Studies on magnetic monopole solutions of non-abelian gauge theories and related problems

In 1931 Dirac studied the motion of an electron in the field of a magnetic monopole and found that the quantization of electric charge can be explained by postulating the mere existence of a magnetic monopole. Since 1974 there has been a resurgence of interest in magnetic monopole due to the work of ‘t’ Hooft and Polyakov who independently observed that monopoles can exist as finite energy topologically stable solutions to certain spontaneously broken gauge theories. The thesis, “Studies on Magnetic Monopole Solutions of Non-abelian Gauge Theories and Related Problems”, reports a systematic investigation of classical solutions of non-abelian gauge theories with special emphasis on magnetic monopoles and dyons which possess both electric and magnetic charges. The formation of bound states of a dyon with fermions and bosons is also studied in detail. The thesis opens with an account of a new derivation of a relationship between the magnetic charge of a dyon and the topology of the gauge fields associated with it. Although this formula has been reported earlier in the literature, the present method has two distinct advantages. In the first place, it does not depend either on the mechanism of symmetry breaking or on the nature of the residual symmetry group. Secondly, the results can be generalized to finite temperature monopoles.

Stochastic processes and their applications time dependent solutions for some queueing and inventory models

The objective of this thesis is to study the time dependent behaviour of some complex queueing and inventory models. It contains a detailed analysis of the basic stochastic processes underlying these models. In the theory of queues, analysis of time dependent behaviour is an area.very little developed compared to steady state theory. Tine dependence seems certainly worth studying from an application point of view but unfortunately, the analytic difficulties are considerable. Glosod form solutions are complicated even for such simple models as M/M /1. Outside M/>M/1, time dependent solutions have been found only in special cases and involve most often double transforms which provide very little insight into the behaviour of the queueing systems themselves. In inventory theory also There is not much results available giving the time dependent solution of the system size probabilities. Our emphasis is on explicit results free from all types of transforms and the method used may be of special interest to a wide variety of problems having regenerative structure.

Queueing Theory And Other Applications Of Stochastic Processes Queueing And Inventory Models With Rest Periods

In this thesis we study the effect of rest periods in queueing systems without exhaustive service and inventory systems with rest to the server. Most of the works in the vacation models deal with exhaustive service. Recently some results have appeared for the systems without exhaustive service.

Probability Theory. Stochastic Processes And Their Applications Probabilistic Analysis Of Some Queueing And Inventory Models

In this thesis we attempt to make a probabilistic analysis of some physically realizable, though complex, storage and queueing models. It is essentially a mathematical study of the stochastic processes underlying these models. Our aim is to have an improved understanding of the behaviour of such models, that may widen their applicability. Different inventory systems with randon1 lead times, vacation to the server, bulk demands, varying ordering levels, etc. are considered. Also we study some finite and infinite capacity queueing systems with bulk service and vacation to the server and obtain the transient solution in certain cases. Each chapter in the thesis is provided with self introduction and some important references

GABAA and GABAB Receptor Gene Expression and Functional Regulation During Pancreatic Regeneration and Insulin Secretion in Rats

The present study demonstrate the functional alterations of the GABAA and GABAB receptors and the gene expression during the regeneration of pancreas following partial pancreatectomy. The role of these receptors in insulin secretion and pancreatic DNA synthesis using the specific agonists and antagonists also are studied in vitro. The alterations of GABAA and GABAR receptor function and gene expression in the brain stem, crebellum and hypothalamus play an important role in the sympathetic regulation of insulin secretion during pancreatic regeneration. Previous studies have given much information linking functional interaction between GABA and the peripheral nervous system. The involvement of specific receptor subtypes functional regulation during pancreatic regeneration has not given emphasis and research in this area seems to be scarce. We have observed a decreased GABA content, down regulation of GABAA receptors and an up regulation of GABAB receptors in the cerebral cortex, brain stem and hypothalamus. Real Time-PCR analysis confirmed the receptor data in the brain regions. These alterations in the GABAA and GABAB receptors of the brain are suggested to govern the regenerative response and growth regulation of the pancreas through sympathetic innervation. In addition, receptor binding studies and Real Time-PCR analysis revealed that during pancreatic regeneration GABAA receptors were down regulated and GABAB receptors were up regulated in pancreatic islets. This suggests an inhibitory role for GABAA receptors in islet cell proliferation i.e., the down regulation of this receptor facilitates proliferation. Insulin secretion study during 1 hour showed GABA has inhibited the insulin secretion in a dose dependent manner in normal and hyperglycaemic conditions. Bicuculline did not antagonize this effect. GABAA agonist, muscimol inhibited glucose stimulated insulin secretion from pancreatic islets except in the lowest concentration of 1O-9M in presence of 4mM glucose.Musclmol enhanced insulin secretion at 10-7 and 10-4M muscimol in presence of 20mM glucose- 4mM glucose represents normal and 20mM represent hyperglycaemic conditions. GABAB agonist, baclofen also inhibited glucose induced insulin secretion and enhanced at the concentration of 1O-5M at 4mM glucose and at 10-9M baclofen in presence of 20mM glucose. This shows a differential control of the GABAA and GABAB receptors over insulin release from the pancreatic islets. During 24 hours in vitro insulin secretion study it showed that low concentration of GABA has inhibited glucose stimulated insulin secretion from pancreatic islets. Muscimol, the GABAA agonist, inhibited the insulin secretion but, gave an enhanced secretion of insulin in presence of 4mM glucose at 10-7 , 10-5 and 1O-4M muscimol. But in presence of 20mM glucose muscimol significantly inhibited the insulin secretion. GABAB agonist, baclofen also inhibited glucose induced insulin secretion in presence of both 4mM and 20mM glucose. This shows the inhibitory role of GABA and its specific receptor subtypes over insulin synthesis from pancreatic bete-islets. In vitro DNA synthesis studies showed that activation of GABAA receptor by adding muscimol, a specific agonist, inhibited islet DNA synthesis. Also, the addition of baclofen, a specific agonist of GABAB receptor resulted in the stimulation of DNA synthesis.Thus the brain and pancreatic GABAA and GABAB receptor gene expression differentially regulates pancreatic insulin secretion and islet cell proliferation during pancreatic regeneration. This will have immense clinical significance in therapeutic applications in the management of Diabetes mellitus.

Catalysis By Ferrites And Cobaltites For The Alkylation And Oxidation Of Organic Compounds

Catalysis is a very important process from an industrial point of view since the production of most industrially important chemicals involves catalysis.Solid acid catalysts are appealing since the nature of acid sites is known and their chemical behavior in acid catalyzed reactions can be rationalized by means of existing theories and models. Mixed oxides crystallizing in spinel structure are of special interest because the spinel lattice imparts extra stability to the catalyst under various reaction conditions so that theses systems have sustained activities for longer periods. The thesis entitled" Catalysis By Ferrites And Cobaltites For The Alkylation And Oxidation Of Organic Compounds " presents the preparation ,characterization ,and activity studies of the prepared spinels were modified by incorporating other ions and by changing the stoichiometry.The prepared spinels exhibiting better catalytic activity towards the studied reactions with good product selectivity.Acid-base properties and cation distribution of the spinels were found to control the catalytic activity.

Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Studies on the structural, electrical and magnetic properties of composites based on spinel ferrites

This thesis mainly deals with the preparation and studies on magnetic composites based on spinel ferrites prepared both chemically and mechanically. Rubber ferrite composites (RFC) are chosen because of their mouldability and flexibility and the ease with which the dielectric and magnetic properties can be manipulated to make them as useful devices. Natural rubber is chosen as the Matrix because of its local availability and possible value addition. Moreover, NR represents a typical unsaturated nonpolar matrix. The work can be thought of as two parts. Part l concentrates on the preparation and characterization of nanocomposites based on y-Fe203. Part 2 deals with the preparation and characterization of RFCs containing Nickel zinc ferrit In the present study magnetic nanocomposites have been prepared by ionexchange method and the preparation conditions have been optimized. The insitu incorporation of the magnetic component is carried out chemically. This method is selected as it is the easiest and simplest method for preparation of nanocomposite. Nanocomposite samples thus prepared were studied using VSM, Mossbauer spectroscopy, Iron content estimation, and ESR spectroscopy. For the preparation of RFCs, the filler material namely nickel zinc ferrite having the general formula Ni)_xZnxFez04, where x varies from 0 to 1 in steps of 0.2 have been prepared by the conventional ceramic techniques. The system of Nil_xZn"Fe204 is chosen because of their excellent high frequency characteristics. After characterization they are incorporated into the polymer matrix of natural rubber by mechanical method. The incorporation is done according to a specific recipe and for various Loadings of magnetic fillers and also for all compositions. The cure characteristics, magnetic properties and dielectric properties of these composites are evaluated. The ac electrical conductivity of both ceramic nickel zinc ferrites and rubber ferrite composites are also calculated using a simple relation. The results are correlated.

Bivariate distributions with weighted marginals and reliablity modelling

In this paper, a family of bivariate distributions whose marginals are weighted distributions in the original variables is studied. The relationship between the failure rates of the derived and original models are obtained. These relationships are used to provide some characterizations of specific bivariate models