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.

Development of a portable composite equipment for coastal fishery and hydrographic investigations

This thesis reports on the details of the works done to develop a complete system for acquisition of the important marine environmental parameters namely, current, current direction, salinity, temperature and depth. It encompaéps transducers,signalconditioners display arrangements and remote controlled multiplexer which constitue the system. The various associate instruentation and environmental requisites and problems have been discussed and solved to considerable extend. The design and development features of this composite system includes an integrated approach in order to make the final equipment to be simple, inexpensive and easy for operation from small and large boats. This could be achieved with the successful development of all required components with features matching between them, such as sensors, signals conditioners remote operated multiplexers, comon display methods, quick performance check and calibration methods. The major success rests on the development of sensors with excellent performance characteristics suitable for marine environment. out of the 5 sensors. that of current salinity and depth are quite noval types with specific advantages. The environmental effects have been eliminated to the required extend. The common signal conditioner for salinity, temperature and depth has noval design features for achieving simplicity, reliability and accomodating the three sensors of different functional requirements.

Crystal Structures and Spectral Investigation of Aroylhydrazones and their Mixed Ligand Metal Chelates

Supra molecular architectures of coordination complexes of liydrazones through non covalent interactions have been explored. Molecular self—assernbly driven by weak interactions such as hydrogen— bonding, K '”T[, C-1-I‘ "TE, van der Waals interactions, and so forth are currently of tremendous research interest in the fields of molecule based materials. The directional properties of the hydrogembonding interaction associate discrete molecules into aggregate structures that are sufficiently stable to be considered as independent chemical species. Chemistry can borrow nature’s strategy to utilize hydrogen-bonding as Well as other noncovalent interactions as found in secondary and tertiary structures of proteins such as the double helix folding of DNA, hydrophobic selflorganization of phospholipids in cell membrane etc. In supramolecular chemistry hydrogen bonding plays an important role in forming a variety of architectures. Thus, the wise modulation and tuning of the complementary sites responsible for hydrogen—bond formation have led to its application in supramolecular electronics, host-guest chemistry, self-assembly of molecular capsules, nanotubes etc. The work presented in this thesis describes the synthesis and characterization of metal complexes derived from some substituted aroylhydrazones. The thesis is divided into seven chapters.