Fuzzy Topological Games and Related Topics

The main purpose of study is to extend the concept of the topological game G(K, X) and some other kinds of games into fuzzy topological games and to obtain some results regarding them. Owing to the fact that topological games have plenty of applications in covering properties, it made an attempt to explore some inter relations of games and covering properties in fuzzy topological spaces. Even though the main focus is on fuzzy para-meta compact spaces and closure preserving shading families, some brief sketches regarding fuzzy P-spaces and Shading Dimension is also provided. In a topological game players choose some objects related to the topological structure of a space such as points, closed subsets, open covers etc. More over the condition on a play to be winning for a player may also include topological notions such as closure, convergence, etc. It turns out that topological games are related to the Baire property, Baire spaces, Completeness properties, Convergence properties, Separation properties, Covering and Base properties, Continuous images, Suslin sets, Singular spaces etc.

Structure Absorption Spectra Correlation in a Series of 2,6-Dimethyl-4-arylpyrylium Salts

A combined experimental and theoretical study of the absorption spectra of a group of closely related pyrylium perchlorates 1-11 are presented. Minor changes in the position of the substituents lead to drastic changes in the absorption spectra in this series of compounds. We have attempted to explain the observed changes using the x,y-band notation developed by Balaban and co-workers. Absorption spectra of all compounds are compared with results from time-dependent density functional theory (TDDFT) and Zerner’s intermediate neglect of differential overlap (ZINDO/S) level calculations. Results of the calculations are in good agreement with experimental observations and an interesting correlation between Balaban’s notations and the MO transitions are obtained for simple derivatives. It is suggested that for more complex systems such as R- and â-naphthyl substituted systems, the empirical method is not appropriate.

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.

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.

Implications of Hydrobiology and Nutrient dynamics on trophic structure and interactions in Cochin backwaters

In the present thesis entitled” Implications of Hydrobiology and Nutrient dynamics on Trophic structure and Interactions in Cochin backwaters”, an attempt has been made to assess the influence of general hydrography, nutrients and other environmental factors on the abundance, distribution and trophic interactions in Cochin backwater system. The study was based on five seasonal sampling campaigns carried out at 15 stations spread along the Cochin backwater system. The thesis is presented in the following 5 chapters. Salient features of each chapter are summarized below: Chapter 1- General Introduction: Provides information on the topic of study, environmental factors, back ground information, the significance, review of literature, aim and scope of the present study and its objectives.Chapter 2- Materials and Methods: This chapter deals with the description of the study area and the methodology adopted for sample collection and analysis. Chapter 3- General Hydrograhy and Sediment Characteristics: Describes the environmental setting of the study area explaining seasonal variation in physicochemical parameters of water column and sediment characteristics. Data on hydrographical parameters, nitrogen fractionation, phosphorus fractionation and biochemical composition of the sediment samples were assessed to evaluate the trophic status. Chapter 4- Nutrient Dynamics on Trophic Structure and Interactions: Describes primary, secondary and tertiary production in Cochin backwater system. Primary production related to cell abundance, diversity of phytoplankton that varies seasonally, concentration of various pigments and primary productivitySecondary production refers to the seasonal abundance of zooplankton especially copepod abundance and tertiary production deals with seasonal fish landings, gut content analysis and proximate composition of dominant fish species. The spatiotemporal variation, interrelationships and trophic interactions were evaluated by statistical methods. Chapter 5- Summary: The results and findings of the study are summarized in the fifth chapter of the thesis.

Novel [3+2] annulation reaction of nitrones with Burgess reagent and a few related reactions

Burgess reagent first prepared by E. M. Burgess in 1968, is a mild and selective dehydrating agent for secondary and tertiary alcohols and due to the amphipolar nature it is gainfully employed in a number of creative synthetic ventures. A close examination of the structure of Burgess reagent reveals that it can act as a 1,2-dipole. To the best of our knowledge, no attempts have been made to tap full synthetic potential of the amphipolar nature of this reagent and no reports on 1,3-dipolar addition to a σ-bond in acyclic systems are available in literature. In this context, we propose to unravel novel applications of Burgess reagent based on its amphipolar nature. Rich and multifaceted chemistry of nitrones form the basis of many successful chemical transformations used in attractive synthetic strategies. For the last 50 years special attention has been given to nitrones due to their successful application as building blocks in the synthesis of various natural and biologically active compounds. Our interest in nitrones stems out of its unique character: i.e. it is a 1,3-dipole exhibiting distinct nucleophilic activity. We reasoned that 1,3-dipole possessing significant nucleophilicity should react with amphipolar Burgess reagent with elimination of triethylamine to give the corresponding five-membered ring product by formal dipolar addition to a σ bond. To test this hypothesis we studied the reaction of nitrones with Burgess reagent. This thesis reveals our attempts to explore the [3+2] annulation reaction of nitrones with Burgess reagent which was found to be followed by a rearrangementinvolving C-to-N aryl migration, ultimately resulting in diarylamines and carbamates. We have also examined the reaction of cyanuric chloride with nitrones in DMF with a view to exploit the nucleophilicty of nitrones and to unravel the migratory aptitude, if any, observed in this reaction

A study on semigroup action on fuzzy subsets, inverse fuzzy automata and related topics

This thesis comprises five chapters including the introductory chapter. This includes a brief introduction and basic definitions of fuzzy set theory and its applications, semigroup action on sets, finite semigroup theory, its application in automata theory along with references which are used in this thesis. In the second chapter we defined an S-fuzzy subset of X with the extension of the notion of semigroup action of S on X to semigroup action of S on to a fuzzy subset of X using Zadeh's maximal extension principal and proved some results based on this. We also defined an S-fuzzy morphism between two S-fuzzy subsets of X and they together form a category S FSETX. Some general properties and special objects in this category are studied and finally proved that S SET and S FSET are categorically equivalent. Further we tried to generalize this concept to the action of a fuzzy semigroup on fuzzy subsets. As an application, using the above idea, we convert a _nite state automaton to a finite fuzzy state automaton. A classical automata determine whether a word is accepted by the automaton where as a _nite fuzzy state automaton determine the degree of acceptance of the word by the automaton. 1.5. Summary of the Thesis 17 In the third chapter we de_ne regular and inverse fuzzy automata, its construction, and prove that the corresponding transition monoids are regular and inverse monoids respectively. The languages accepted by an inverse fuzzy automata is an inverse fuzzy language and we give a characterization of an inverse fuzzy language. We study some of its algebraic properties and prove that the collection IFL on an alphabet does not form a variety since it is not closed under inverse homomorphic images. We also prove some results based on the fact that a semigroup is inverse if and only if idempotents commute and every L-class or R-class contains a unique idempotent. Fourth chapter includes a study of the structure of the automorphism group of a deterministic faithful inverse fuzzy automaton and prove that it is equal to a subgroup of the inverse monoid of all one-one partial fuzzy transformations on the state set. In the fifth chapter we define min-weighted and max-weighted power automata study some of its algebraic properties and prove that a fuzzy automaton and the fuzzy power automata associated with it have the same transition monoids. The thesis ends with a conclusion of the work done and the scope of further study.