Extension theorems for homogenization on lattice structures

Extension Preservation Theorems on Classes of Acyclic Finite Structures

A class of structures satisfies the extension preservation theorem if, on this class, every first order sentence is preserved under extension iff it is equivalent to an existential sentence. We consider different acyclicity notions for hypergraphs (γ, β and α-acyclicity and also acyclicity on hypergraph quotients) and estimate their influence on the validity of the extension preservation theore...

Relational Representation Theorems for Some Lattice-Based Structures

The major elements of the method of proving relational representation theorems presented in this paper are, on the one hand, Urquhart representation theorem for lattices [17] and Allwein and Dunn developments on Kripke semantics for linear logic (see [1] and also [4]), and on the other hand, a generalisation of Jonsson and Tarski ideas [9] which inspired the developments in [5], [6] and [13]. W...

Homogenization of Lattice Systems

These notes contain the material related to the three lectures that I have delivered at the Workshop ‘Recent Advances in Homogenization’ held at INdAM, Rome in the week 23–27 May 2005. The notes are thought just as a complement and reference for the single lectures, and not as a whole: I must warn that the chapters are unevenly written. Some are elaboration of articles that have already appeare...

Two theorems on lattice expansions

On hierarchical structures and reiterated homogenization

In this paper we consider the concept of reiterated homogenization, introduced on the physical level by Bruggeman in the 30's and justi ed mathematically by Bensoussan, Lions and Papanicolaou in 1978. We present and discuss some recent developments of this theory and also give some applications to linear and nonlinear problems.