Threshold Autoregressive Model for a Time Series Data

In this paper we try to fit a threshold autoregressive (TAR) model to time series data of monthly coconut oil prices at Cochin market. The procedure proposed by Tsay [7] for fitting the TAR model is briefly presented. The fitted model is compared with a simple autoregressive (AR) model. The results are in favour of TAR process. Thus the monthly coconut oil prices exhibit a type of non-linearity which can be accounted for by a threshold model.

Weather and climate of Penisular India modulated by Extrinsic factors- Empirical and Numerical Perspectives

The Doctoral thesis focuses on the factors that influence the weather and climate over Peninsular Indias. The first chapter provides a general introduction about the climatic features over peninsular India, various factors dealt in subsequent chapters, such as solar forcing on climate, SST variability in the northern Indian Ocean and its influence on Indian monsoon, moisture content of the atmosphere and its importance in the climate system, empirical formulation of regression forecast of climate and some aspects of regional climate modeling. Chapter 2 deals with the variability in the vertically integrated moisture (VIM) over Peninsular India on various time scales. The third Chapter discusses the influence of solar activity in the low frequency variability in the rainfall of Peninsular India. The study also investigates the influence of solar activity on the horizontal and vertical components of wind and the difference in the forcing before and after the so-called regime shift in the climate system before and after mid-1970s.In Chapter 4 on Peninsular Indian Rainfall and its association with meteorological and oceanic parameters over adjoining oceanic region, a linear regression model was developed and tested for the seasonal rainfall prediction of Peninsular India.

Modelling and Analysis of Some Time Series

The thesis deals with some of the non-linear Gaussian and non-Gaussian time models and mainly concentrated in studying the properties and application of a first order autoregressive process with Cauchy marginal distribution. In this thesis some of the non-linear Gaussian and non-Gaussian time series models and mainly concentrated in studying the properties and application of a order autoregressive process with Cauchy marginal distribution. Time series relating to prices, consumptions, money in circulation, bank deposits and bank clearing, sales and profit in a departmental store, national income and foreign exchange reserves, prices and dividend of shares in a stock exchange etc. are examples of economic and business time series. The thesis discuses the application of a threshold autoregressive(TAR) model, try to fit this model to a time series data. Another important non-linear model is the ARCH model, and the third model is the TARCH model. The main objective here is to identify an appropriate model to a given set of data. The data considered are the daily coconut oil prices for a period of three years. Since it is a price data the consecutive prices may not be independent and hence a time series based model is more appropriate. In this study the properties like ergodicity, mixing property and time reversibility and also various estimation procedures used to estimate the unknown parameters of the process.

The tautomerism, solvatochromism and non-linear optical properties of fluorescent 3-hydroxyquinoxaline-2-carboxalidine-4-aminoantipyrine

The Schiff base, 3-hydroxyquinoxaline-2-carboxalidine-4-aminoantipyrine, was synthesized by the condensation of 3-hydroxyquinoxaline-2-carboxaldehyde with 4-aminoantipyrine. HPLC, FT-IR and NMR spectral data revealed that the compound exists predominantly in the amide tautomeric form and exhibits both absorption and fluorescence solvatochromism, large stokes shift, two electron quasireversible redox behaviour and good thermal stability, with a glass transition temperature of 104oC. The third-order non-linear optical character was studied using open aperture Z-scan methodology employing 7 ns pulses at 532 nm. The third-order non-linear absorption coefficient, b, was 1.48 x 10-6 cm W-1 and the imaginary part of the third-order non-linear optical susceptibility, Im c(3), was 3.36 x10-10 esu. The optical limiting threshold for the compound was found to be 340 MW cm-2.

The tautomerism, solvatochromism and non-linear optical properties of fluorescent 3-hydroxyquinoxaline-2-carboxalidine-4-aminoantipyrine

The Schiff base, 3-hydroxyquinoxaline-2-carboxalidine-4-aminoantipyrine, was synthesized by the condensation of 3-hydroxyquinoxaline-2-carboxaldehyde with 4-aminoantipyrine. HPLC, FT-IR and NMR spectral data revealed that the compound exists predominantly in the amide tautomeric form and exhibits both absorption and fluorescence solvatochromism, large stokes shift, two electron quasireversible redox behaviour and good thermal stability, with a glass transition temperature of 104 oC. The third-order non-linear optical character was studied using open aperture Z-scan methodology employing 7 ns pulses at 532 nm. The third-order non-linear absorption coefficient, b, was 1.48 x 10-6 cm W-1 and the imaginary part of the third-order non-linear optical susceptibility, Im c(3), was 3.36x10-10 esu. The optical limiting threshold for the compound was found to be 340 MW cm-2.

Studies on Pseudoscalar Meson Bound States and Semileptonic Decays in a Relativistic Potential Model

In this thesis quark-antiquark bound states are considered using a relativistic two-body equation for Dirac particles. The mass spectrum of mesons includes bound states involving two heavy quarks or one heavy and one light quark. In order to analyse these states within a unified formalism, it is desirable to have a two-fermion equation that limits to one body Dirac equation with a static interaction for the light quark when the other particle's mass tends to infinity. A suitable two-body equation has been developed by Mandelzweig and Wallace. This equation is solved in momentum space and is used to describe the complete spectrum of mesons. The potential used in this work contains a short range one-gluon exchange interaction and a long range linear confining and constant potential terms. This model is used to investigate the decay processes of heavy mesons. Semileptonic decays are more tractable since there is no final state interactions between the leptons and hadrons that would otherwise complicate the situation. Studies on B and D meson decays are helpful to understand the nonperturbative strong interactions of heavy mesons, which in turn is useful to extract the details of weak interaction process. Calculation of form factors of these semileptonic decays of pseudo scalar mesons are also presented.

Linear and nonlinear optical characteristics of ZnO-SiO2 nanocomposites.

We present the spectral and nonlinear optical properties of ZnO-SiO2 nanocomposites prepared by colloidal chemical synthesis. Obvious enhancement of ultraviolet (UV) emission of the samples is observed, and the strongest UV emission of a typical ZnO-SiO2 nanocomposite is over three times stronger than that of pure ZnO. The nonlinearity of the silica colloid is low, and its nonlinear response can be improved by making composites with ZnO. These nanocomposites show self-defocusing nonlinearity and good nonlinear absorption behavior. The observed nonlinear absorption is explained through two photon absorption followed by weak free carrier absorption and nonlinear scattering. The nonlinear refractive index and the nonlinear absorption increase with increasing ZnO volume fraction and can be attributed to the enhancement of exciton oscillator strength. ZnO-SiO2 is a potential nanocomposite material for the UV light emission and for the development of nonlinear optical devices with a relatively small limiting threshold.

Fluid mechanics-non-linear waves studies on korteweg-de vries equations

In this thesis the author has presented qualitative studies of certain Kdv equations with variable coefficients. The well-known KdV equation is a model for waves propagating on the surface of shallow water of constant depth. This model is considered as fitting into waves reaching the shore. Renewed attempts have led to the derivation of KdV type equations in which the coefficients are not constants. Johnson's equation is one such equation. The researcher has used this model to study the interaction of waves. It has been found that three-wave interaction is possible, there is transfer of energy between the waves and the energy is not conserved during interaction.

Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

A Copy detection Method for Malayalam Text Documents using N-grams Model

In this paper a method of copy detection in short Malayalam text passages is proposed. Given two passages one as the source text and another as the copied text it is determined whether the second passage is plagiarized version of the source text. An algorithm for plagiarism detection using the n-gram model for word retrieval is developed and found tri-grams as the best model for comparing the Malayalam text. Based on the probability and the resemblance measures calculated from the n-gram comparison , the text is categorized on a threshold. Texts are compared by variable length n-gram(n={2,3,4}) comparisons. The experiments show that trigram model gives the average acceptable performance with affordable cost in terms of complexity