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.

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.

Resonance Frequencies of Compact Microstrip Antenna

The arrow shaped microstrip antenna, which produces dual frequency dual polarisation operation with considera-ble size reduction compared to conventional patches has been reported [I]. These antennas provide greater area reduction and improved gain compared to drum shaped patches [2]. Prediction of the resonance frequency of drum shaped patches [3] and circular patches for broadband operation [4] are available in the literature. In this Letter, we propose empirical formulas for calculating the resonance frequencies of the arrow shaped microstrip antenna. These antennas can be employed for obtaining dual frequency with the same polarisation, bandwidth enhancement, circular polarisation etc. by varying its different parameters or by introducing slots. The proposed design equations provide an easier and simple way of predicting the resonant frequencies of these patches.

New compact microstrip antenna

A new microstrip antenna geometry with considerable reduction in size, with similar radiation characteristics to those of an equivalent rectangular patch antenna is proposed. A relationship has been suggested for fmding out the resonant frequency of the new geometry, and its validity has been established by the experimental results. Without increasing the aperture area, this geometry also offers a facility for considerably reducing the resonant frequency compared to conventional patches.

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

Resonance frequencies of compact microstrip antenna

A simple technique for calculating the resonance frequencies of a compact arrow-shaped microstrip antenna is presented and discussed . The accuracy of the method is validated by experimental results

Compact Wideband Antenna for 2.4 GHz WLAN Applications

A novel compact wideband antenna for wireless local area network (WLAN) applications in the 2.4 GHz band are presented. The proposed low profile antenna of dimensions 15 x 14.5 x 1.6 mm offers 18.6% bandwidth and an average gain of~5 dBi. The antenna can be excited directly using a 50 coaxial probe

Compact Planar Multiband Antenna for GPS, DCS, 2.4/5.8 GHz WLAN Applications

A compact single –feed multiband planar antenna configuration Suitable for GPS, DCS. 2.4/5.8 GHz WLAN applications are presented. The antenna has dimensions 38 x 3 x 1.6 mm and offers good radiation and reflection characteristics in the above frequency bands. The antenna has a simple geometry and can be easily fed using a 50 coaxial probe

Compact asymmetric coplanar waveguide filter

The design and implementation of a novel asymmetric coplanar waveguide (ACPW ) band rejection filter using defected ground structure ( DGS) is presented . The proposed ACPW DGS technology provides band gap characteristics with only one cell in the lateral ground plane . The equivalent circuit model of the proposed DGS unit section is described . Measurements of ACPW DGS showed good agreement with simulation and the proposed model

Analysis of a New Compact Microstrip Antenna

A new compact micro strip antenna element is analyzed. The analysis can accurately predict the resonant frequency, input impedance, and radiation patterns. The predicted results are compared with experimental results and excellent agreement is observed . These antenna elements are more suitable in applications where limited antenna real estate is available

Aircraft down-range profiles formed from simulated and compact-range radar backscatter

Compact-range radar backscatter measurements are taken of aircraft scale models. In addition, computer software is used to predict the RCS of the aircraft. Synthetic down-range profiles formed from the two sources of backscatter data are compared and visualized in an innovative manner. Similar discrimination rates between the two aircraft are obtained on data from both source

Circularly Polarized Compact Microstrip Antenna

A compact microstrip antenna with circular polarization radiation is demonstrated.A reducation in the required parameters for achieving CP radiation makes the present antenna design simpler