On Truncated Versions of Certain Measures of Inequality and Stability

The present study focuses attention on defining certain measures of income inequality for the truncated distributions and characterization of probability distributions using the functional form of these measures, extension of some measures of inequality and stability to higher dimensions, characterization of bivariate models using the above concepts and estimation of some measures of inequality using the Bayesian techniques. The thesis defines certain measures of income inequality for the truncated distributions and studies the effect of truncation upon these measures. An important measure used in Reliability theory, to measure the stability of the component is the residual entropy function. This concept can advantageously used as a measure of inequality of truncated distributions. The geometric mean comes up as handy tool in the measurement of income inequality. The geometric vitality function being the geometric mean of the truncated random variable can be advantageously utilized to measure inequality of the truncated distributions. The study includes problem of estimation of the Lorenz curve, Gini-index and variance of logarithms for the Pareto distribution using Bayesian techniques.

Biochemical Investigations on the Stability of Biological Membranes

In this project, an attempt has been made to study the stability of erythrocyte and lysosomal membranes biochemically. Erythrocytes were chosen for the study because of their ready availability and relative simplicity. Biological membranes forming closed boundaries between compartments of varying composition consist mainly of proteins and lipids. They are asymmetric, fluid structures that are thermodynamically stable and metabolically active. Normal cellular function begins with normal membrane structure and any variation in it may upset the normal functions. The degree of fluidity of a membrane depends on the chain length of its lipids and degree of unsaturation of constituent fatty acids. In response to environmental changes, many cells can regulate composition of their membranes to maintain the overall semi fluid environment necessary for many membrane associated functions. The assembly and Maintenance of membrane structures in cells is a dynamic process. The components are not only synthesized and inserted into a growing membrane but are also continuously degraded at a slower rate. This turnover process varies with each individual molecule.Lysosomes are important in the catabolic processes occurring in the cell. Lysosomes contain hydrolytic enzymes and are stable under normal conditions. In certain pathological conditions, the lysosomal membrane may rupture, releasing the hydrolytic enzymes into the cell and digestion of cell takes place as a whole. This is very dangerous. In normal life processes of multi cellular organisms, lysosomes rupture following the death of a cell and it may have some value as a built in mechanism for selfremoval of dead cells.An attempt has also been made in this project towards developing lysosome membrane stability as an index of fish spoilage during storage. Different membranes within the cell and between cells have different compositions as reflected in the ratio of protein to lipid. The difference is not surprising given the very different functions of membranes

Enzyme reactions as index of freshness of Fish and Shellfish

An attempt has been made in this study to screen some fish muscle enzymes to assess their potential worth in testing the degree of freshness of fish. A problem with routine enzyme activity determinations is the complexity of the method of enzyme assay. Hence, in the present study as far as possible simple assay techniques were adopted. Several species were screened to assess the possibility of employing this procedure on a large scale. It is hoped that findings of this study will lead to the development of meaningful criteria in testing the freshness of fish. This thesis has been divided into five chapters

Assessment of Convective Activity Using Stability Indices as Inferred from Radiosonde and MODIS Data

The combined use of both radiosonde data and three-dimensional satellite derived data over ocean and land is useful for a better understanding of atmospheric thermodynamics. Here, an attempt is made to study the ther-modynamic structure of convective atmosphere during pre-monsoon season over southwest peninsular India utilizing satellite derived data and radiosonde data. The stability indices were computed for the selected stations over southwest peninsular India viz: Thiruvananthapuram and Cochin, using the radiosonde data for five pre- monsoon seasons. The stability indices studied for the region are Showalter Index (SI), K Index (KI), Lifted In-dex (LI), Total Totals Index (TTI), Humidity Index (HI), Deep Convective Index (DCI) and thermodynamic pa-rameters such as Convective Available Potential Energy (CAPE) and Convective Inhibition Energy (CINE). The traditional Showalter Index has been modified to incorporate the thermodynamics over tropical region. MODIS data over South Peninsular India is also used for the study. When there is a convective system over south penin-sular India, the value of LI over the region is less than −4. On the other hand, the region where LI is more than 2 is comparatively stable without any convection. Similarly, when KI values are in the range 35 to 40, there is a possibility for convection. The threshold value for TTI is found to be between 50 and 55. Further, we found that prior to convection, dry bulb temperature at 1000, 850, 700 and 500 hPa is minimum and the dew point tem-perature is a maximum, which leads to increase in relative humidity. The total column water vapor is maximum in the convective region and minimum in the stable region. The threshold values for the different stability indices are found to be agreeing with that reported in literature.