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.

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.

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

Relative survival of Escherichia coli and Salmonella typhimurium in a tropical estuary

Microcosm studies have been carried out to find out the relative survival of Escherichia coli and Salmonella typhimurium in a tropical estuary. Survival has been assessed in relation to the important self-purifying parameters such as biotic factors contained in the estuarine water, toxicity due to the dissolved organic and antibiotic substances in the water and the sunlight. The results revealed that sunlight is the most important inactivating factor on the survival of E. coli and S. typhimurium in the estuarine water. While the biological factors contained in the estuarine water such as protozoans and bacteriophages also exerted considerable inactivation of these organisms, the composition of the water with all its dissolved organic and inorganic substances was not damaging to the test organisms. Results also indicated better survival capacity of E. coli cells under all test conditions when compared to S. typhimurium

Length-weight relationship, relative condition factor (Kn) and morphometry of Arius subrostratus (Valenciennes, 1840) from a coastal wetland in Kerala

The length – weight relationship and relative condition factor of the shovel nose catfish, Arius subrostratus (Valenciennes, 1840) from Champakkara backwater were studied by examination of 392 specimens collected during June to September 2008. These fishes ranged from 6 to 29 cm in total length and 5.6 to 218 g in weight. The relation between the total length and weight of Arius subrostratus is described as Log W = -1.530+2.6224 log L for males, Log W = - 2.131 + 3.0914 log L for females and Log W = - 1.742 + 2.8067 log L for sexes combined. The mean relative condition factor (Kn) values ranged from 0.75 to 1.07 for males, 0.944 to 1.407 for females and 0.96 to 1.196 for combined sexes. The length-weight relationship and relative condition factor showed that the well-being of A. subrostratus is good. The morphometric measurements of various body parts and meristic counts were recorded. The morphometric measurements were found to be non-linear and there is no significant difference observed between the two sexes. From the present investigation, the fin formula can be written as D: I, 7; P: I, 12; A: 17 – 20; C: 26 – 32. There is no change in meristic counts with the increase in body length.