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

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.

Fuzzy Absolutes and Related Topics

The study on the fuzzy absolutes and related topics. The different kinds of extensions especially compactification formed a major area of study in topology. Perfect continuous mappings always preserve certain topological properties. The concept of Fuzzy sets introduced by the American Cyberneticist L. A Zadeh started a revolution in every branch of knowledge and in particular in every branch of mathematics. Fuzziness is a kind of uncertainty and uncertainty of a symbol lies in the lack of well-defined boundaries of the set of objects to which this symbol belongs. Introduce an s-continuous mapping from a topological space to a fuzzy topological space and prove that the image of an H-closed space under an s-continuous mapping is f-H closed. Here also proved that the arbitrary product fi and sum of  fi of the s-continuous maps fi are also s-continuous. The original motivation behind the study of absolutes was the problem of characterizing the projective objects in the category of compact spaces and continuous functions.

Propagation of Microwaves in the Troposphere with Potential Application to GPS based Navigation and Meteorology with emphasis on Indian region

Global Positioning System (GPS), with its high integrity, continuous availability and reliability, revolutionized the navigation system based on radio ranging. With four or more GPS satellites in view, a GPS receiver can find its location anywhere over the globe with accuracy of few meters. High accuracy - within centimeters, or even millimeters is achievable by correcting the GPS signal with external augmentation system. The use of satellite for critical application like navigation has become a reality through the development of these augmentation systems (like W AAS, SDCM, and EGNOS, etc.) with a primary objective of providing essential integrity information needed for navigation service in their respective regions. Apart from these, many countries have initiated developing space-based regional augmentation systems like GAGAN and IRNSS of India, MSAS and QZSS of Japan, COMPASS of China, etc. In future, these regional systems will operate simultaneously and emerge as a Global Navigation Satellite System or GNSS to support a broad range of activities in the global navigation sector.Among different types of error sources in the GPS precise positioning, the propagation delay due to the atmospheric refraction is a limiting factor on the achievable accuracy using this system. The WADGPS, aimed for accurate positioning over a large area though broadcasts different errors involved in GPS ranging including ionosphere and troposphere errors, due to the large temporal and spatial variations in different atmospheric parameters especially in lower atmosphere (troposphere), the use of these broadcasted tropospheric corrections are not sufficiently accurate. This necessitated the estimation of tropospheric error based on realistic values of tropospheric refractivity. Presently available methodologies for the estimation of tropospheric delay are mostly based on the atmospheric data and GPS measurements from the mid-latitude regions, where the atmospheric conditions are significantly different from that over the tropics. No such attempts were made over the tropics. In a practical approach when the measured atmospheric parameters are not available analytical models evolved using data from mid-latitudes for this purpose alone can be used. The major drawback of these existing models is that it neglects the seasonal variation of the atmospheric parameters at stations near the equator. At tropics the model underestimates the delay in quite a few occasions. In this context, the present study is afirst and major step towards the development of models for tropospheric delay over the Indian region which is a prime requisite for future space based navigation program (GAGAN and IRNSS). Apart from the models based on the measured surface parameters, a region specific model which does not require any measured atmospheric parameter as input, but depends on latitude and day of the year was developed for the tropical region with emphasis on Indian sector.Large variability of atmospheric water vapor content in short spatial and/or temporal scales makes its measurement rather involved and expensive. A local network of GPS receivers is an effective tool for water vapor remote sensing over the land. This recently developed technique proves to be an effective tool for measuring PW. The potential of using GPS to estimate water vapor in the atmosphere at all-weather condition and with high temporal resolution is attempted. This will be useful for retrieving columnar water vapor from ground based GPS data. A good network of GPS could be a major source of water vapor information for Numerical Weather Prediction models and could act as surrogate to the data gap in microwave remote sensing for water vapor over land.

On the magnetic and dielectric properties of nickel–neoprene nanocomposites

Nickel nanocomposites were prepared by incorporating nickel nanoparticles in a neoprene matrix according to a specific recipe for various loadings of nickel particles. The dielectric properties of these composites were evaluated for different frequencies ranging from 100 kHz to 8MHz at different temperatures from 30 ◦C to 120 ◦C. The dielectric permittivity increases with increase of nickel concentration. Increase in temperature enhances the permittivity initially, till 40 ◦C and thereafter the permittivity decreases. The dielectric loss exhibits relaxation peaks and the peaks shift to lower frequencies with increase in volume fraction of the nickel nanoparticles in the matrix. The evaluation of magnetic and dielectric properties of these composites suggests that the dielectric permittivity can be tailored by an appropriate loading of the filler using semi-empirical equations and the magnetic properties vary according to simple mixture equations