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.

Development of Safety and Quality Management System in Shrimp Farming

Shrimp Aquaculture has provided tremendous opportunity for the economic and social upliftment of rural communities in the coastal areas of our country Over a hundred thousand farmers, of whom about 90% belong to the small and marginal category, are engaged in shrimp farming. Penaeus monodon is the most predominant cultured species in India which is mainly exported to highly sophisticated, quality and safety conscious world markets. Food safety has been of concem to humankind since the dawn of history and the concern about food safety resulted in the evolution of a cost effective, food safety assurance method, the Hazard Analysis Critical Control Point (HACCP). Considering the major contribution of cultured Penaeus monodon to the total shrimp production and the economic losses encountered due to disease outbreak and also because traditional methods of quality control and end point inspection cannot guarantee the safety of our cultured seafood products, it is essential that science based preventive approaches like HACCP and Pre requisite Programmes (PRP) be implemented in our shrimp farming operations. PRP is considered as a support system which provides a solid foundation for HACCP. The safety of postlarvae (PL) supplied for brackish water shrimp farming has also become an issue of concern over the past few years. The quality and safety of hatchery produced seeds have been deteriorating and disease outbreaks have become very common in hatcheries. It is in this context that the necessity for following strict quarantine measures with standards and code of practices becomes significant. Though there were a lot of hue and cry on the need for extending the focus of seafood safety assurance from processing and exporting to the pre-harvest and hatchery rearing phases, an experimental move in this direction has been rare or nil. An integrated management system only can assure the effective control of the quality, hygiene and safety related issues. This study therefore aims at designing a safety and quality management system model for implementation in shrimp farming and hatchery operations by linking the concepts of HACCP and PRP.

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.

Judicial Creativity in Constitutional Interpretation

The focus of study in this thesis is on the necessity and extent of judicial creativity in interpreting provisions in certain crucial areas in the Constitution of India. Judicial innovation was essential to adapt the constitutional provisions to modern changed context. Creativity of the Court has been mainly in the creation and introduction of certain new concepts not found in any specific provision of the Constitution which, but were essential for its meaningful interpretation.Independence of the judiciary, basic structure and certain elements of social justice cherished as ideal by the makers of the Constitution are some such concepts infused into the Constitution by the judiciary. The second aspect of creativity lies in the attempt of the Court to construe provisions in the Constitution with a view to upholding and maintaining the concepts so infused into the Constitution. Introduction of those concepts into the Constitution was necessary and is justified. all important features of the Constitution like democratic form of government, federal structure, judicial review, independence of judiciary and rule of law were thus included in the doctrine to prevent their alteration by amendments.As a result of such a construction, the nature of those directive principles itself has changed. They ceased to be mere directives for state action but became mandate for it. If left to legislative or executive will for their implementation, the directives would have remained enforceable as ordinary right.To conclude, notwithstanding the errors committed by the Supreme Court in construing the provisions in the above areas, they stand testimony to its creative and innovative response in interpreting the Constitution. If this trend is continued, it will be possible to achieve through the judicial process, maintenance of independence of the judiciary, avoidance of destruction of the Constitution through the process of amendment and realisation of social justice envisaged in the directive principles. It can be hoped that the Court would maintain its energetic and vibrant mind and rise up to the occasions and extend the same to other areas in future.

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.

‘Reliability Concepts in Quantile-based Analysis of Lifetime Data

Reliability analysis is a well established branch of statistics that deals with the statistical study of different aspects of lifetimes of a system of components. As we pointed out earlier that major part of the theory and applications in connection with reliability analysis were discussed based on the measures in terms of distribution function. In the beginning chapters of the thesis, we have described some attractive features of quantile functions and the relevance of its use in reliability analysis. Motivated by the works of Parzen (1979), Freimer et al. (1988) and Gilchrist (2000), who indicated the scope of quantile functions in reliability analysis and as a follow up of the systematic study in this connection by Nair and Sankaran (2009), in the present work we tried to extend their ideas to develop necessary theoretical framework for lifetime data analysis. In Chapter 1, we have given the relevance and scope of the study and a brief outline of the work we have carried out. Chapter 2 of this thesis is devoted to the presentation of various concepts and their brief reviews, which were useful for the discussions in the subsequent chapters .In the introduction of Chapter 4, we have pointed out the role of ageing concepts in reliability analysis and in identifying life distributions .In Chapter 6, we have studied the first two L-moments of residual life and their relevance in various applications of reliability analysis. We have shown that the first L-moment of residual function is equivalent to the vitality function, which have been widely discussed in the literature .In Chapter 7, we have defined percentile residual life in reversed time (RPRL) and derived its relationship with reversed hazard rate (RHR). We have discussed the characterization problem of RPRL and demonstrated with an example that the RPRL for given does not determine the distribution uniquely