Box Products in Fuzzy Topological Spaces and Related Topics

The topology as the product set with a base chosen as all products of open sets in the individual spaces. This topology is known as box topology. The main objective of this study is to extend the concept of box products to fuzzy box products and to obtain some results regarding them. Owing to the fact that box products have plenty of applications in uniform and covering properties, here made an attempt to explore some inter relations of fuzzy uniform properties and fuzzy covering properties in fuzzy box products. Even though the main focus is on fuzzy box products, some brief sketches regarding hereditarily fuzzy normal spaces and fuzzy nabla product is also provided. The main results obtained include characterization of fuzzy Hausdroffness and fuzzy regularity of box products of fuzzy topological spaces. The investigation of the completeness of fuzzy uniformities in fuzzy box products proved that a fuzzy box product of spaces is fuzzy topologically complete if each co-ordinate space is fuzzy topologically complete. The thesis also prove that the fuzzy box product of a family of fuzzy α-paracompact spaces is fuzzy topologically complete. In Fuzzy box product of hereditarily fuzzy normal spaces, the main result obtained is that if a fuzzy box product of spaces is hereditarily fuzzy normal ,then every countable subset of it is fuzzy closed. It also deals with the notion of fuzzy nabla product of spaces which is a quotient of fuzzy box product. Here the study deals the relation connecting fuzzy box product and fuzzy nabla product

A Study on the Kerridge's Inaccuracy Measure and Related Conceptss

Department of Statistics, Cochin University of Sciene ans Technology

Studies on some graph operators and related topics

Department of Mathematics, Cochin University of Science and Technology

Studies on Surface Properties and Catalytic Activity of Some Chromites and Related Spinels

The prime intension of the present work was a synthetic investigation of the preparation, surface properties and catalytic activity of some transition metal substituted copper chromite catalysts. Homogeneous co-precipitation method is employed for the preparation of catalysts. Since the knowledge about the structure and composition of the surface is critical in explaining the reactivity and selectivity of a solid catalyst. a systematic investigation of the physico-chemical properties of the prepared systems was carried out. The catalytic activity of these systems has also been measured in several oxidation reactions of industrial as well as environmental relevance. The thesis is dedicated to several aspects of chromite spinels giving emphasis to its preparation, characterization and catalytic performance towards oxidation reactions.

2(3H)-Furanones and related substrates: Synthetic strategies and selectivity profile in their reactivity

The synthesis and reactions of simple derivatives of 2(3H)- and 3(2H)furanones have attracted considerable attention in recent years, primarily in connection with development of routes to antitumor agents that contain this ring as central structural unit. They also serve as useful synthetic building blocks for lactones and furans and are the precursors of a wide variety of biologically important heterocyclic systems. Although a number of syntheses of furanones were known they were in many cases limited to specific substitution pattems. The development of altemative strategies for the preparation of these heterocycles is therefore of considerable importance or continues to be a challenge.We propose to develop new and general approaches to the synthesis of furanone ring systems from simple and readily available starting materials since we were interested in examining their rich photochemistry. The photochemical reactivity of Beta,gama-unsaturated lactams and lactones is a subject of current interest. Some of the prominent photoreaction pathways of unsaturated lactones include decarbonylation, solvent addition to double bonds, decarboxylation, migration of aryl substituents and dimerisation. lt was reported earlier that the critical requirement for clean photochemical cleavage of the acyl-oxygen bond is the presence ofa double bond adjacent to the ether oxygen and 2(3H)-furanones possessing this structural requirement undergo facile decarbonylation. But related phenanthrofuranones are isolated as photostable end products upon irradiation. Hence we propose to synthesis a few phenanthro-2(3H)-furanones to study the effect of a radical stabilising group at 3-position of furanone ring on photolysis. To explore the tripletmediated transformations of 2(3H)-furanones in polar and nonpolar solvents a few 3,3-bis(4-chlorophenyl)-5-aryl-3H-furan-2-ones and 3,3-di(p-tolyl)-5-aryl- 3H-furan-2-ones were synthesised from the corresponding dibenzoylstyrene precursors by neat thermolysis. Our aim was to study the nature of intermediates involved in these transformations.We also explored the possibility of developing a new and general approach to the synthesis of 3(2H)-furanones from simple and readily available starting materials since such general procedures are not available. The protocol developed by us employs readily available phenanthrenequinone and various 4-substituted acetophenones as starting materials and provides easy access to the required 3(2H)-furanone targets. These furanone derivatives have immense potential for further investigations .We also aimed the synthesis of a few dibenzoylalkene-type systems such as acenaphthenone-2—ylidene ketones and phenanthrenone-9-ylidene ketones. These systems were expected to undergo thermal rearrangement to give furanones and spirofuranones. Also these systems can be categorised as quinonemethides which are valuable synthetic intermediates.