On Some Infinite Convex Invariants

The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions

lntemet utilization and academic activities of faculty members in the universities of Kerala : an analytical study

This thesis Entitled Internet Utilization and Academic Activities of Faculty Members in the Universities of kerala: an analytical study. Today, scientific research is throwing up new discoveries, inventions and vistas by the hour. We are witnessing a veritable knowledge explosion. It is important for members of university faculty members to keep abreast of it for giving up-t-date information to their students about the new development in the subject of their study. The internet is an invaluable tool for achieving it. Most of the universities have sufficient internet facility, but the accessibility to all the faculty members is not adequate. University Libraries also provides standard supplementary service in the internet area. This study indicates differential level of awareness and utilization of the internet services by the faculty members in the areas of teaching, research and publication. However the overall impression is that the awareness and utilization is inadequate. This point to the urgent need to devise programs and schemes to promote internet utilization among the faculty members. The suggestions indicate the key areas that deserve attention by policy makers and administrators. Thanks to the internet, every new development in every field of study is just a click away for faculty members, research scholars and students.