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.

Characterization of Probability Distributions Using the Residual Entropy Function

The present study on the characterization of probability distributions using the residual entropy function. The concept of entropy is extensively used in literature as a quantitative measure of uncertainty associated with a random phenomenon. The commonly used life time models in reliability Theory are exponential distribution, Pareto distribution, Beta distribution, Weibull distribution and gamma distribution. Several characterization theorems are obtained for the above models using reliability concepts such as failure rate, mean residual life function, vitality function, variance residual life function etc. Most of the works on characterization of distributions in the reliability context centers around the failure rate or the residual life function. The important aspect of interest in the study of entropy is that of locating distributions for which the shannon’s entropy is maximum subject to certain restrictions on the underlying random variable. The geometric vitality function and examine its properties. It is established that the geometric vitality function determines the distribution uniquely. The problem of averaging the residual entropy function is examined, and also the truncated form version of entropies of higher order are defined. In this study it is established that the residual entropy function determines the distribution uniquely and that the constancy of the same is characteristics to the geometric distribution

Characterization of Probability Distributions by Variance Bounds and its Applications

Department of Statistics, Cochin University of Science and Technology

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

DNA Sequence Representation methods

DNA sequence representation methods are used to denote a gene structure effectively and help in similarities/dissimilarities analysis of coding sequences. Many different kinds of representations have been proposed in the literature. They can be broadly classified into Numerical, Graphical, Geometrical and Hybrid representation methods. DNA structure and function analysis are made easy with graphical and geometrical representation methods since it gives visual representation of a DNA structure. In numerical method, numerical values are assigned to a sequence and digital signal processing methods are used to analyze the sequence. Hybrid approaches are also reported in the literature to analyze DNA sequences. This paper reviews the latest developments in DNA Sequence representation methods. We also present a taxonomy of various methods. A comparison of these methods where ever possible is also done