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.

Haematology of Fenneropenaeus indicus in response to environmental alterations and microbial infections

Aquaculture has developed to become one of the fastest growing food producing sectors in the world.Today India is one among the major shrimp producing countries in the world.There are extensive and intensive shrimp culture practices. In extensive shrimp culture, shrimps are stocked at low densities (< 25 PLs m'2)in large ponds or tidal enclosures in which little or no management is exercised or possible. Farmers depend almost entirely on natural conditions in extensive cultures. Intensive shrimp culture is carried out in high densities (>200 PLs m'2). Much of the world shrimp production still comes from extensive culture.There is a growing demand for fish and marine products for human and animal consumption. This demand has led to rapid growth of aquaculture, which some times has been accompanied by ecological impacts and economic loss due to diseases. The expansion of shrimp culture always accompanies local environmental degradation and occurrence of diseases.Disease out breaks is recognised as a significant constraint to aquaculture production. Environmental factors, water quality, pollution due to effluent discharge and pathogenic invasion due to vertical and horizontal transmission are the main causes of shrimp disease out breaks. Nutritional imbalance, toxicant and other pollutants also account for the onset of diseases. pathogens include viruses, bacteria, fungi and parasites.Viruses are the most economically significant pathogens of the cultured shrimps world wide. Disease control in shrimp aquaculture should focus first on preventive measures for eliminating disease promoting factors.ln order to design prophylactic and proactive measures against shrimp diseases, it is mandatory to understand the immune make up of the cultivable species, its optimum culture conditions and the physico chemical parameters of the rearing environment. It has been proven beyond doubt that disease is an end result of complex interaction of environment, pathogen and the host animal. The aquatic environment is abounded with infectious microbes.The transmission of disease in this environment is extremely easy, especially under dense, culture conditions. Therefore, a better understanding of the immune responses of the cultured animal in relation to its environmental alterations and microbial invasions is essential indevising strategic measures against aquaculture loss due to diseases. This study accentuate the importance of proper and regular health monitoring in shrimps employing the most appropriate haematological biomarkers for application of suitable prophylactic measures in order to avoid serious health hazards in shrimp culture systems.

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

Almost Self-Centered Median And Chordal Graphs

Almost self-centered graphs were recently introduced as the graphs with exactly two non-central vertices. In this paper we characterize almost selfcentered graphs among median graphs and among chordal graphs. In the first case P4 and the graphs obtained from hypercubes by attaching to them a single leaf are the only such graphs. Among chordal graph the variety of almost self-centered graph is much richer, despite the fact that their diameter is at most 3. We also discuss almost self-centered graphs among partial cubes and among k-chordal graphs, classes of graphs that generalize median and chordal graphs, respectively. Characterizations of almost self-centered graphs among these two classes seem elusive