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

An analogue of the logistic map in two dimensions

This is a sequel to our earlier work on the modulated logistic map. Here, we first show that the map comes under the universality class of Feigenbaum. We then give evidence for the fact that our model can generate strange attractors in the unit square for an uncountable number of parameter values in the range μ∞<μ<1. Numerical plots of the attractor for several values of μ are given and the self-similar structure is explicity shown in one case. The fractal and information dimensions of the attractors for many values of μ are shown to be greater than one and the variation in their structure is analysed using the two Lyapunov exponents of the system. Our results suggest that the map can be considered as an analogue of the logistic map in two dimensions and may be useful in describing certain higher dimensional chaotic phenomena.

On infinite graphs and related matrices

This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix

Socio-Economic Dimensions of Health Care Development Among Tribals in Kerala: A Study of Tribal Communities in Wynad

The contemporary explanations and discussions of the relationship between medicine and health, and society centre around assumptions that can be broadly classified into three setsl. The first set considers health and illness as predominantly ‘biological’ and therefore, having nothing to do with the social and economic environment in which it occurs. The struggle to combat illness therefore, lies entirely within the purview of modern medicine which is neutral to economic or social change. The second considers practice of medicine as a natural science. It allows the doctor to separate himself from his subject matter, the patient, in the samelway as the natural scientist is assumed to separate himself from his subject matter, the natural world. As a 'science' and with the scientific method, it can produce unchallengable and autonomous body of knowledge which is free from the wider social and economic context. The third, different from the above, recognises the relationship between health, medicine and society. Social and environmental aspects as determinants of illness or of health comes to sharp focus here and it assigns to medicine the status of a mediator, the only viable mediator, between people and diseases. In this scheme of things the usefulness of medicine is unquestionable but the problem lies in not having enough of it to go arounds.

SUBKAVYA: KATHYA KE VIBHINNA AYAM (POETRY OF SURDAS-DIFFERENT DIMENSIONS OF POETIC CONTENT)

HINDI

THE CHANGING DIMENSIONS or SOCIAL c0NsI0usNEss IN THE REPRESENTATIVE NOVELS or SEVENTIES

Hindi

DIMENSIONS OF CULTURAL CRISIS IN CONTEMPORARY HINDI POETRY

Hindi