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

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.

Study on Fuzzy Ordered FuzzyTopological Spaces

In this study we combine the notions of fuzzy order and fuzzy topology of Chang and define fuzzy ordered fuzzy topological space. Its various properties are analysed. Product, quotient, union and intersection of fuzzy orders are introduced. Besides, fuzzy order preserving maps and various fuzzy completeness are investigated. Finally an attempt is made to study the notion of generalized fuzzy ordered fuzzy topological space by considering fuzzy order defined on a fuzzy subset.

Use of an open photoacoustic cell for the thermal characterisation of liquid crystals

In this paper, we describe the use of an open cell photoacoustic configuration for the evaluation of the thermal effusivity of liquid crystals. The feasibility, precision and reliability of the method are initially established by measuring the thermal effusivities of water and glycerol, for which the effusivity values are known accurately. In order to demonstrate the use of the present method in the thermal characterization of liquid crystals, we have measured the thermal effusivity values in various mesophases of 4-cyano-4 - octyloxybiphenyl (8OCB) and 4-cyano-4 -heptyloxybiphenyl (7OCB) liquid crystals using a variable temperature open photoacoustic cell. A comparison of the measured values for the two liquid crystals shows that the thermal effusivities of 7OCB in the nematic and isotropic phases are slightly less than those of 8OCB in the corresponding phases

Use of an open photoacoustic cell for the thermal characterisation of liquid crystals

In this paper, we describe the use of an open cell photoacoustic configuration for the evaluation of the thermal effusivity of liquid crystals. The feasibility, precision and reliability of the method are initially established by measuring the thermal effusivities of water and glycerol, for which the effusivity values are known accurately. In order to demonstrate the use of the present method in the thermal characterization of liquid crystals, we have measured the thermal effusivity values in various mesophases of 4-cyano-4 - octyloxybiphenyl (8OCB) and 4-cyano-4 -heptyloxybiphenyl (7OCB) liquid crystals using a variable temperature open photoacoustic cell. A comparison of the measured values for the two liquid crystals shows that the thermal effusivities of 7OCB in the nematic and isotropic phases are slightly less than those of 8OCB in the corresponding phases

Use of an open photoacoustic cell for the thermal characterisation of liquid crystals

In this paper, we describe the use of an open cell photoacoustic configuration for the evaluation of the thermal effusivity of liquid crystals. The feasibility, precision and reliability of the method are initially established by measuring the thermal effusivities of water and glycerol, for which the effusivity values are known accurately. In order to demonstrate the use of the present method in the thermal characterization of liquid crystals, we have measured the thermal effusivity values in various mesophases of 4-cyano-4 - octyloxybiphenyl (8OCB) and 4-cyano-4 -heptyloxybiphenyl (7OCB) liquid crystals using a variable temperature open photoacoustic cell. A comparison of the measured values for the two liquid crystals shows that the thermal effusivities of 7OCB in the nematic and isotropic phases are slightly less than those of 8OCB in the corresponding phases

Open-cell photoacoustic investigation of the thermal effusivity of liquid crystals

We report the use of an open photoacoustic cell configuration for the evaluation of thermal effusivity of liquid crystals. Initially, the method is calibrated using water and glycerol as transparent liquid samples, and the role of thermal conductivity of these liquids on the photoacoustic signal amplitude is discussed. To demonstrate the application of the present method for the evaluation of thermal effusivity of liquid crystals, we have used certain multicomponent nematic liquid crystal mixtures, namely BL001, BL002, BL032, and BL035. Each of these liquid crystal mixtures contains four to nine components and are primarily based on the cyanobiphenyl structure. The measured values of thermal effusivity of BL001 and BL002 were found to be almost the same, but differ from those of BL032 and BL035, which implies a difference in composition of the latter two from the former two mixtures.

Photoacoustic investigation of doped InP using open cell configuration

An open cell photoacoustic (PA) configuration has been employed to evaluate the thermal diffusivity of intrinsic InP as well as InP doped with tin and iron. Thermal diffusivity data have been evaluated from variation of phase of PA signal as a function of modulation frequency. In doped samples, we observe a reduced value for thermal diffusivity in comparison with intrinsic InP. We also observed that, while the phase of the PA signal varies linearly with the square root of chopping frequency for doped samples, the intrinsic material does not exhibit such behaviour in the experimental frequency range. These results have been interpreted in terms of the heat generation and phonon assisted heat diffusion mechanisms in semiconductors.

Effect of Te doping on thermal diffusivity of Bi2Se3 crystals: A study using open cell photoacoustic technique

An open cell configuration has been employed for the photoacoustic measurement of the thermal diffusivity of undoped Bi2Se3 crystals and Bi2Se3 crystals doped with various concentrations of Te. The amplitude of the photoacoustic signal obtained under heat transmission configuration as a function of chopping frequency is used to evaluate the numerical value of thermal diffusivity, α. Doped samples show a substantial reduction in the value of α compared to undoped samples. The variations in the thermal diffusivity of the doped samples are explained in terms of the phonon assisted heat transfer mechanism. It is seen that α is very sensitive to structural variations arising from doping. The experimentally observed results are correlated with X-ray diffraction studies.

Microstrip band rejection filter using open loop resonator

Design of a compact microstrip band reject filter is proposed. The device consists of an Open Loop Rectangular Resonator (OLRR) coupled to a microstrip line. The transmission line has a U-bend which enhances the coupling with the OLRR element and reduces the size of the filter. The filter can be made tunable by mounting variable capacitance to the system. Simulated and experimental results are presented.

A Study of Closure and Fuzzy Closure Spaces with Reference to H-Closedness and Convexity

Department of Mathematics, Cochin University of Science and Technology.