Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

ARMA modeling of time series based on rational approximation of spectral density function

This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study.

Studies on Thermoplastic Elastomer Based on Linear Low-Density Polyethylene and Latex Product Waste Modified with Thiocarbanilide

Latex waste like glove waste was effectively modified using a new reclaiming agent, thiocarbanilide. This modified waste was blended with linear low-density polyethylene (LLDPE) to develop a novel thermoplastic elastomer. Both uncrosslinked and dynamically crosslinked blends were prepared and their properties were studied. The results were found to be comparable to those of conventional thermoplastic elastomers.

Chemical Modification of Blends of Poly (Vinyl Chloride) With Linear Low Density Polyethylene

The effects of modifying blends of poly(vinyl chloride) (PVC) with linear low density polyethylene (LLDPE) by means of acrylic acid, maleic anhydride, phenolic resins and p-phenylene diamine were investigated. Modification by acrylic acid and maleic anhydride in the presence of dicumyl peroxide was found to be the most useful procedure for improving the mechanical behaviour and adhesion properties of the blend. The improvement was found to be due mainly to the grafting of the carboxylic acid to the polymer chains; grafting was found to be more effective in LLDPE/PVC blends than in pure LLDPE.

Transient response of wavelength-switchable erbium -doped fiber lasers with linear coupled cavities

The transient characteristics of an erbium-doped fiber (F.DF) laser, which can switch between wavelengths. are investigated. 77te laser has a set of coupled linear cavities. The slow gain dynamics of EDFs and the cross-gain saturation in the coupled cavities give rise to delayed switching responses and relocation oscillations, which are respertively measured to be l ins and 3.5 ms for the worst rase, and which mar be decreased by increasing the pump power. Thus, the switching speed of the laser may be higher than 100 Hz

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.

ON APPROXIMATION METHODS FOR UNBOUNDED OPERATORS

Department of Mathematics, Cochin University of Science and Technology

PSWT Based Linear Predictive Coding and Development of a Parallel Multiple Subsequence Structure for DWT Computation

During 1990's the Wavelet Transform emerged as an important signal processing tool with potential applications in time-frequency analysis and non-stationary signal processing.Wavelets have gained popularity in broad range of disciplines like signal/image compression, medical diagnostics, boundary value problems, geophysical signal processing, statistical signal processing,pattern recognition,underwater acoustics etc.In 1993, G. Evangelista introduced the Pitch- synchronous Wavelet Transform, which is particularly suited for pseudo-periodic signal processing.The work presented in this thesis mainly concentrates on two interrelated topics in signal processing,viz. the Wavelet Transform based signal compression and the computation of Discrete Wavelet Transform. A new compression scheme is described in which the Pitch-Synchronous Wavelet Transform technique is combined with the popular linear Predictive Coding method for pseudo-periodic signal processing. Subsequently,A novel Parallel Multiple Subsequence structure is presented for the efficient computation of Wavelet Transform. Case studies also presented to highlight the potential applications.

A simple linear magnetic field sweep generator for magnetic resonance experiments

A simple and inexpensive linear magnetic field sweep generating system suitable for magnetic resonance experiments is described. The circuit, utilising a modified IC bootstrap configuration, generates field sweep over a wide range of sweep durations with excellent sweep linearity.