A Cryptosystem Using the Concepts of Algebraic Geometric Code

Cryptosystem using linear codes was developed in 1978 by Mc-Eliece. Later in 1985 Niederreiter and others developed a modified version of cryptosystem using concepts of linear codes. But these systems were not used frequently because of its larger key size. In this study we were designing a cryptosystem using the concepts of algebraic geometric codes with smaller key size. Error detection and correction can be done efficiently by simple decoding methods using the cryptosystem developed. Approach: Algebraic geometric codes are codes, generated using curves. The cryptosystem use basic concepts of elliptic curves cryptography and generator matrix. Decrypted information takes the form of a repetition code. Due to this complexity of decoding procedure is reduced. Error detection and correction can be carried out efficiently by solving a simple system of linear equations, there by imposing the concepts of security along with error detection and correction. Results: Implementation of the algorithm is done on MATLAB and comparative analysis is also done on various parameters of the system. Attacks are common to all cryptosystems. But by securely choosing curve, field and representation of elements in field, we can overcome the attacks and a stable system can be generated. Conclusion: The algorithm defined here protects the information from an intruder and also from the error in communication channel by efficient error correction methods.

Studies on Fuzzy Graphs

In this thesis an attempt to develop the properties of basic concepts in fuzzy graphs such as fuzzy bridges, fuzzy cutnodes, fuzzy trees and blocks in fuzzy graphs have been made. The notion of complement of a fuzzy graph is modified and some of its properties are studied. Since the notion of complement has just been initiated, several properties of G and G available for crisp graphs can be studied for fuzzy graphs also. Mainly focused on fuzzy trees defined by Rosenfeld in [10] , several other types of fuzzy trees are defined depending on the acyclicity level of a fuzzy graph. It is observed that there are selfcentered fuzzy trees. Some operations on fuzzy graphs and prove that complement of the union two fuzzy graphs is the join of their complements and complement of the join of two fuzzy graphs is union of their complements. The study of fuzzy graphs made in this thesis is far from being complete. The wide ranging applications of graph theory and the interdisciplinary nature of fuzzy set theory, if properly blended together could pave a way for a substantial growth of fuzzy graph theory.

Studies in Fuzzy Commutative Algebra

The main objective of this thesis was to extend some basic concepts and results in module theory in algebra to the fuzzy setting.The concepts like simple module, semisimple module and exact sequences of R-modules form an important area of study in crisp module theory. In this thesis generalising these concepts to the fuzzy setting we have introduced concepts of ‘simple and semisimple L-modules’ and proved some results which include results analogous to those in crisp case. Also we have defined and studied the concept of ‘exact sequences of L-modules’.Further extending the concepts in crisp theory, we have introduced the fuzzy analogues ‘projective and injective L-modules’. We have proved many results in this context. Further we have defined and explored notion of ‘essential L-submodules of an L-module’. Still there are results in crisp theory related to the topics covered in this thesis which are to be investigated in the fuzzy setting. There are a lot of ideas still left in algebra, related to the theory of modules, such as the ‘injective hull of a module’, ‘tensor product of modules’ etc. for which the fuzzy analogues are not defined and explored.

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.

Studies on Fuzzy Matroitls and Related Topics

The doctoral thesis focuses on the Studies on fuzzy Matroids and related topics.Since the publication of the classical paper on fuzzy sets by L. A. Zadeh in 1965.the theory of fuzzy mathematics has gained more and more recognition from many researchers in a wide range of scientific fields. Among various branches of pure and applied mathematics, convexity was one of the areas where the notion of fuzzy set was applied. Many researchers have been involved in extending the notion of abstract convexity to the broader framework of fuzzy setting. As a result, a number of concepts have been formulated and explored. However. many concepts are yet to be fuzzified. The main objective of this thesis was to extend some basic concepts and results in convexity theory to the fuzzy setting. The concept like matroids, independent structures. classical convex invariants like Helly number, Caratheodoty number, Radon number and Exchange number form an important area of study in crisp convexity theory. In this thesis, we try to generalize some of these concepts to the fuzzy setting. Finally, we have defined different types of fuzzy matroids derived from vector spaces and discussed some of their properties.

Influence of short term climatic fluctuations on the agricultural land use in Kerala

In the present study, the land use over Kerala State and its spatial and temporal variations, spatio-temporal variations of water budget elements, climatic shifts, incidence of droughts and the influence of inter-annual fluctuations of rainfall on area. production and yield of selected crops, have been studied in detail. The thesis consists of seven chapters including the introduction. The first section of the Second Chapter deals with the importance of agrocliinatological studies in general and its application in agricultural land use in particular. It also gives an overview of the short term climatic fluctuations, water balance studies, crop weather relationships, land use patterns and various agricultural indices. This includes a detailed review of available literature in this field. The basic concepts. data used and the methodology adopted in the study forms, the second section of this Chapter. The Third Chapter gives the details of the physical features of the State such as the relief, geology, geomorphologysoils, drainage, and vegetation. The agroclimatology of the State is discussed in detail in Chapter Four. The first Section presents annual and seasonal variations of temperature and rainfall of the State along with a discussion on the water balance of the State. The secondSection of this Chapter deals with the influence of rainfall and water balance elements on various crops. The district-wise general land use pattern of theState and its spatio-temporal variations are discussed in Chapter Five. The first Section of Chapter Six gives an overview of the agricultural land use pattern of the State, cropping patterns, cropping intensity, crop combination and their spatio-temporal variations. The inter-annual variability of water balances of various stations of the State computed using the method of Thornthwaite (1948) and Thornthwaite & Mather (1955) is presented in the second Section of Chapter Six. This also includes a discussion of how the climatic shifts have occurred over the State and the influence of variations of climatic and water balance elements on the crops. The Seventh Chapter gives the summary of the work carried out and the results obtained from the study. Interpretations of the results, conclusions and suggestions made,based on the observations of the study are incorporated in this Chapter.

classification and content based retrieval of digital mammograms and placental sonograms

Image processing has been a challenging and multidisciplinary research area since decades with continuing improvements in its various branches especially Medical Imaging. The healthcare industry was very much benefited with the advances in Image Processing techniques for the efficient management of large volumes of clinical data. The popularity and growth of Image Processing field attracts researchers from many disciplines including Computer Science and Medical Science due to its applicability to the real world. In the meantime, Computer Science is becoming an important driving force for the further development of Medical Sciences. The objective of this study is to make use of the basic concepts in Medical Image Processing and develop methods and tools for clinicians’ assistance. This work is motivated from clinical applications of digital mammograms and placental sonograms, and uses real medical images for proposing a method intended to assist radiologists in the diagnostic process. The study consists of two domains of Pattern recognition, Classification and Content Based Retrieval. Mammogram images of breast cancer patients and placental images are used for this study. Cancer is a disaster to human race. The accuracy in characterizing images using simplified user friendly Computer Aided Diagnosis techniques helps radiologists in detecting cancers at an early stage. Breast cancer which accounts for the major cause of cancer death in women can be fully cured if detected at an early stage. Studies relating to placental characteristics and abnormalities are important in foetal monitoring. The diagnostic variability in sonographic examination of placenta can be overlooked by detailed placental texture analysis by focusing on placental grading. The work aims on early breast cancer detection and placental maturity analysis. This dissertation is a stepping stone in combing various application domains of healthcare and technology.

Design, Development and Realization of Quadratic Volterra Filters for Selected Applications

The basic concepts of digital signal processing are taught to the students in engineering and science. The focus of the course is on linear, time invariant systems. The question as to what happens when the system is governed by a quadratic or cubic equation remains unanswered in the vast majority of literature on signal processing. Light has been shed on this problem when John V Mathews and Giovanni L Sicuranza published the book Polynomial Signal Processing. This book opened up an unseen vista of polynomial systems for signal and image processing. The book presented the theory and implementations of both adaptive and non-adaptive FIR and IIR quadratic systems which offer improved performance than conventional linear systems. The theory of quadratic systems presents a pristine and virgin area of research that offers computationally intensive work. Once the area of research is selected, the next issue is the choice of the software tool to carry out the work. Conventional languages like C and C++ are easily eliminated as they are not interpreted and lack good quality plotting libraries. MATLAB is proved to be very slow and so do SCILAB and Octave. The search for a language for scientific computing that was as fast as C, but with a good quality plotting library, ended up in Python, a distant relative of LISP. It proved to be ideal for scientific computing. An account of the use of Python, its scientific computing package scipy and the plotting library pylab is given in the appendix Initially, work is focused on designing predictors that exploit the polynomial nonlinearities inherent in speech generation mechanisms. Soon, the work got diverted into medical image processing which offered more potential to exploit by the use of quadratic methods. The major focus in this area is on quadratic edge detection methods for retinal images and fingerprints as well as de-noising raw MRI signals

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.