Some aspects of history of Indian mathematics in 18th and early 19th century

This thesis is an attempt to throw light on the works of some Indian Mathematicians who wrote in Arabic or persian In the Introductory Chapter on outline of general history of Mathematics during the eighteenth Bnd nineteenth century has been sketched. During that period there were two streams of Mathematical activity. On one side many eminent scholers, who wrote in Sanskrit, .he l d the field as before without being much influenced by other sources. On the other side there were scholars whose writings were based on Arabic and Persian text but who occasionally drew upon other sources also.

Studies on Some Aspects of the Physics of the Early Universe Using Gravitationally Coupled Scalar Field –

This thesis deals with some aspects of the Physics of the early universe, like phase transitions, bubble nucleations and premodial density perturbations which lead to the formation structures in the universe. Quantum aspects of the gravitational interaction play an essential role in retical high-energy physics. The questions of the quantum gravity are naturally connected with early universe and Grand Unification Theories. In spite of numerous efforts, the various problems of quantum gravity remain still unsolved. In this condition, the consideration of different quantum gravity models is an inevitable stage to study the quantum aspects of gravitational interaction. The important role of gravitationally coupled scalar field in the physics of the early universe is discussed in this thesis. The study shows that the scalar-gravitational coupling and the scalar curvature did play a crucial role in determining the nature of phase transitions that took place in the early universe. The key idea in studying the formation structure in the universe is that of gravitational instability.

Spray Pyrolysed Tin Chalcogenide Thin Films: Optimization of optoelectronic properties of SnS for possible photovoltaic application as an absorber layer

In the early 19th century, industrial revolution was fuelled mainly by the development of machine based manufacturing and the increased use of coal. Later on, the focal point shifted to oil, thanks to the mass-production technology, ease of transport/storage and also the (less) environmental issues in comparison with the coal!! By the dawn of 21st century, due to the depletion of oil reserves and pollution resulting from heavy usage of oil the demand for clean energy was on the rising edge. This ever growing demand has propelled research on photovoltaics which has emerged successful and is currently being looked up to as the only solace for meeting our present day energy requirements. The proven PV technology on commercial scale is based on silicon but the recent boom in the demand for photovoltaic modules has in turn created a shortage in supply of silicon. Also the technology is still not accessible to common man. This has onset the research and development work on moderately efficient, eco-friendly and low cost photovoltaic devices (solar cells). Thin film photovoltaic modules have made a breakthrough entry in the PV market on these grounds. Thin films have the potential to revolutionize the present cost structure of solar cells by eliminating the use of the expensive silicon wafers that alone accounts for above 50% of total module manufacturing cost.Well developed thin film photovoltaic technologies are based on amorphous silicon, CdTe and CuInSe2. However the cell fabrication process using amorphous silicon requires handling of very toxic gases (like phosphene, silane and borane) and costly technologies for cell fabrication. In the case of other materials too, there are difficulties like maintaining stoichiometry (especially in large area films), alleged environmental hazards and high cost of indium. Hence there is an urgent need for the development of materials that are easy to prepare, eco-friendly and available in abundance. The work presented in this thesis is an attempt towards the development of a cost-effective, eco-friendly material for thin film solar cells using simple economically viable technique. Sn-based window and absorber layers deposited using Chemical Spray Pyrolysis (CSP) technique have been chosen for the purpose

Analysis of Fluctuations in the Early Universe Using Fokker-Planck Formalism

The thesis begins with a review of basic elements of general theory of relativity (GTR) which forms the basis for the theoretical interpretation of the observations in cosmology. The first chapter also discusses the standard model in cosmology, namely the Friedmann model, its predictions and problems. We have also made a brief discussion on fractals and inflation of the early universe in the first chapter. In the second chapter we discuss the formulation of a new approach to cosmology namely a stochastic approach. In this model, the dynam ics of the early universe is described by a set of non-deterministic, Langevin type equations and we derive the solutions using the Fokker—Planck formalism. Here we demonstrate how the problems with the standard model, can be eliminated by introducing the idea of stochastic fluctuations in the early universe. Many recent observations indicate that the present universe may be approximated by a many component fluid and we assume that only the total energy density is conserved. This, in turn, leads to energy transfer between different components of the cosmic fluid and fluctuations in such energy transfer can certainly induce fluctuations in the mean to factor in the equation of state p = wp, resulting in a fluctuating expansion rate for the universe. The third chapter discusses the stochastic evolution of the cosmological parameters in the early universe, using the new approach. The penultimate chapter is about the refinements to be made in the present model, by means of a new deterministic model The concluding chapter presents a discussion on other problems with the conventional cosmology, like fractal correlation of galactic distribution. The author attempts an explanation for this problem using the stochastic approach.

Squeezed Coherent State Representation of Scalar Field and Particle Production in the Early Universe

The present work is an attempt to explain particle production in the early univese. We argue that nonzero values of the stress-energy tensor evaluated in squeezed vacuum state can be due to particle production and this supports the concept of particle production from zero-point quantum fluctuations. In the present calculation we use the squeezed coherent state introduced by Fan and Xiao [7]. The vacuum expectation values of stressenergy tensor defined prior to any dynamics in the background gravitational field give all information about particle production. Squeezing of the vacuum is achieved by means of the background gravitational field, which plays the role of a parametric amplifier [8]. The present calculation shows that the vacuum expectation value of the energy density and pressure contain terms in addition to the classical zero-point energy terms. The calculation of the particle production probability shows that the probability increases as the squeezing parameter increases, reaches a maximum value, and then decreases.

Squeezed Coherent State Representation of Scalar Field and Particle Production in the Early Universe

The present work is an attempt to explain particle production in the early univese. We argue that nonzero values of the stress-energy tensor evaluated in squeezed vacuum state can be due to particle production and this supports the concept of particle production from zero-point quantum fluctuations. In the present calculation we use the squeezed coherent state introduced by Fan and Xiao [7]. The vacuum expectation values of stressenergy tensor defined prior to any dynamics in the background gravitational field give all information about particle production. Squeezing of the vacuum is achieved by means of the background gravitational field, which plays the role of a parametric amplifier [8]. The present calculation shows that the vacuum expectation value of the energy density and pressure contain terms in addition to the classical zero-point energy terms. The calculation of the particle production probability shows that the probability increases as the squeezing parameter increases, reaches a maximum value, and then decreases.