem to not necessarily total preorders that are weakly upper semicontinuous.Weakly upper semicontinuous preorder; utility function

Sublinear and continuous order-preserving functions for noncomplete preorders

We characterize the existence of a nonnegative, sublinear and continuous order-preserving function for a not necessarily complete preorder on a real convex cone in an arbitrary topological real vector space. As a corollary of the main result, we present necessary and sufficient conditions for the existence of such an order-preserving function for a complete preorder.Comment: 8 page

Weak continuity of preferences with nontransitive indifference

We characterize weak continuity of an interval order on a topological space by using the concept of a scale in a topological space.Weakly continuous interval order; continuous numerical representation

Equilibrium a la Cournot and Supply FunctionEquilibrium in Electricity Markets underLinear Price/Demand and Quadratic Costs

We present a comparison between the Cournot and the Supply Function Equilibrium models under linear price/demand, linear supply functions and quadratic costs

A note on maximal elements for acyclic binary relations on compact topological spaces

I introduce the concept of a weakly tc-upper semicontinuous acyclic binary relation on a topological space (X,t), which appears as slightly more general than other concepts of continuity which have been introduced in the literature in connection with the problem concerning the existence of maximal elements. By using such a notion, I show that if an acyclic binary relation on a compact topological space is weakly tc-upper semicontinuous, then there exists a maximal element relative to such a binary relation. In this way I generalize existing results concerning the existence of maximal elements on compact topological spaces

The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour

The resort to utility-theoretical issues will permit us to propose a constructive procedure for deriving a homogeneous of degree one, continuous function that gives raise to a primitive demand function under suitably mild conditions. This constitutes the first elementary proof of a necessary and sufficient condition for an integrability problem to have a solution by continuous (subjective utility) functions. Such achievement reinforces the relevance of a technique that was succesfully formalized in Alcantud and Rodríguez-Palmero (2001). The analysis of these two works exposes deep relationships between two apparently separate fields: mathematical utility theory and the revealed preference approach to the integrability problem.Strong Axiom of Homothetic Revelation; revealed preference; continuous homogeneous of degree one utility; integrability of demand.

Conditions for the Upper Semicontinuous Representability of Preferences with Nontransitive Indifference

We present different conditions for the existence of a pair of upper semicontinuous functions representing an interval order on a topological space without imposing any restrictive assumptions neither on the topological space nor on the representing functions. The particular case of second countable topological spaces, which is particularly interesting and frequent in economics, is carefully considered. Some final considerations concerning semiorders finish the paper

A selection of maximal elements under non-transitive indifferences

In this work we are concerned with maximality issues under intransitivity of the indifference. Our approach relies on the analysis of "undominated maximals" (cf., Peris and Subiza, J Math Psychology 2002). Provided that an agent's binary relation is acyclic, this is a selection of its maximal elements that can always be done when the set of alternatives is finite. In the case of semiorders, proceeding in this way is the same as using Luce's selected maximals. We put forward a sufficient condition for the existence of undominated maximals for interval orders without any cardinality restriction. Its application to certain type of continuous semiorders is very intuitive and accommodates the well-known "sugar example" by Luce.Maximal element; Selection of maximals; Acyclicity; Interval order; Semiorder

EXISTENCE OF MAXIMAL ELEMENTS OF SEMICONTINUOUS PREORDERS

We discuss the existence of an upper semicontinuous multi-utility representation of a preorder on a topological space. We then prove that every weakly upper semicontinuous preorder $\precsim$ is extended by an upper semicontinuous preorder and use this fact in order to show that every weakly upper semicontinuous preorder on a compact topological space admits a maximal element

Sur la présence de Mylesinus paraschomburgkii Jégu et al., 1989 (Characiformes, Serrasalmidae) dans le bassin du rio Jari (Brésil, Amapa)

Des récoltes postérieures à la description de #Mylesinus paraschomburgkii permettent d'étendre son aire de distribution au bassin du Jari et au principal affluent du Uatuma. Une analyse en composantes principales sur 18 descripteurs morphologiques montrent que la morphologie générale de la population du Jari est différente de celle des populations du Trombetas et du Uatuma. L'isolement de la population du Jari serait donc plus ancien que la séparation des populations du Trombetas et du Uatuma. La dispersion de #Mylesinus paraschomburgkii le long de la marge sud du plateau des Guyanes serait reliée aux transgressions marines du Quaternaire. (Résumé d'auteur