Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

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

Detection of microcalcifications in mammograms using local maxima andadaptive wavelet transform analysis

A method for computer- aided diagnosis of micro calcification clusters in mammograms images presented . Micro calcification clus.eni which are an early sign of bread cancer appear as isolated bright spots in mammograms. Therefore they correspond to local maxima of the image. The local maxima of the image is lint detected and they are ranked according to it higher-order statistical test performed over the sub band domain data

A Variational Calculation of TE and TM Cutoff Wavenumbers in Circular Eccentric Guides by Conformal Mapping

The cutoff wavenumbers of higher order modes in circular eccentric guides are computed with the variational analysis combined with a conformal mapping. A conformal mapping is applied to the variational formulation, and the variational equation is solved by the finite-element method. Numerical results for TE and TM cutoff wavenumbers are presented for different distances between the centers and ratio of the radii. Comparisons with numerical results found in the literature validate the presented method

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 Non-Resonant Multiphoton Processes in Atomic Hydrogen

In the present thesis we have formulated the Dalgarno-Lewis procedure for two-and three-photon processes and an elegant alternate expressions are derived. Starting from a brief review on various multiphoton processes we have discussed the difficulties coming in the perturbative treatment of multiphoton processes. A small discussion on various available methods for studying multiphoton processes are presented in chapter 2. These theoretical treatments mainly concentrate on the evaluation of the higher order matrix elements coming in the perturbation theory. In chapter 3 we have described the use of Dalgarno-Lewis procedure and its implimentation on second order matrix elements. The analytical expressions for twophoton transition amplitude, two-photon ionization cross section, dipole dynamic polarizability and Kramers-Heiseberg are obtained in a unified manner. Fourth chapter is an extension of the implicit summation technique presented in chapter 3. We have clearly mentioned the advantage of our method, especially the analytical continuation of the relevant expressions suited for various values of radiation frequency which is also used for efficient numerical analysis. A possible extension of the work is to study various multiphoton processcs from the stark shifted first excited states of hydrogen atom. We can also extend this procedure for studying multiphoton processes in alkali atoms as well as Rydberg atoms. Also, instead of going for analytical expressions, one can try a complete numerical evaluation of the higher order matrix elements using this procedure.

Southern Hemispheric Features and their Teleconnection with Indian Summer Monsoon

This thesis entitled southern hemispheric features and their Teleconnection with indian summer monsoon.Southern hemisphere is entirely distinct from the northern hemisphere in many aspects, which is well reflected in atmospheric and oceanic properties.The thesis consists of eight chapters, in which the first chapter contains an overview of southern hemisphere. In this chapter, variability in southern hemisphere is described along with Indian summer monsoon and its teleconnection. The different types of data sets used and various methodologies adopted in the present thesis were described in Chapter 2. The period of climate shift and the magnitude of anomalies after the climate shift, which extended from troposphere to stratopause level, were investigated in detail and presented in chapter 3. Chapter 4 depicts the recent trend and variability in southern stratosphere. The higher order variability during various months and the frequency of extremity is included in this chapter.Climatology of divergence and convergence after the documented shift is reported in chapter 5.Southern extratropical connection to Indian summer monsoon through the modulation of SAM is presented in Chapter 6.Chapter 7 deals with the modulation of SAM‐Monsoon link through North Atlantic Oscillation.

Implementation of a Neural Network Classifier for Noise Sources in the Ocean

The paper investigates the feasibility of implementing an intelligent classifier for noise sources in the ocean, with the help of artificial neural networks, using higher order spectral features. Non-linear interactions between the component frequencies of the noise data can give rise to certain phase relations called Quadratic Phase Coupling (QPC), which cannot be characterized by power spectral analysis. However, bispectral analysis, which is a higher order estimation technique, can reveal the presence of such phase couplings and provide a measure to quantify such couplings. A feed forward neural network has been trained and validated with higher order spectral features

Spectral dependence of third order nonlinear optical susceptibility of zinc phthalocyanine

Wavelength dependence of saturable absorption (SA) and reverse saturable absorption (RSA) of zinc phthalocyanine was studied using 10 Hz, 8 ns pulses from a tunable laser, in the wavelength range of 520–686 nm, which includes the rising edge of the Q band in the electronic absorption spectrum. The nonlinear response is wavelength dependent and switching from RSA to SA has been observed as the excitation wavelength changes from the low absorption window region to higher absorption regime near the Q band. The SA again changes back to RSA when we further move over to the infrared region. Values of the imaginary part of third order susceptibility are calculated for various wavelengths in this range. This study is important in identifying the spectral range over which the nonlinear material acts as RSA based optical limiter.

Spectral dependence of third order nonlinear optical susceptibility of zinc phthalocyanine

Wavelength dependence of saturable absorption (SA) and reverse saturable absorption (RSA) of zinc phthalocyanine was studied using 10 Hz, 8 ns pulses from a tunable laser, in the wavelength range of 520–686 nm, which includes the rising edge of the Q band in the electronic absorption spectrum. The nonlinear response is wavelength dependent and switching from RSA to SA has been observed as the excitation wavelength changes from the low absorption window region to higher absorption regime near the Q band. The SA again changes back to RSA when we further move over to the infrared region. Values of the imaginary part of third order susceptibility are calculated for various wavelengths in this range. This study is important in identifying the spectral range over which the nonlinear material acts as RSA based optical limiter.

Human Resources Development in Higher Education in Kerala

The study is entitled “HUMAN RESOURCES DEVELOPMENT IN HIGHER EDUCATION IN KERALA”. The concept “Human Resource Development” is of high value in business and industry and has been used and applied since years. In industry and business the 'human' element is considred as a resource and hence its development and protection is very essential and inevitable. Of all the factors of production, human resource is the only factor having rational faculty and therefore, it must be handled with utmost care. Right recruitment, right training and right induction followed by faultless monitoring and welfare measures are but decisive factors in business and industry. Altogether there is a constant attention up on human factor there. But this is not a practice at all in education. So far there has not been any such measure of care and close watch and performance analysis of human resource on education front. This may be the main reason for lack of accountability in the sphere of education. The present study reveals the importance of introducing HRD practices in higher educational institutions in Kerala. In order to promise human capital formation through education, it is basic requirement. The higher educational institutions must follow the method of industry and commerce because education can be treated as an industry in service sector. There also we can follow the methods of right recruitment, right training and promotion, delegation, performance analysis and accountability checking of human resource. HRD is a powerful idea of transformation of human being into highly productive and contributing factor The HRD of students is the sum total of HRD of teachers. Reminding the primordial usage 'Yatha Raja Thadha Praja’ the quality of faculty resembles in students. The quality of administrative staff in colleges also affects the quality of higher education. Hence, it is high time to introduce the managerial method of HRD with all its paraphernalia in higher educational institutions so as to assure proper human capital formation in higher education in India.

Human Resources Development in Higher Education in Kerala

The study is entitled “HUMAN RESOURCES DEVELOPMENT IN HIGHER EDUCATION IN KERALA”. The concept “Human Resource Development” is of high value in business and industry and has been used and applied since years. In industry and business the ‘human’ element is considred as a resource and hence its development and protection is very essential and inevitable. Of all the factors of production, human resource is the only factor having rational faculty and therefore, it must be handled with utmost care. Right recruitment, right training and right induction followed by faultless monitoring and welfare measures are but decisive factors in business and industiy. Altogether there is a constant attention up on human factor there. But this is not a practice at all in education. So far there has not been any such measure of care and close watch and performance analysis of human resource on education front. This may be the main reason for lack of accountability in the sphere of education. The present study reveals the importance of introducing HRD practices in higher educational institutions in Kerala. In order to promise human capital formation through education, it is basic requirement. The higher educational institutions must follow the method of industry and commerce because education can be treated as an industry in service sector. There also we can follow the methods of right recruitment, right training and promotion, delegation, performance analysis and accountability checking of human resource. HRD is a powerful idea of transformation of human being into highly productive and contributing factor The HRD of students is the sum total of HRD of teachers. Reminding the primordial usage ‘Yatha Raja Thadha Praja’ the quality of faculty resembles in students. The quality of administrative staff in colleges also affects the quality of higher education. Hence, it is high time to introduce the managerial method of HRD with all its paraphernalia in higher educational institutions so as to assure proper human capital formation in higher education in India.

Studies on improved practices of prawn farming for higher production in central Kerala

The thesis entitled "Studies on improved practices of prawn farming for higher production in central Kerala" prepared by the author describes various practices prevailing in the study area in order to elucidate their relative merits. The study on semi-intensive farming at Mundapuram, Kannur was also carried out and included in the thesis for comparison.The author felt it important to make a critical study of the existing culture practices in the central Kerala, a region where it has been existing since time immemorial.Careful analysis of data accrued by the author has helped him to identify strength, weakness, opportunities and threats confronting the shrimp farming. As a result it was possible to evolve an appropriate management technology taking into consideration the various ecological (location specific), social and economical conditions prevalent in the vast study area.

Management of Higher Educational Institutions in Kerala

Economists consider education as an investment in man. Education develops human resources necessary for the economic and political growth of any nation. Adam Smith stressed the importance of education and included the acquired and useful activities of all the inhabitants or members of society in his concept of fixed capital.‘ Karl Marx shared with Smith's view when he laid down that the function of education in a socialist society will be to overcome the alienation of the worker from the means of production; while developing the technical skill it will make him a complete man as well as a producer.2 Education is also considered as a powerful instrument for social change. By inculcating moral and spiritual values, it brings changes both in the individual and in the society. It aims at creating a social order founded on the values of freedom, social justice and equal opportunity.3 The objective of this exploratory study is to enquire into the existing system of managing higher educational institutions in Kerala, compare it with the accepted principles of management believed to be applicable to all organisations, and develop a model capable of introducing more effective management practices