Geometric Algebra and Einstein’s Electron

This thesis entitled Geometric algebra and einsteins electron: Deterministic field theories .The work in this thesis clarifies an important part of Koga’s theory.Koga also developed a theory of the electron incorporating its gravitational field, using his substitutes for Einstein’s equation.The third chapter deals with the application of geometric algebra to Koga’s approach of the Dirac equation. In chapter 4 we study some aspects of the work of mendel sachs (35,36,37,).Sachs stated aim is to show how quantum mechanics is a limiting case of a general relativistic unified field theory.Chapter 5 contains a critical study and comparison of the work of Koga and Sachs. In particular, we conclude that the incorporation of Mach’s principle is not necessary in Sachs’s treatment of the Dirac equation.

Studies in Fuzzy Commutative Algebra

The main objective of this thesis was to extend some basic concepts and results in module theory in algebra to the fuzzy setting.The concepts like simple module, semisimple module and exact sequences of R-modules form an important area of study in crisp module theory. In this thesis generalising these concepts to the fuzzy setting we have introduced concepts of ‘simple and semisimple L-modules’ and proved some results which include results analogous to those in crisp case. Also we have defined and studied the concept of ‘exact sequences of L-modules’.Further extending the concepts in crisp theory, we have introduced the fuzzy analogues ‘projective and injective L-modules’. We have proved many results in this context. Further we have defined and explored notion of ‘essential L-submodules of an L-module’. Still there are results in crisp theory related to the topics covered in this thesis which are to be investigated in the fuzzy setting. There are a lot of ideas still left in algebra, related to the theory of modules, such as the ‘injective hull of a module’, ‘tensor product of modules’ etc. for which the fuzzy analogues are not defined and explored.

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. Even mathematicians like H. Poincare worried about this. He observed that mathematical models are over idealizations, for instance, he said that only in Mathematics, equality is a transitive relation. A first attempt to save this situation was perhaps given by K. Menger in 1951 by introducing the concept of statistical metric space in which the distance between points is a probability distribution on the set of nonnegative real numbers rather than a mere nonnegative real number. Other attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A. Sklar and others. An aspect in common to all these approaches is that they model impreciseness in a probabilistic manner. They are not able to deal with situations in which impreciseness is not apparently of a probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces.

Some Problems In Algebra And Topology A Study Of Fuzzy Convexity With Special Reference To Separation Properties

This thesis is a study of abstract fuzzy convexity spaces and fuzzy topology fuzzy convexity spaces No attempt seems to have been made to develop a fuzzy convexity theoryin abstract situations. The purpose of this thesis is to introduce fuzzy convexity theory in abstract situations

Mobility Metric based LEACH-Mobile Protocol

Cluster based protocols like LEACH were found best suited for routing in wireless sensor networks. In mobility centric environments some improvements were suggested in the basic scheme. LEACH-Mobile is one such protocol. The basic LEACH protocol is improved in the mobile scenario by ensuring whether a sensor node is able to communicate with its cluster head. Since all the nodes, including cluster head is moving it will be better to elect a node as cluster head which is having less mobility related to its neighbours. In this paper, LEACH-Mobile protocol has been enhanced based on a mobility metric “remoteness” for cluster head election. This ensures high success rate in data transfer between the cluster head and the collector nodes even though nodes are moving. We have simulated and compared our LEACH-Mobile-Enhanced protocol with LEACHMobile. Results show that inclusion of neighbouring node information improves the routing protocol.

Mobility Metric based LEACH-Mobile Protocol

Cluster based protocols like LEACH were found best suited for routing in wireless sensor networks. In mobility centric environments some improvements were suggested in the basic scheme. LEACH-Mobile is one such protocol. The basic LEACH protocol is improved in the mobile scenario by ensuring whether a sensor node is able to communicate with its cluster head. Since all the nodes, including cluster head is moving it will be better to elect a node as cluster head which is having less mobility related to its neighbours. In this paper, LEACH-Mobile protocol has been enhanced based on a mobility metric “remoteness” for cluster head election. This ensures high success rate in data transfer between the cluster head and the collector nodes even though nodes are moving. We have simulated and compared our LEACH-Mobile-Enhanced protocol with LEACHMobile. Results show that inclusion of neighbouring node information improves the routing protocol.