A translation surface on (S,Σ) gives rise to two transverse measured foliations F ,G on S with singularities in Σ, and by integration, to a pair of cohomology classes [F ], [G] ∈ H(S,Σ;R). Given a measured foliation F , we characterize the set of cohomology classes b for which there is a measured foliation G as above with b = [G]. This extends previous results of Thurston [Th] and Sullivan [Su]...

The cardinality of the minimal generating set of a module M i.e g(M) plays a very important role in the study of QTAG-Modules. Fuchs [1] mentioned the importance of upper and lower basic subgroups of primary groups. A need was felt to generalize these concepts for modules. An upper basic submodule B of a QTAG-Module M reveals much more information about the structure of M . We find that each ba...

A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules.Over the past several years QTAG-modules have been the subject of intense investigation yet there is much to explore.The impetus for these efforts stems from the fact that the rings considered here are almost restriction free....

Let T : 0;1] ! 0;1] be an expanding piecewise monotonic map, and consider the set R of all points, whose orbits omit a certain nite union of open intervals. It is shown that the Hausdorr dimension HD (R) depends continuously on small perturbations of the endpoints of these open intervals. A similar result for the topological pressure is also obtained. Furthermore it is shown that for every t 2 ...