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.

Microbial Biosurfactants – Review

Biosurfactants are surface active compounds released by microorganisms. They are biodegradable non-toxic and eco-friendly materials. In this review we have updated the information about different microbial surfactants. The biosurfactant production depends on the fermentation conditions, environmental factors and nutrient availability. The extraction of the biosurfactants from the cell-free supernatant using the solvent extraction procedure and the qualitative and quantitative analysis has been discussed with appropriate equipment details. The application of the biosurfactant includes biomedical, cosmetic and bioremediation. The type of microbial biosurfactants include trehalose lipids, rhamnolipids, sophorolipids, glycolipids, cellobiose lipids, polyol lipids, diglycosyl diglycerides, lipoloysaccharides, arthrofactin, lichensyn A and B, surfactin, viscosin, phospholipids, sulphonyl lipids and fatty acids. Rhamnolipid biosurfactants produced by Pseudomonas aeruginosa DS10-129 showed significant applications in the bioremediation of hydrocarbons in gasoline spilled soil and petroleum oily sludge. Rhamnolipid biosurfactant enhanced the bioremediation process by releasing the weathered oil from the soil matrices and enhanced the bioavailability of hydrocarbons for microbial degradation. It is having potential applications in the remediation of hydrocarbon contaminated sites. Biosurfactants from marine microorganisms also offer great potential in bioremediation of oil contaminated oceanic environments