ON APPROXIMATION METHODS FOR UNBOUNDED OPERATORS

Department of Mathematics, Cochin University of Science and Technology

An approximation method for evaluating centrifugal distortion constants in XH2 bent symmetric molecules

University of Cochin

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.

‘Sudden Stratospheric Warming and its Influence on the Tropical Atmosphere'

The stratospheric warming events are categorized into major and minor warming depending on the temperature increase in the polar stratosphere. The warming is called a ‘major’, when the polar temperature increases poleward from 60 degree latitude and followed by a reversal in the zonal wind at 10 hPa (~32 Km). Usually major warming events are associated with the displacement of polar vortex from high to mid latitudes or the splitting of vortices in to two. The warming is called a "Minor", when the polar temperature increases more than 25 degree in a period of a week or less, at any stratospheric level with less intensified easterly wind anomalies. The stratospheric warmings generated during the transition period of winter to spring are called final warmings. The warming events observed in the early winter period (November to early December) over Canadian region are called Canadian warmings. There is strong interaction between stratosphere and troposphere during SSW period over high and low latitudes regions. The thesis consists of 7 chapters

“Investigations on Vibrational Overtones in the NIR region and Laser Induced Fluorescence in some selected compounds”

The central theme of this research concerns the study of vibrationally excited molecules. We have used the local mode description of such vibrational states, and this -model has now gained general acceptance. A central feature of the model is the Wloealizafion of vibrational energy. A study of these high—energy localized states provides example, becauseof this localization, overtone spectra, which measure the absorption of T vibrational energy, are extremely sensitive to the properties of X-H bonds. We also use -overtone spectra to study the conformation of molecules, i.e., the relative internal orientation of their bonds. The thesis comprises six chapters

Vibrational spectroscopic studies and computational study of quinoline-2-carbaldehyde benzoyl hydrazone

FT-IR spectrum of quinoline-2-carbaldehyde benzoyl hydrazone (HQb H2O) was recorded and analyzed. The synthesis and crystal structure data are also described. The vibrational wavenumbers were examined theoretically using the Gaussian03 package of programs using HF/6-31G(d) and B3LYP/6-31G(d) levels of theory. The data obtained from vibrational wavenumber calculations are used to assign vibrational bands obtained in infrared spectroscopy of the studied molecule. The first hyperpolarizability, infrared intensities and Raman activities are reported. The calculated first hyperpolarizability is comparable with the reported values of similar derivatives and is an attractive object for future studies of non-linear optics. The geometrical parameters of the title compound obtained from XRD studies are in agreement with the calculated values. The changes in the CAN bond lengths suggest an extended p-electron delocalization over quinoline and hydrazone moieties which is responsible for the non-linearity of the molecule

Vibrational spectroscopic studies of Guanidinium metal (MII) sulphate hexahydrates [MII = Co, Fe, Ni]

The Raman and FTIR spectra of [C(NH2)3]2M(SO4)2 ·6H2O (withM= Co, Fe, Ni) were recorded and analysed. The observed spectral bands are assigned in terms of vibrations of guanidinium ions, sulphate groups and water molecules. The analysis shows that the sulphate tetrahedra are distorted from their free state symmetry Td to C1. This is attributed to the presence of hydrogen bonds from water molecules. The order of distortion of the metal oxygen octahedra influenced the distortion of the sulphate tetrahedra. The appearance of 1– 3 modes of water molecules above 3300 cm−1 indicates the presence of weak hydrogen bonds

X-Ray Crysatllographic and Vibrational Spectroscopic Studies of Thorium Bromate Hydrate

Th(BrO3)3·H2O single crystals were grown from its aqueous solution at room temperature. Single crystal XRD, Raman and FTIR techniques were used to investigate the crystal structure. The crystal structure was solved by Patterson method. The as grown crystals are in monoclinic system with space group P21/c. The unit cell parameters are a = 12.8555(18) Å, b = 7.8970(11) Å, c = 9.0716(10) Å,  = 90°,  = 131.568° and  = 90° and unit cell volume is 689.1(2) Å3. Z = 8, R factor is 5.9. The Raman and FTIR studies indicate the lowering of symmetry of bromate anion from C3V to C1. Hydrogen bonds with varying strengths are present in the crystal. The centrosymmetric space group P21/c of the crystal is confirmed by the non-coincidence of majority of Raman and IR bands

Vibrational spectroscopic studies of FeClMoO4, Na2MoO4 and Na2MoO4·2H2O:D2O

FTIR and Raman spectra of FeClMoO4 single crystal and polycrystalline Na2MoO4, Na2MoO4·2H2O and Na2MoO4·2D2O are recorded and analysed. The band positions for different modes suggest that MoO4 tetrahedron is more distorted in FeClMoO4. The larger splitting observed for the bending modes and partial retention of degeneracy of the asymmetric stretching mode indicate that angular distortion is greater than liner distortion in MoO4 2 ion in FeClMoO4 confirming x-ray data. The non-appearance of the n1 and n2 modes in the IR and partial retention of the degeneracies of various modes show that MoO4 2 ion retains Td symmetry in Na2MoO4. Wavenumber values of the n1 mode indicate that the distortion of MoO4 tetrahedra in the four crystals are in the order FeClMoO4\ Na2MoO4·2H2O\Na2MoO4·2D2O\Na2MoO4. The water bands suggest the presence of two crystallographically distinct water molecules in Na2MoO4·2H2O. They form strong hydrogen bonds