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.

ON (s,S) inventory policy with/without retrial and interruption of services/production

In this thesis we have developed a few inventory models in which items are served to the customers after a processing time. This leads to a queue of demand even when items are available. In chapter two we have discussed a problem involving search of orbital customers for providing inventory. Retrial of orbital customers was also considered in that chapter; in chapter 5 also we discussed retrial inventory model which is sans orbital search of customers. In the remaining chapters (3, 4 and 6) we did not consider retrial of customers, rather we assumed the waiting room capacity of the system to be arbitrarily large. Though the models in chapters 3 and 4 differ only in that in the former we consider positive lead time for replenishment of inventory and in the latter the same is assumed to be negligible, we arrived at sharper results in chapter 4. In chapter 6 we considered a production inventory model with production time distribution for a single item and that of service time of a customer following distinct Erlang distributions. We also introduced protection of production and service stages and investigated the optimal values of the number of stages to be protected.

Studies on Fuzzy Matroitls and Related Topics

The doctoral thesis focuses on the Studies on fuzzy Matroids and related topics.Since the publication of the classical paper on fuzzy sets by L. A. Zadeh in 1965.the theory of fuzzy mathematics has gained more and more recognition from many researchers in a wide range of scientific fields. Among various branches of pure and applied mathematics, convexity was one of the areas where the notion of fuzzy set was applied. Many researchers have been involved in extending the notion of abstract convexity to the broader framework of fuzzy setting. As a result, a number of concepts have been formulated and explored. However. many concepts are yet to be fuzzified. The main objective of this thesis was to extend some basic concepts and results in convexity theory to the fuzzy setting. The concept like matroids, independent structures. classical convex invariants like Helly number, Caratheodoty number, Radon number and Exchange number form an important area of study in crisp convexity theory. In this thesis, we try to generalize some of these concepts to the fuzzy setting. Finally, we have defined different types of fuzzy matroids derived from vector spaces and discussed some of their properties.

Studies on magnetic monopole solutions of non-abelian gauge theories and related problems

In 1931 Dirac studied the motion of an electron in the field of a magnetic monopole and found that the quantization of electric charge can be explained by postulating the mere existence of a magnetic monopole. Since 1974 there has been a resurgence of interest in magnetic monopole due to the work of ‘t’ Hooft and Polyakov who independently observed that monopoles can exist as finite energy topologically stable solutions to certain spontaneously broken gauge theories. The thesis, “Studies on Magnetic Monopole Solutions of Non-abelian Gauge Theories and Related Problems”, reports a systematic investigation of classical solutions of non-abelian gauge theories with special emphasis on magnetic monopoles and dyons which possess both electric and magnetic charges. The formation of bound states of a dyon with fermions and bosons is also studied in detail. The thesis opens with an account of a new derivation of a relationship between the magnetic charge of a dyon and the topology of the gauge fields associated with it. Although this formula has been reported earlier in the literature, the present method has two distinct advantages. In the first place, it does not depend either on the mechanism of symmetry breaking or on the nature of the residual symmetry group. Secondly, the results can be generalized to finite temperature monopoles.

Studies On The Synthesis Of Vitamin A And Related Compounds

In the present work different new approaches for the synthesis of Vitamin A are investigated. In these synthetic schemes, all the twenty carbon atoms of the target molecule are derived either fully from components isolated from common essential oils or partially from commercially available materials. By retrosynthetic analysis, Vitamin A molecule can be disconnected into a cyclic and a linear unit. Different methods for the synthesis of the linear and the cyclic components are described. The monoterpenes, geraniol and citral, major constituents of palmarosa and lemongrass oils, have the required basic carbon framework for consideration as starting materials for the synthesis of Vitamin A. The potential of these easily available naturally occurring compounds as promising starting materials for Vitamin A synthesis is demonstrated. Organoselenium and organosulfur mediated functional group transformations for the synthesis of the functionalised conjugated C10 linear components (ie., the dimethyloctatriene derivatives) are reported. The classical approaches as well as the attempted preparation of cyclic C10 and C13 units employed in the present study as intermediates for Vitamin A synthesis are described. The utility of commercially available materials namely 2-acetylbutyrolactone and levulinic acid in -the preparation of C5 intermediates for Vitamin A synthesis is demonstrated.

Kinetics and mechanism of urea - formaldehyde and related reactions

Urea-formaldehyde resins find numerous applications in adhesive, textile finishing and moulded plastic industries. Kinetic investigations of the reactions of urea and its related compounds with formaldehyde in aqueous acid, alkaline and neutral media have been carried out. A thin—layer chromatographic method was developed for the separation and estimation of the products of these reactions. Using this technique the various initial steps in the reactions were analysed and the rate constants have been determined.

Fermentation Of Rice And Related Products By Bacillus Sp.

Recently’ recognition cnf immobilization ‘technology for the rapid conversion of several substrates into metabolites and repeated reuse of the biocatalysts have drawn the attention of the fermentation scientists and technologists to try these new technologies for the rapid production of pnxkmt and enhancement of the efficiencies of the systems Hence in the present study rice was selected,as a substrate since it is a rich source of starch, available and cultivated throughout the year almost in all part of our country. Rice although known for its use as a staple food in many forms as rice, idli, dosai etc., has not been used in industry extensively. However, it ii; a potential resource for’ the production of alcohol, high protein food anui for sugar and sugar syrups as it is evidenced by the few reports mentioned in the review of literature. Of the several microorganisms available, Bacillus sp, is a known candidate for the production of amylases. Hence in the present study Bacillus sp, was desired for its known efficiencies in starch conversion