We present a new non perturbative renormalization group for classical simple fluids. The theory is built in the Grand Canonical ensemble and in the framework of two equivalent scalar field theories as well. The exact mapping between the three renormalization flows is established rigorously. In the Grand Canonical ensemble the theory may be seen as an extension of the Hierarchical Reference Theo...

Thisnotedescrib esrecen tresearc h usingstructural propertiesofflnitegroupstodevise–cien talgorithms forgroupcomputation. 1991Mathematics SubjectClassiflcation: 20B40,20D05,68Q40 KeywordsandPhrases: grouptheoretic algorithms, implegroups

We show that Thompson’s group F is the symmetry group of the ‘generic idempotent’. That is, take the monoidal category freely generated by an object A and an isomorphism A ⊗ A A; then F is the group of automorphisms of A.

Let G be a group, F a field, and A a finite-dimensional central simple algebra over F on which G acts by F -algebra automorphisms. We study the ideals and subalgebras of A which are preserved by the group action. Let V be the unique simple module of A. We show that V is a projective representation of G and A = EndD(V ) makes V into a projective representation. We then prove that there is a natu...

Mathematical modeling and analysis of collective behavior of multi-agent systems is an important tool that will enable researchers to study even very large systems, validate agent models and get insight into multi-agent system design. Biologists, for example, can compare the model’s predictions to the observed collective behavior of simple organisms, such as social insects, to understand indivi...