The aim of this paper is to introduce and study two new classes of spaces, called g∗-pre regular and g∗-pre normal spaces. Some basic properties of these separation axioms are studied by utilizing g∗-preclosed and g∗-preopen sets. A subset A of a space X is called g∗-preclosed (briefly g∗p-closed) set if pcl(A) ⊆ U whenever A ⊆ U and U is g-open in X. Mathematics Subject Classification: 54D10, ...

Regular g-measures are discrete-time processes determined by conditional expectations with respect to the past. One-dimensional Gibbs measures, on the other hand, are fields determined by simultaneous conditioning on past and future. For the Markovian and exponentially continuous cases both theories are known to be equivalent. Its equivalence for more general cases was an open problem. We prese...

The group PGL(2, q) has an embedding into PGL(3, q) such that it acts as the group fixing a nonsingular conic in PG(2, q). This action affords a coherent configuration R(q) on the set L(q) of non-tangent lines of the conic. We show that the relations can be described by using the cross-ratio. Our results imply that the restrictions R+(q) and R−(q) of R(q) to the set L+(q) of secant (hyperbolic)...