Invariant density for a class of initial distributions under quadratic mapping

For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.

Oligo(p-Phenylenevinylene) Derived Organogels: A Novel Class of Functional Supramolecular Materials

The main objective of the present study is to have a detailed investigation on the gelation properties, morphology and optical properties of small π-conjugated oligomers. For this purpose we have chosen oligo(p-phenylenevinylene)s (OPVs), a class of molecules which have received considerable attention due to their unique optical and electronic properties. Though a large number of reports are available in the literature on the self-assembly properties of tailor made OPVs, none of them pertain to the design of nanostructures based on organogels. In view of this, we aimed at the creation of functional chromophoric assemblies of π-conjugated OPVs through the formation of organogels, with the objective of crafting nanoscopic assemblies of different size and shape thereby modulating their optical and electronic properties.In order to fulfill the above objectives, the design and synthesis of a variety of OPVs with appropriate structural variations were planned. The design principle involves the derivatization of OPVs with weak H-bonding hydroxymethyl end groups and with long aliphatic hydrocarbon side chains. The noncovalent interactions in these molecules were expected to lead the formation of supramolecular assembly and gels in hydrocarbon solvents. In such an event, detailed study of gelation and extensive analysis of the morphology of the gel structures were planned using advanced microscopic techniques. Since OPVs are strongly fluorescent molecules, gelation is expected to perturb the optical properties. Therefore, detailed study on the gelation induced optical properties as a way to probe the nature and stability of the selfassembly was planned. Apart from this, the potential use of the modulation of the optical properties for the purpose of light harvesting was aimed. The approach to this problem was to entrap an appropriate energy trap to the OPV gel matrix which may lead to the efficient energy transfer from the OPV gel based donor to the entrapped acceptor. The final question that we wanted to address in this investigation was the creation of helical nanostructures through proper modification of the OPV backbone With chiral handles.The present thesis is a detailed and systematic approach to the realization of the above objectives which are presented in different chapters of the thesis.

Contribution of size fractions of planktonic algae to primary organic productivity in the coastal waters of Cochin- south west coast of lndia

This thesis entitled “Contribution of size fractions of planktonic algae to primary organic productivity in the coastal waters of cochin,south west coast of india”. Marine ecosystems planktonic algae are the most important primary producers on wliich considerable attention is being given on account of their supreme status in the marine food chain.The study of primary production in the Indian Ocean started With DANA (I928-30),, John Murray t I933-34). Discovery ( I934) and Albatross (I947-48) expeditions which tried to evaluate productivity from nutrients and standing crop of phytoplankton .The bioproductivity of the marine environment is dependent on various primary producers. ranging in size from picoplankton to larger macro phytoplankton. The quantity and quality of various size fractions of planktonic algae at any locality depend mainly on the hydrographic conditions of the area .In the coastal waters of Cochin- south west coast of lndia. Planktonic algal community is composed mainly of the diatoms, the dinoflagellates, the blue-green algae and the silicoflagellates, the former two contributing the major flora and found distributed in the all size fractions. The maximum number of species of diatoms at station 1 and station 2 was found in the pre-monsoon season.. The size groups of planktonic algae greater than 53 um are dominated by filamentous- chain forming and colonial diatoms. The coastal waters of Cochin. planktonic algae less than 53 um in size contribute significantly to primary productivity and the biodiversity of the microflora, indicating the presence of rich fishery resources in the south west coast of india.The study of different size fractions of planktonic algae and their relative contribution to the primary organic production is a useful tool for the estimation of the quantity and quality of fisheries.A deeper investigation on the occurrence of these microalgae and proper identification of their species would be of immense help for the assessment of the specificity and magnitude of fishery resources.

IIEPICTIIIN (IF CLASS-WNFLICT IN THE WIIRKS (IF NAGARJUN)

HINDI