Finite digraphs and KMS states

Kms States and the Chemical Potential for Disordered Systems

We extend the theory of the chemical potential associated to a compact separable gauge group to the case of disordered quantum systems. This is done in the natural framework of operator algebras. Among the other results, we show that the chemical potential does not depend on the disorder. The situation of the n–torus is treated in some detail. Indeed, provided that the zero– point is fixed inde...

MINIMIZATION OF DETERMINISTIC FINITE AUTOMATA WITH VAGUE (FINAL) STATES AND INTUITIONISTIC FUZZY (FINAL) STATES

In this paper, relations among the membership values of gener- alized fuzzy languages such as intuitionistic fuzzy language, interval-valued fuzzy language and vague language are studied. It will aid in studying the properties of one language when the properties of another are known. Further, existence of a minimized nite automaton with vague ( final) states for any vague regular language recog...

Green's Symmetries in Finite Digraphs

The semigroup DV of digraphs on a set V of n labeled vertices is defined. It is shown that DV is faithfully represented by the semigroup Bn of n × n Boolean matrices and that the Green’s L, R, H, and D equivalence classifications of digraphs in DV follow directly from the Green’s classifications already established for Bn. The new results found from this are: (i) L, R, and H equivalent digraphs...

Digraphs of finite linear transformations

If T is a function from a finite set V to itself, we form the digraph D of T as follows. It has V for its vertex set, and there is an arc from x to T (x) for each x E V. Here we answer the following question. Given a finite field F, which digraphs arise as digraphs of a linear transformation from some finite dimensional vector space over F to itself?

Perturbation Theory of W*-Dynamics, Liouvilleans and KMS-States