Some Generalizations of Fuzzy Metrizability

The main purpose of the study is to extent concept of the class of spaces called ‘generalized metric spaces’ to fuzzy context and investigates its properties. Any class of spaces defined by a property possessed by all metric spaces could technically be called as a class of ‘generalized metric spaces’. But the term is meant for classes, which are ‘close’ to metrizable spaces in some under certain kinds of mappings. The theory of generalized metric spaces is closely related to ‘metrization theory’. The class of spaces likes Morita’s M- spaces, Borges’s w-spaces, Arhangelskii’s p-spaces, Okuyama’s  spaces have major roles in the theory of generalized metric spaces. The thesis introduces fuzzy metrizable spaces, fuzzy submetrizable spaces and proves some characterizations of fuzzy submetrizable spaces, and also the fuzzy generalized metric spaces like fuzzy w-spaces, fuzzy Moore spaces, fuzzy M-spaces, fuzzy k-spaces, fuzzy -spaces study of their properties, prove some equivalent conditions for fuzzy p-spaces. The concept of a network is one of the most useful tools in the theory of generalized metric spaces. The -spaces is a class of generalized metric spaces having a network.

Studies on some generalizations of line graph and the power domination problem in graphs

Department of Mathematics, Cochin University of Science and Technology

Muscarinic M1 and M3 Receptors,IP3 and cGMP Functional Regulation in Streptozotocin Induced Diabetic Rats: Insulin and Somatotropin Induced Rejuvenation as a Function of Age

The present study describes that acetylcholine through muscarinic Ml and M3 receptors play an important role in the brain function during diabetes as a function of age. Cholinergic activity as indicated by acetylcholine esterase, a marker for cholinergic function, decreased in the brain regions - the cerebral cortex, brainstem and corpus striatum of old rats compared to young rats. in diabetic condition, it was increased in both young and old rats in cerebral cortex, and corpus striatum while in brainstem it was decreased. The functional changes in the muscarinic receptors were studied in the brain regions and it showed that muscarinic M I receptors of old rats were down regulated in cerebral cortex while in corpus striatum and brainstem it was up regulated. Muscarinic M3 receptors of old rats showed no significant change in cerebral cortex while in corpus striatum and brainstem muscarinic receptors were down regulated. During diabetes, muscarinic M I receptors were down regulated in cerebral cortex and brainstem of young rats while in corpus striatum they were up regulated. In old rats, M I receptors were up regulated in cerebral cortex, corpus striatum and in brainstem they were down regulated. Muscarinic M3 receptors were up regulated in cerebral cortex and brainstem of young rats while in corpus striatum they were down regulated. In old rats, muscarinic M l receptors were up regulated in cerebral cortex, corpus striatum and brainstem. In insulin treated diabetic rats the activity of the receptors were reversed to near control. Pancreatic muscarinic M3 receptor activity increased in the pancreas of both young and old rats during diabetes. In vitro studies using carbachol and antagonists for muscarinic Ml and M3 receptor subtypes confirmed the specific receptor mediated neurotransmitter changes during diabetes. Calcium imaging studies revealed muscarinic M I mediated Ca2 + release from the pancreatic islet cells of young and old rats. Electrophysiological studies using EEG recording in young and old rats showed a brain activity difference during diabetes. Long term low dose STH and INS treated rat brain tissues were used for gene expression of muscarinic Ml, M3, glutamate NMDARl, mGlu-5,alpha2A, beta2, GABAAa1 and GABAB, DAD2 and 5-HT 2C receptors to observe the neurotransmitter receptor functional interrelationship for integrating memory, cognition and rejuvenating brain functions in young and old. Studies on neurotransmitter receptor interaction pathways and gene expression regulation by second messengers like IP3 and cGMP in turn will lead to the development of therapeutic agents to manage diabetes and brain activity.From this study it is suggested that functional improvement of muscarinic Ml, M3, glutamate NMDAR1, mGlu-5, alpha2A, beta2, GABAAa1 and GABAB, DAD2 and 5-HT 2C receptors mediated through IP3 and cGMP will lead to therapeutic applications in the management of diabetes. Also, our results from long term low dose STH and INS treatment showed rejuvenation of the brain function which has clinical significance in maintaining healthy period of life as a function of age.

Neurotransmitters Functional Balance in Neurodegenerative Disease Management:recent Advances

The recent developments in neurobiology have rendered new prominence and potential to study about the structure and function of brain and related disorders. Human behaviour is the net result of neural control of the communication between brain cells. Neurotransmitters are chemicals that are used to relay, amplify and modulate electrical signals between neurons and/or another cell. It mediates rapid intercellular communication through the nervous system by interacting with cell surface receptors. These receptors often trigger second messenger signaling pathways that regulate the activity of ion channels. The functional balance of different neurotransmitters such as Acetylcholine (Ach), Dopamine (DA), Serotonin (5-HT), Norepinephrine (NE), Epinephrine (EPI), Glutamate and Gamma amino butyric acid (GABA) regulates the growth, division and other vital functions of a normal cell / organism (Sudha, 1998). Any change in neurotransmitters' functional balance will result in the failure of cell function and may lead to the occurrence of diseases. Abnormalities in the production or functioning of neurotransmitters have been implicated in a number of neurological disorders like Schizophrenia, Alzheimer's, Epilepsy, Depression and Parkinson's disease. Changes in central and peripheral neuronal signaling system is also noted in diabetes, cancer, cell proliferation, alcoholism and aging. Elucidation of neurotransmitters receptor interaction pathways and gene expression regulation by second messengers and transcriptional factors in health and disease conditions can lead to new small molecules for development of therapeutic agents to improve neurological disease conditions. Increased awareness of the global effects of neurological disorders should help health care planners and the neurological community set appropriate priorities in research, prevention, and management of these diseases.

Bivariate semi-Pareto distributions and processes

A bivariate semi-Pareto distribution is introduced and characterized using geometric minimization. Autoregressive minification models for bivariate random vectors with bivariate semi-Pareto and bivariate Pareto distributions are also discussed. Multivariate generalizations of the distributions and the processes are briefly indicated.

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

Studies on finfish and shellfish diseases

In the present study, fifteen typee of diseases occurring in twenty one species of finfishes end shellfishes are documented and the causes studied. All these are being reported from India for the first time which adds considerably to our existinq knowledge on the subject.In fact, the candidate's studies embodied in this Thesis has also an applied significance aimed at the proper management_of finfish and shellfish aquaculture systems in this country.The thesis is presented in seven main chapters.