We give a survey of the problem of describing the nite covers of a given aleph-zero categorical base structure, particularly those where the automorphism group over the base structure is nite.

We construct a new family of simple modules over orthogonal complex Lie algebra associated with Gelfand-Zetlin formulae for simple nite dimensional modules and study the corresponding Gelfand-Zetlin subalgebra.

Finite abelian groups are among the most simple and useful of all algebraic ob jects possessing a pleasant but non trivial classi cation a perfect theory of duality and a penchant for cropping up in interesting places When one thinks of generalizations of this theory within the nite setting the theory of non abelian nite groups immediately comes to mind This theory has now achieved a very high ...

We present a simple generic framework to solve constraints on any domain ( nite or in nite) which has a lattice structure. The approach is based on the use of a single constraint similar to the indexicals used by CLP over nite domains and on a particular de nition of an interval lattice built from the computation domain. We provide the theoretical foundations for this framework, a schematic pro...

We start with a simple proof of Leivant's normal form theorem for 1 1 formulas over nite successor structures. Then we use that normal form to prove the following: (i) over all nite structures, every 1 2 formula is equivalent to a 1 2 formula whose rst-order part is a boolean combination of existential formulas, and (ii) over nite successor structures, the Kolaitis-Thakur hierarchy of minimizat...

In this paper we describe how wavelets may be used to solve partial diierential equations. These problems are currently solved by techniques such as nite diierences, nite elements and multi-grid. The wavelet method, however, ooers several advantages over traditional methods. Wavelets have the ability to represent functions at diierent levels of resolution, thereby providing a logical means of d...

Using a simple nite integral representation for the bivari-ate Rayleigh cumulative distribution function recently discovered by the authors, we present expressions for the out-age probability and average error probability performances of a dual selective diversity system with correlated slow Rayleigh fading either in closed form (in particular for binary diierential phase-shift keying) or in te...

We present a simple and powerful method for extrapolating nite-volume Monte Carlo data to in nite volume, based on nite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the twodimensional O(3) and O(1) -models. In favorable cases it is possi...

We model physical systems with \hard constraints" by the space Hom(G;H) of homomorphisms from a locally nite graph G to a xed nite constraint graph H. For any assignment of positive real activities to the nodes of H, there is at least one Gibbs measure on Hom(G;H); when G is in nite, there may be more than one. When G is a regular tree, the simple, invariant Gibbs measures on Hom(G;H) correspon...