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 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.

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

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 coagulase-positive staphylococci and Vibrio parahaemollticus in selected items of fish, crustaceans and fishery products

In India much work has been done on different aspects of quality of processed fish and fishery products (Pillai et al., 1965; Iyer and Chaudhuri, 1966; Iyer et al., 1966; Sreenivasan and Joseph, 1966; Pillai and Rao, 1969; Mathen et al., 1975; Valsan et al., 1985) and standards have been formulated for almost all the fishery products. Quality standards for fresh fish cover only a few fish species available in the markets. For the formulation and recommendation of quality standards for fish and fishery products for domestic trade detailed background informations are necessary. Khot et al., (1982), Valsan et al. J (1985) and Iyer et al. (1986) have reported on the bacterial flora of sea foods at retail level in Bombay. Cochin is a major fish landing centre of the south west coast of India, and an average of 25,000. tonnes of fish/shell fish are landed annually at this harbour which is about 10 percent of the total catch of fish in Kerala (Lakshmanan -et -al., 1984). All the varieties of marine, brackish water and fresh water fishes are available in Cochln throughout the year for catering to Its cosmopolitan. population and informations regarding their bacteriological quality are scanty. Hence the present study was undertaken to investigate the bacteriological quality of fish and fishery products available in the markets and cold storages situated in and around Cochin meant for internal consumption.

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.

Effect Of Raw Material Quality On The Shelf Life Of Frozen Stored Fish And Fishery Products

Frozen storage characteristics and shelflife vary considerably among species as well as within the species (Powrie, 1973; Fennema. 1973). This can be attributed to the variation in the composition of fish among various species. In certain species like sardines and mackerel. wide seasonal variation in chemical composition occur within the species. These variations affect the quality and shelflife. The nutritional level of water. spawning, method of catching, struggling etc. are found to have profound influence on the condition of the fresh fish. Soon after death the deteriorative changes in fish start due to autolysis and bacterial growth. The rate of these changes depends mainly on temperature. The handling methods have great influence on bacterial contamination. Thus the type oi'handling. temperature control. period of chill storage. processing methods. type of freezing, condition of frozen storage and period of storage affect the quality and shelflife Of the fisho In the present study extensive investigations were carried out on various factors affecting the quality of fish as well as their effect on the physical. chemical and sensory qualities of fish during frozen storage and the shelflife

Studies on the histological and biochemical changes during spermatogenesis in MUGIL CEPHALUS linnaeus and related species

Several studies on the biology and fisheries of mullets, particularly of M cephalus are now available. Different aspects of breeding, larval rearing, seed production, field culture and ecophysiology have also been investigated. However, information on the spermatogenesis in M cephalus as well as L parsia is scanty. Since an understanding of the reproductive strategies is an essential pre-requisite for evolving successful breeding programmes through artificial fertilization and gametic preservation, investigations on spermatogenesis in these species were taken up and the results are presented in this thesis. The thesis is presented in 9 chapters