On Rank One Convex Functions that are Homogeneous of Degree One

Subadditive and Homogeneous of Degree One Games Are Totally Balanced

A cooperative game with transferable utility is said to be homogeneous of degree one if for any integer m, the value of cloning m times all players at any given coalition, leads to m times the value of the original coalition. We show that this property coupled with sub-additivity, guarantee the non-emptyness of the core of the game and of all its subgames, namely the game is totally balanced. E...

Numerical Computation of Rank - One Convex

We describe an algorithm for the numerical computation of the rank-one convex envelope of a function f : Mm×n → R. We prove its convergence and an error estimate in L∞.

Harmonic Functions on Classical Rank One Balls

On the Local Structure of Rank-one Convex Hulls

In this note we prove that if K is a compact set of m×n matrices containing an isolated point X with no rank-one connection into the convex hull of K \ {X}, then the rank-one convex hull separates as K = ( K \ {X} )rc ∪ {X}. This is an extension of a result of P. Pedregal, which holds for 2× 2 matrices.

On Sets with Rank One in Simple Homogeneous Structures

We study de nable sets D of SU-rank 1 inM, whereM is a countable homogeneous and simple structure in a language with nite relational vocabulary. Each such D can be seen as a `canonically embedded structure', which inherits all relations on D which are de nable inM, and has no other de nable relations. Our results imply that if no relation symbol of the language of M has arity higher than 2, the...