3 resultados para Dirichlet L-function

em Cochin University of Science


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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.

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There is a recent trend to describe physical phenomena without the use of infinitesimals or infinites. This has been accomplished replacing differential calculus by the finite difference theory. Discrete function theory was first introduced in l94l. This theory is concerned with a study of functions defined on a discrete set of points in the complex plane. The theory was extensively developed for functions defined on a Gaussian lattice. In 1972 a very suitable lattice H: {Ci qmxO,I qnyo), X0) 0, X3) 0, O < q < l, m, n 5 Z} was found and discrete analytic function theory was developed. Very recently some work has been done in discrete monodiffric function theory for functions defined on H. The theory of pseudoanalytic functions is a generalisation of the theory of analytic functions. When the generator becomes the identity, ie., (l, i) the theory of pseudoanalytic functions reduces to the theory of analytic functions. Theugh the theory of pseudoanalytic functions plays an important role in analysis, no discrete theory is available in literature. This thesis is an attempt in that direction. A discrete pseudoanalytic theory is derived for functions defined on H.

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The thesis is divided into nine chapters including introduction. Mainly we determine ultra L-topologies in the lattice of L- topologies and study their properties. We nd some sublattices in the lattice of L-topologies and study their properties. Also we study the lattice structure of the set of all L-closure operators on a set X.