Fuzzy Absolutes and Related Topics

The study on the fuzzy absolutes and related topics. The different kinds of extensions especially compactification formed a major area of study in topology. Perfect continuous mappings always preserve certain topological properties. The concept of Fuzzy sets introduced by the American Cyberneticist L. A Zadeh started a revolution in every branch of knowledge and in particular in every branch of mathematics. Fuzziness is a kind of uncertainty and uncertainty of a symbol lies in the lack of well-defined boundaries of the set of objects to which this symbol belongs. Introduce an s-continuous mapping from a topological space to a fuzzy topological space and prove that the image of an H-closed space under an s-continuous mapping is f-H closed. Here also proved that the arbitrary product fi and sum of  fi of the s-continuous maps fi are also s-continuous. The original motivation behind the study of absolutes was the problem of characterizing the projective objects in the category of compact spaces and continuous functions.

On Chaos and Fractals in General Topological Spaces

The present study on chaos and fractals in general topological spaces. Chaos theory originated with the work of Edward Lorenz. The phenomenon which changes order into disorder is known as chaos. Theory of fractals has its origin with the frame work of Benoit Mandelbrot in 1977. Fractals are irregular objects. In this study different properties of topological entropy in chaos spaces are studied, which also include hyper spaces. Topological entropy is a measures to determine the complexity of the space, and compare different chaos spaces. The concept of fractals can’t be extended to general topological space fast it involves Hausdorff dimensions. The relations between hausdorff dimension and packing dimension. Regular sets in Metric spaces using packing measures, regular sets were defined in IR” using Hausdorff measures. In this study some properties of self similar sets and partial self similar sets. We can associate a directed graph to each partial selfsimilar set. Dimension properties of partial self similar sets are studied using this graph. Introduce superself similar sets as a generalization of self similar sets and also prove that chaotic self similar self are dense in hyper space. The study concludes some relationships between different kinds of dimension and fractals. By defining regular sets through packing dimension in the same way as regular sets defined by K. Falconer through Hausdorff dimension, and different properties of regular sets also.

Biogeochemistry of trace metals in the Indian EEZ of the Arabian Sea and Bay of Bengal

The present study has been initiated to unravel the distribution of trace metals and its geochemical behavior in the Indian EEZ of the Arabian Sea and Bay of Bengal. Trace metal accumulation in aquatic consumers is of interest to ecologists and environmentalists so as to understand the fate and effect of contaminants in the food web dynamics and the biogeochemical cycling of trace metals. It is well established that oceanic distribution of macronutrients such as nitrate, phosphate and silicate provide critical to biological growth and related geochemical processes. In this study it can be inferred, that there is a need for a better understanding of background informations on trace metal concentrations with respect to space and time and their fluctuations in the Arabian Sea and Bay of Bengal zooplankton. Without a sound knowledge on spatio-temporal fluctuations, it will be impossible to differentiate anthropogenic metal inputs from natural background concentrations with a routine biomonitoring programme. Fe, Cu, Zn, Cd & Pb showed a slight enrichment in zooplankton from the Arabian Sea during spring intermonsoon compared to intermonsoon fall. The relative enrichment of Fe, Cu & Zn in zooplankton from the Arabian Sea during intermonsoon spring than intermonsoon fall was due to favourable bioaccumulation factors of these elements during this season. Nevertheless this study can be looked upon as a starting point for further investigations on these biogeochemically important processes, which are vital in addressing the dynamics of productivity of waters.

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.

Some observations on the ecology and biochemical aspects of the seaweeds of Kerala coast

In the present thesis , observations on the ecology of seaweed flora of Kerala, their distribution and zonation pattern, monthly/seasonal density of seaweeds at each station, frequency of occurrence, standing crop, monthly/seasonal/place-wise data on physico—chemical characters of ambient waters at the stations and their influence on seaweed density have been made. This data will help us in the farming of economically important seaweeds, by providing information on the ideal conditions of seaweed biomass production. Biochemical observations on protein, carbohydrate and lipid contents of different species of nutritive value. Seaweeds with high content of proteins, carbohydrates and lipids can be recommended for food and feed formulations after subjecting them to toxicological studies. The study on monthly/seasonal/placewise variation in biochemical composition of seaweeds will provide necessary information on the appropriate time and place of harvesting the algal species for exploiting its constituents .

Theory of differential inequalities with appliciations to singular perturbiation problems and method of lines

During recent years, the theory of differential inequalities has been extensively used to discuss singular perturbation problems and method of lines to partial differential equations. The present thesis deals with some differential inequality theorems and their applications to singularly perturbed initial value problems, boundary value problems for ordinary differential equations in Banach space and initial boundary value problems for parabolic differential equations. The method of lines to parabolic and elliptic differential equations are also dealt The thesis is organised into nine chapters

Some problems in set topology relating group of homeomorphisms and order

In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention

Physical characteristics of the coastal waters off the south-west coast of india with an attempt to study the possible relationship with sardine mackerel and anchovy fisheries

The present study is aimed at observing the variations, in space and time, of see of the important hydrographic parameters such as sea water temperature, salinity and Resolved oxygen within the coastal waters along the south-west coast of Indiametween Ratnagiri (17°OO*N,73°20'E) and cape comorin ( 8°10'N,77°30*E). Specific data relating to the process of upwelling and sinking was collected mainly to evaluate the extent and intensity of the vertical mixing processes active in the area under study. The study also attempted possible correlations between the observed parameters and the occurrence and migrations of some of the major pelagic fishery resources such as sardine,mackerel and anchovy in the area under study

Mesozooplankton of the Arabian Sea and the Bay of Bengal with special reference to planktonic ostracods

The Arabian Sea and the Bay of Bengal are both highly dynamic ecosystems, due to the seasonally reversing monsoon winds, but the processes affecting the mesozooplankton community remain poorly understood. These are important basins exhibiting enhanced biological production as a result of upwelling, winter cooling and other episodic events such as eddies and gyres. Zooplankters are primarily the prey for almost all fish larvae. Seasonal changes in the biogeochemical processes can strongly affect zooplankton density and distribution, which in turn, strongly affect the larval growth, and consequently, the pelagic fish recruitment. It is clear that plankton biomass and biogeochemical fluxes are not in steady state. Acoustic data on mesozooplankton abundance suggests that they also exist in the mesopelagic zone. Earlier studies were confined only to the upper 200 m and hence the structure of mesozooplankton community in the deeper layers was not well known. Copepods are the dominant mesoplankton group, and therefore the majority of the studies were focused on them. The planktonic ostracods are the second major crustacean group and at times, their swarms can outnumber all other planktonic groups. The understanding of the community structure of the ostracods is essential to establish their role in the marine food web. Mesozooplankton is responsible for the vertical flux of organic matter produced by phytoplankton and is assumed to be equivalent to new production (Eppley & Peterson, 1979). Since the fate of newly produced organic matter depends upon their consumers, the zooplankton biomass must be estimated in size fractions or taxonomic components to understand the vertical flux of organic carbon. It is thus important to update our knowledge on different groups of zooplankton on the basis of seasonal and temporal distribution. The distribution in space and time is essential for modeling the carbon cycling that structure the marine ecosystems

Investigations on the radiation characteristics of flanged sectoral horn antennas and corner reflector systems

Antennas play an important role in determining the characteristics of any electronic system which depends on free space as the propagation medium. Basically, an antenna can be considered as the connecting link between free space and the transmitter or receiver. For radar and navigational purposes the directional properties of an antenna is its most basic requirement as it determines the distribution of radiated energy. Hence the study of directional properties of antennas has got special significance and several useful applications.

CBIR Using Local and Global Properties of Image Sub-blocks

This paper proposes a content based image retrieval (CBIR) system using the local colour and texture features of selected image sub-blocks and global colour and shape features of the image. The image sub-blocks are roughly identified by segmenting the image into partitions of different configuration, finding the edge density in each partition using edge thresholding, morphological dilation and finding the corner density in each partition. The colour and texture features of the identified regions are computed from the histograms of the quantized HSV colour space and Gray Level Co- occurrence Matrix (GLCM) respectively. A combined colour and texture feature vector is computed for each region. The shape features are computed from the Edge Histogram Descriptor (EHD). Euclidean distance measure is used for computing the distance between the features of the query and target image. Experimental results show that the proposed method provides better retrieving result than retrieval using some of the existing methods