Studies in the geometry of the discrete plane

This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis

Analysis and Design of an Adaptive Polynomial Predistorter with the Loop Delay Estimator

Most adaptive linearization circuits for the nonlinear amplifier have a feedback loop that returns the output signal oj'tne eunplifier to the lineurizer. The loop delay of the linearizer most be controlled precisely so that the convergence of the linearizer should be assured lot this Letter a delay control circuit is presented. It is a delay lock loop (ULL) with it modified early-lute gate and can he easily applied to a DSP implementation. The proposed DLL circuit is applied to an adaptive linearizer with the use of a polynomial predistorter, and the simulalion for a 16-QAM signal is performed. The simulation results show that the proposed DLL eliminates the delay between the reference input signal and the delayed feedback signal of the linearizing circuit perfectly, so that the predistorter polynomial coefficients converge into the optimum value and a high degree of linearization is achieved

Development of Directionally Adaptive Techniques for Single Image Super-Resolution

Super Resolution problem is an inverse problem and refers to the process of producing a High resolution (HR) image, making use of one or more Low Resolution (LR) observations. It includes up sampling the image, thereby, increasing the maximum spatial frequency and removing degradations that arise during the image capture namely aliasing and blurring. The work presented in this thesis is based on learning based single image super-resolution. In learning based super-resolution algorithms, a training set or database of available HR images are used to construct the HR image of an image captured using a LR camera. In the training set, images are stored as patches or coefficients of feature representations like wavelet transform, DCT, etc. Single frame image super-resolution can be used in applications where database of HR images are available. The advantage of this method is that by skilfully creating a database of suitable training images, one can improve the quality of the super-resolved image. A new super resolution method based on wavelet transform is developed and it is better than conventional wavelet transform based methods and standard interpolation methods. Super-resolution techniques based on skewed anisotropic transform called directionlet transform are developed to convert a low resolution image which is of small size into a high resolution image of large size. Super-resolution algorithm not only increases the size, but also reduces the degradations occurred during the process of capturing image. This method outperforms the standard interpolation methods and the wavelet methods, both visually and in terms of SNR values. Artifacts like aliasing and ringing effects are also eliminated in this method. The super-resolution methods are implemented using, both critically sampled and over sampled directionlets. The conventional directionlet transform is computationally complex. Hence lifting scheme is used for implementation of directionlets. The new single image super-resolution method based on lifting scheme reduces computational complexity and thereby reduces computation time. The quality of the super resolved image depends on the type of wavelet basis used. A study is conducted to find the effect of different wavelets on the single image super-resolution method. Finally this new method implemented on grey images is extended to colour images and noisy images

Some Generalizations of Fuzzy Metrizability

The main purpose of the study is to extent concept of the class of spaces called ‘generalized metric spaces’ to fuzzy context and investigates its properties. Any class of spaces defined by a property possessed by all metric spaces could technically be called as a class of ‘generalized metric spaces’. But the term is meant for classes, which are ‘close’ to metrizable spaces in some under certain kinds of mappings. The theory of generalized metric spaces is closely related to ‘metrization theory���. The class of spaces likes Morita’s M- spaces, Borges’s w-spaces, Arhangelskii’s p-spaces, Okuyama’s  spaces have major roles in the theory of generalized metric spaces. The thesis introduces fuzzy metrizable spaces, fuzzy submetrizable spaces and proves some characterizations of fuzzy submetrizable spaces, and also the fuzzy generalized metric spaces like fuzzy w-spaces, fuzzy Moore spaces, fuzzy M-spaces, fuzzy k-spaces, fuzzy -spaces study of their properties, prove some equivalent conditions for fuzzy p-spaces. The concept of a network is one of the most useful tools in the theory of generalized metric spaces. The -spaces is a class of generalized metric spaces having a network.

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

Department of Mathematics, Cochin University of Science and Technology.

Some Problems In Algebra And Topology A Study Of Fuzzy Convexity With Special Reference To Separation Properties

This thesis is a study of abstract fuzzy convexity spaces and fuzzy topology fuzzy convexity spaces No attempt seems to have been made to develop a fuzzy convexity theoryin abstract situations. The purpose of this thesis is to introduce fuzzy convexity theory in abstract situations

Performance Improvement of Fuzzy and Neuro Fuzzy Systems: Prediction of Learning Disabilities in School-age Children

Learning Disability (LD) is a classification including several disorders in which a child has difficulty in learning in a typical manner, usually caused by an unknown factor or factors. LD affects about 15% of children enrolled in schools. The prediction of learning disability is a complicated task since the identification of LD from diverse features or signs is a complicated problem. There is no cure for learning disabilities and they are life-long. The problems of children with specific learning disabilities have been a cause of concern to parents and teachers for some time. The aim of this paper is to develop a new algorithm for imputing missing values and to determine the significance of the missing value imputation method and dimensionality reduction method in the performance of fuzzy and neuro fuzzy classifiers with specific emphasis on prediction of learning disabilities in school age children. In the basic assessment method for prediction of LD, checklists are generally used and the data cases thus collected fully depends on the mood of children and may have also contain redundant as well as missing values. Therefore, in this study, we are proposing a new algorithm, viz. the correlation based new algorithm for imputing the missing values and Principal Component Analysis (PCA) for reducing the irrelevant attributes. After the study, it is found that, the preprocessing methods applied by us improves the quality of data and thereby increases the accuracy of the classifiers. The system is implemented in Math works Software Mat Lab 7.10. The results obtained from this study have illustrated that the developed missing value imputation method is very good contribution in prediction system and is capable of improving the performance of a classifier.