Study on Fuzzy Ordered FuzzyTopological Spaces

In this study we combine the notions of fuzzy order and fuzzy topology of Chang and define fuzzy ordered fuzzy topological space. Its various properties are analysed. Product, quotient, union and intersection of fuzzy orders are introduced. Besides, fuzzy order preserving maps and various fuzzy completeness are investigated. Finally an attempt is made to study the notion of generalized fuzzy ordered fuzzy topological space by considering fuzzy order defined on a fuzzy subset.

Studies on Catalysis by Ordered Mesoporous SBA-15 Materials Modified with Transition Metals

To meet the challenges related to the chemical industry,development of efficient catalysts is necessary.The mesoporous materials like SBA-15 are considered as good catalyst candidates of 21st century.SBA-15 mesoporous materials are catalytically inactive,but allow the dispersion of catalytically active phases into the framework.So these materials can be considered as an interesting alternative for preparing catalytically active metal nanoparticles in-situ into it.In the present work various transition metals are incorporated to improve the catalytic activity of SBA-15 material.The fundamental aspects of the preparation,characterization and the activity studies are briefly viewed in this thesis. Systematic investigation of the physico-chemical properties and catalytic activity studies of the prepared materials were carried out and presented in this Study.

Ordered mesoporous silica as supports for immobilization of biocatalyst

Mesoporous materials are of great interest to the materials community because of their potential applications for catalysis,separation of large molecules,medical implants,semiconductors,magnetoelectric devices.The thesis entitled 'Ordered Mesoporous Silica as supports for immobilization of Biocatalyst' presents how the pore size can be tuned without the loss in ordered structure for the entrapment of an industially important biocatalyst-amylase.Immobilization of enzymes on ordered mesoporous material has triggered new ooportunities for stabilizing enzymes with improved intrinsic and operational stabilities.

Some problems in set topology relating group of homeomorphisms and order

In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out