Transcendance de l'invariant modulaire en caractéristique finie

Transcendence of the modular invariant in finite characteristic Abstract. Let J be the Fourier expansion at infinity of the modular invariant j associated to a Drinfeld module of rank 2 defined on the algebraic closure of and t an element of the completion of . Then at least one of the two elements t, J(t) is transcendental over .

Received: October 22, 1997; in final form January 21, 1998     

Self-Adjoint Extensions of Discrete Magnetic Schrödinger Operators

Using the concept of an intrinsic metric on a locally finite weighted graph, we give sufficient conditions for the magnetic Schrödinger operator to be essentially self-adjoint. The present paper is an extension of some recent results proven in the context of graphs of bounded degree.     

Discretization orders and efficient computation of cartesian coordinates for distance geometry

Distance geometry is a class of problems where the position of points in space is to be identified by using information about some relative distances between these points. Although continuous approaches are usually employed, problems belonging to this class can be discretized when some particular assumptions are satisfied. These assumptions strongly depend on the order in which the points to be positioned are considered. We discuss new discretization assumptions that are weaker than previously proposed ones, and present a greedy algorithm for an automatic identification of discretization orders. The use of these weaker assumptions motivates the development of a new method for computing point coordinates. Computational experiments show the effectiveness and efficiency of the proposed approaches when applied to protein instances.     

A Square of Oppositions in Intuitionistic Logic with Strong Negation

In this paper, we introduce a Hilbert style axiomatic calculus for intutionistic logic with strong negation. This calculus is a preservative extension of intuitionistic logic, but it can express that some falsity are constructive. We show that the introduction of strong negation allows us to define a square of opposition based on quantification on possible worlds.     

Self-Concordant Barriers for Convex Approximations of Structured Convex Sets

We show how to approximate the feasible region of structured convex optimization problems by a family of convex sets with explicitly given and efficient (if the accuracy of the approximation is moderate) self-concordant barriers. This approach extends the reach of the modern theory of interior-point methods, and lays the foundation for new ways to treat structured convex optimization problems with a very large number of constraints. Moreover, our approach provides a strong connection from the theory of self-concordant barriers to the combinatorial optimization literature on solving packing and covering problems.