On Chaos and Fractals in General Topological Spaces

The present study on chaos and fractals in general topological spaces. Chaos theory originated with the work of Edward Lorenz. The phenomenon which changes order into disorder is known as chaos. Theory of fractals has its origin with the frame work of Benoit Mandelbrot in 1977. Fractals are irregular objects. In this study different properties of topological entropy in chaos spaces are studied, which also include hyper spaces. Topological entropy is a measures to determine the complexity of the space, and compare different chaos spaces. The concept of fractals can’t be extended to general topological space fast it involves Hausdorff dimensions. The relations between hausdorff dimension and packing dimension. Regular sets in Metric spaces using packing measures, regular sets were defined in IR” using Hausdorff measures. In this study some properties of self similar sets and partial self similar sets. We can associate a directed graph to each partial selfsimilar set. Dimension properties of partial self similar sets are studied using this graph. Introduce superself similar sets as a generalization of self similar sets and also prove that chaotic self similar self are dense in hyper space. The study concludes some relationships between different kinds of dimension and fractals. By defining regular sets through packing dimension in the same way as regular sets defined by K. Falconer through Hausdorff dimension, and different properties of regular sets also.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Carbon/Nitrogen Ratio Optimization and Periphyton Development on the Production and Sustainability of Penaeus Monodon(Fabricius)in Extensive Culture System

Controlling the inorganic nitrogen by manipulating carbon / nitrogen ratio is a method gaining importance in aquaculture systems. Nitrogen control is induced by feeding bacteria with carbohydrates and through the subsequent uptake of nitrogen from the water for the synthesis of microbial proteins. The relationship between addition of carbohydrates, reduction of ammonium and the production of microbial protein depends on the microbial conversion coefficient. The carbon / nitrogen ratio in the microbial biomass is related to the carbon contents of the added material. The addition of carbonaceous substrate was found to reduce inorganic nitrogen in shrimp culture ponds and the resultant microbial proteins are taken up by shrimps. Thus, part of the feed protein is replaced and feeding costs are reduced in culture systems.The use of various locally available substrates for periphyton based aquaculture practices increases production and profitability .However, these techniques for extensive shrimp farming have not so far been evaluated. Moreover, an evaluation of artificial substrates together with carbohydrate source based farming system in reducing inorganic nitrogen production in culture systems has not yet been carried-out. Furthermore, variations in water and soil quality, periphyton production and shrimp production of the whole system have also not been determined so-far.This thesis starts with a general introduction , a brief review of the most relevant literature, results of various experiments and concludes with a summary (Chapter — 9). The chapters are organised conforming to the objectives of the present study. The major objectives of this thesis are, to improve the sustainability of shrimp farming by carbohydrate addition and periphyton substrate based shrimp production and to improve the nutrient utilisation in aquaculture systems.

Impact of teak and eucalypt monoculture on soils in the highlands of Kerala

Impact of teak and eucalypt monoculture on soils in the highlands of kerala .The thesis is arranged under nine chapters. The first chapter introduces the topic, reviews the literature pertaining to the study and presents the aims and objectives of the study. The second chapter briefly describes the study location. experimental design and sampling methodology. The third chapter deals with physical properties of plantation soils. The fourth and fifth chapters cover the chemical properties and macro- and micro nutrient status in plantation soils. The organic matter fractions in plantation soils are described in sixth chapter. First part of the seventh chapter presents the results of factor analysis and the second part deals with fertility index of plantations. All these chapters are self-contained with separate introduction, materials and methods and results and discussions. A general discussion of the results is included in the eighth chapter. The ninth chapter includes conclusions and summary A study that traces the variation in physical and chemical properties and nutrient status of teak soils with age of plantations, till the end of a rotation period is thus highly pertinent. Such a study, with an adjacent natural forest as a reference stand will not only generate information that will help us to understand the pattern of variation in soil properties, but will also aid us in formulating better management strategies. The data generated by such a study will be more useful if accompanied by information on soil changes following a short rotation plantation crop. As Eucalypt, a short rotation crop is the second major plantation crop in Kerala, it was chosen for the study.

Cost accountancy and cost control in hospitals

It is a fact that there now exists a sound framework of accounting theory to ascertain the working results and the investment status of hospitals. Yet, there is no system of accounting in practice to conduct its activities with utmost efficiency. No attempts have hitherto been made for the continuous improvement in the servics rendered by hospitals. Personal investments in hospitals have made the interaction of business to some extent.Planning, decision making and control assume increasing importance as hospitals grow in size and complexity. Moreover, wise and effective utilisation of resources should be ensured. The importance of cost cannot be overlooked in this context. Cost is the most effective factor in the determination of the prices of hospital services rendered. The important managerial functions have to rely heavily on accurate and timely cost information. More people can be provided with services if no services cost more than what is a must to provide the necessary level of care. The price paid for high cost technology for a few is no technology at all for the many. Hence no pains must be spared in ascertaining, presenting, controlling and reducing costs. An effective system of Cost Accountancy and Cost Control is imperative for the survival of hospitals in the intensely competitive conditions of today. The valuable objective of "better patient care" can be attained only if the management can make use of the various tools and techniques to ascertain, control and reduce each item of cost in hospitals. Constant efforts must be made by the management to continuously improve their services and bring down costs and prices of all hospital services. Cost Accountancy has made its impresssive impact on almost all the spheres of human activities. It is high time a comprehensive Cost Accountancy and Cost Control system be implemented in hospitals. The problem under study thus is the designing of a sound and full-fledged Cost Accountancy and Cost Control system that suits the requirements of hospitals. It is for the first time in India during the evolution of Cost Accountancy that a comprehensive cost system is tried in hospitals.

Magnetic and processability studies on rubber ferrite composites based on natural rubber and mixed ferrite

Polycrystalline single phasic mixed ferrites belonging to the series Ni1−xZnxFe2O4 for various values of x have been prepared by conventional ceramic techniques. Pre-characterized nickel zinc ferrites were then incorporated into a natural rubber matrix according to a specific recipe for various loadings. The processability and cure parameters were then determined. The magnetic properties of the ceramic filler as well as the ferrite loaded rubber ferrite composites (RFC) were evaluated and compared. A general equation for predicting the magnetic properties was also formulated. The validity of these equations were then checked and correlated with the experimental data. The coercivity of the RFCs almost resemble that of the ceramic component in the RFC. Percolation threshold is not reached for a maximum loading of 120 phr (parts per hundred rubber by weight) of the filler. These studies indicate that flexible magnets can be made with appropriate magnetic properties namely saturation magnetisation (Ms) and magnetic field strength (Hc) by a judicious choice of x and a corresponding loading. These studies also suggest that there is no possible interaction between the filler and the matrix at least at the macroscopic level. The formulated equation will aid in synthesizing RFCs with predetermined magnetic

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.