Fuzzy Topological Games and Related Topics

The main purpose of study is to extend the concept of the topological game G(K, X) and some other kinds of games into fuzzy topological games and to obtain some results regarding them. Owing to the fact that topological games have plenty of applications in covering properties, it made an attempt to explore some inter relations of games and covering properties in fuzzy topological spaces. Even though the main focus is on fuzzy para-meta compact spaces and closure preserving shading families, some brief sketches regarding fuzzy P-spaces and Shading Dimension is also provided. In a topological game players choose some objects related to the topological structure of a space such as points, closed subsets, open covers etc. More over the condition on a play to be winning for a player may also include topological notions such as closure, convergence, etc. It turns out that topological games are related to the Baire property, Baire spaces, Completeness properties, Convergence properties, Separation properties, Covering and Base properties, Continuous images, Suslin sets, Singular spaces etc.

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.

Box Products in Fuzzy Topological Spaces and Related Topics

The topology as the product set with a base chosen as all products of open sets in the individual spaces. This topology is known as box topology. The main objective of this study is to extend the concept of box products to fuzzy box products and to obtain some results regarding them. Owing to the fact that box products have plenty of applications in uniform and covering properties, here made an attempt to explore some inter relations of fuzzy uniform properties and fuzzy covering properties in fuzzy box products. Even though the main focus is on fuzzy box products, some brief sketches regarding hereditarily fuzzy normal spaces and fuzzy nabla product is also provided. The main results obtained include characterization of fuzzy Hausdroffness and fuzzy regularity of box products of fuzzy topological spaces. The investigation of the completeness of fuzzy uniformities in fuzzy box products proved that a fuzzy box product of spaces is fuzzy topologically complete if each co-ordinate space is fuzzy topologically complete. The thesis also prove that the fuzzy box product of a family of fuzzy α-paracompact spaces is fuzzy topologically complete. In Fuzzy box product of hereditarily fuzzy normal spaces, the main result obtained is that if a fuzzy box product of spaces is hereditarily fuzzy normal ,then every countable subset of it is fuzzy closed. It also deals with the notion of fuzzy nabla product of spaces which is a quotient of fuzzy box product. Here the study deals the relation connecting fuzzy box product and fuzzy nabla product

Phytoplankton Pigment Signatures as a Biomarker in a Tropical Estuary

We are in the cutting edge of a new era of development without leaving any promises to next generation. But the scale and size of the problem are only partially blamed. The juggernaut of Globalisation has trampled upon whatever little hope we might have had making a quick transition to a less energy – intensive world. “Environment friendliness begins at home”. Our quest for productivity and profitability should progress simultaneous with our cooperative responsibility of leaving behind a clean and green earth for the generation to come. Climate change is the most pressing global environmental challenge being faced by humanity, with the quest for better productivity for our fragile ecosystem. It is too late to rely solely on reduction in Green house gas emissions to mitigate climate change although this is undoubtedly crucial. Coastal belts are more prone to these devastating impacts and its protection is an intensive filed of research. The present study describes how the colourful Carotenoids and Chlorophylls can be used in rapid hand on tool in conjunction with molecular biology to open sources and it also explores the fate of organic matter in the aquatic system and underlying sediments.

Signatures of Higher Functions of Brain Dynamics in Electroencephalogram: A Nonlinear Analysis

The brain with its highly complex structure made up of simple units,imterconnected information pathways and specialized functions has always been an object of mystery and sceintific fascination for physiologists,neuroscientists and lately to mathematicians and physicists. The stream of biophysicists are engaged in building the bridge between the biological and physical sciences guided by a conviction that natural scenarios that appear extraordinarily complex may be tackled by application of principles from the realm of physical sciences. In a similar vein, this report aims to describe how nerve cells execute transmission of signals ,how these are put together and how out of this integration higher functions emerge and get reflected in the electrical signals that are produced in the brain.Viewing the E E G Signal through the looking glass of nonlinear theory, the dynamics of the underlying complex system-the brain ,is inferred and significant implications of the findings are explored.

Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

Remote Sensing the Signatures of Upwelling in South Eastern Arabian Sea

In this thesis, a variety of available satellite data products have been made use of to bring out a synergistic analysis on the upwelling phenomenon in SEAS. Basic concepts of remote sensing, upwelling and linked oceanography topics have been dealt in this work .Auxiliary data products utilized in this study are described in chapter 2. The climatological monthly variability of the upwelling signatures are detailed under chapter 3. Chapter 4 presents the forcing factors that trigger the upwelling process in SEAS. Chapter 5 describes the oceanic response to the forcing factors with respect to the SST cooling and CHLA blooms. Chapter 6 presents the heat budget of the region and the variability of heat budget terms with respect to upwelling. Chapter 7 describes the inter-annual variability of upwelling intensity in SEAS and the influence of climatic events on upwelling.

A Prototype for a Multimodal Biometric Security system based on Face and Audio Signatures

Any automatically measurable, robust and distinctive physical characteristic or personal trait that can be used to identify an individual or verify the claimed identity of an individual, referred to as biometrics, has gained significant interest in the wake of heightened concerns about security and rapid advancements in networking, communication and mobility. Multimodal biometrics is expected to be ultra-secure and reliable, due to the presence of multiple and independent—verification clues. In this study, a multimodal biometric system utilising audio and facial signatures has been implemented and error analysis has been carried out. A total of one thousand face images and 250 sound tracks of 50 users are used for training the proposed system. To account for the attempts of the unregistered signatures data of 25 new users are tested. The short term spectral features were extracted from the sound data and Vector Quantization was done using K-means algorithm. Face images are identified based on Eigen face approach using Principal Component Analysis. The success rate of multimodal system using speech and face is higher when compared to individual unimodal recognition systems

Biomarker pigment signatures in Cochin back water system e A tropical estuary south west coast of India

Sedimentary biomarker pigments around Cochin estuary situated in the southwest coast of India were determined by HPLC. Fucoxanthin, an indicator of diatom was observed to be the most abundant carotenoid pigment in the estuary. Dinoflagellate derived carotenoid pigment peridinin was confined in the southern part of estuary and zeaxanthin pigment indicative of cyanobacteria were more found in sites influenced by anthropogenic activities. One compound having close similarity to fucoxanthin was also detected. Alloxanthin (cryptophyceae), chl b (green algae), canthaxanthin, neoxanthin, lutein and peridinin isomer were also detected by spectra and corresponding algal class were identified. The highest concentration of chl a (11.01 mg g 1) found near to the anthropogenic affected area while the lowest chl a (0.65 mg g 1) was recorded in industrial area. Degradation products of chl a, such as pheophorbide and pheophytin were observed and principal mode of mechanism of degradation were derived. Higher pheopigments content than chl a, reflects a density trapping of dead cells and early degradation of phytopigments from grazing activities