A Study on the Reversed Lack of Memory Property and its Generalizations

In this thesis, the concept of reversed lack of memory property and its generalizations is studied.We we generalize this property which involves operations different than the ”addition”. In particular an associative, binary operator ” * ” is considered. The univariate reversed lack of memory property is generalized using the binary operator and a class of probability distributions which include Type 3 extreme value, power function, reflected Weibull and negative Pareto distributions are characterized (Asha and Rejeesh (2009)). We also define the almost reversed lack of memory property and considered the distributions with reversed periodic hazard rate under the binary operation. Further, we give a bivariate extension of the generalized reversed lack of memory property and characterize a class of bivariate distributions which include the characterized extension (CE) model of Roy (2002a) apart from the bivariate reflected Weibull and power function distributions. We proved the equality of local proportionality of the reversed hazard rate and generalized reversed lack of memory property. Study of uncertainty is a subject of interest common to reliability, survival analysis, actuary, economics, business and many other fields. However, in many realistic situations, uncertainty is not necessarily related to the future but can also refer to the past. Recently, Di Crescenzo and Longobardi (2009) introduced a new measure of information called dynamic cumulative entropy. Dynamic cumulative entropy is suitable to measure information when uncertainty is related to the past, a dual concept of the cumulative residual entropy which relates to uncertainty of the future lifetime of a system. We redefine this measure in the whole real line and study its properties. We also discuss the implications of generalized reversed lack of memory property on dynamic cumulative entropy and past entropy.In this study, we extend the idea of reversed lack of memory property to the discrete set up. Here we investigate the discrete class of distributions characterized by the discrete reversed lack of memory property. The concept is extended to the bivariate case and bivariate distributions characterized by this property are also presented. The implication of this property on discrete reversed hazard rate, mean past life, and discrete past entropy are also investigated.

Inventory management in public sector electrical industry in Kerala

The thesis entitled Inventory Management In Public Sector Electrical Industry In Kerala. Investigations were carried out on inventory management in public sector electrical industry in Kerala and suggest methods to improve their efficiency. Various aspects of inventory management, its scope and need in industry are detailed. The objectives of the present study concentrates to get an overall view of the system of inventory management, assess the positions and levels of inventory. It analyzes the inventory management policies and practices, the organizational set-up for materials by the electrical undertakings. The study examines the liquidity of the electrical undertakings as well as techniques of inventory management in the electrical industry in Kerala. Hypotheses state that the existing organizational systems and practices are inadequate to ensure efficient management of inventories in electrical industry. Introduction of scientific inventory techniques has a favourable effect on the workings of inventory departments. The financial performance of the public sector electrical undertakings is not at all satisfactory on account of the high raw material costs, heavy borrowings and huge interest burdens. The scope of this study is limited to the assessment of savings, in inventories of electrical products due to inventory management. The methodology of the study is to project the cost reduction of the inventory department on the basis of data collected and to validate this projection with the aid of analysis and survey. The limitations of the study is that the data obtained relate to the period 1989-90 and earlier and the current position is not available and uniform norms cannot be applied to evaluate different inventory management organisation.

Equality of Opportunity in Public Employment : Judicial Perspectives on Backwardness

This thesis is a study of -Equality of Opportunity in Public Employment : Judicial Perspectives on Backwardness. This study is an attempt to evaluate the concept of backwardness and equality of opportunity in employment and to assess the judicial perspectives in relation to them. The study reveals that the recent review petition of the Constitution Bench did not assess the decision of Chakradhar and its import. The study reveals that the Indian judiciary could successfully locate and apply the above principles. It was-Justice Subba Rao's nascent attempt in Devadasan which marked the starting point of such a jurisprudential enquiry. Later Thomas developed the thoughts by a reading new meaning and content to equality provisions of the Constitution which included the elimination of inequalities as the positive content of Articles 14 and 16(1) and elevated reservation provision to the same status of equality principles under the Constitution. Soshit, Vasanth Kumar and Mandal supplemented further to the jurisprudential contents. In this process, the courts were guided by the theories of John Rawls, David Miller, Ronald Dworkin, Max Weber and Roscoe Pound. Thus there was a slow and steady process of transformation of the reservation provision. From an anti-meritarian, unenforceable and enabling provision, it reached a stage of equally relevant and explanatory part of fundamental right to equality. Mandal viewed it as a part of sharing of State power. Though this can be seen by rereading and re-joining thoughts of judges in this regard, the judicial approach lacks coherence and concerted efforts in evolving a jurisprudential basis for protective discrimination. The deliberations of the framers of the Constitution reveals that there was much confusion and indeterminacy with regard to the concept of Backwardness. The study shows that the judiciary has been keeping intact the framers’ expectation of having a reasonable quantum of reservation, preventing the undeserved sections from enjoying the benefit, avoiding its abuse and evolving a new criteria and rejecting the old ones.

Some problems in set topology relating group of homeomorphisms and order

In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. Even mathematicians like H. Poincare worried about this. He observed that mathematical models are over idealizations, for instance, he said that only in Mathematics, equality is a transitive relation. A first attempt to save this situation was perhaps given by K. Menger in 1951 by introducing the concept of statistical metric space in which the distance between points is a probability distribution on the set of nonnegative real numbers rather than a mere nonnegative real number. Other attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A. Sklar and others. An aspect in common to all these approaches is that they model impreciseness in a probabilistic manner. They are not able to deal with situations in which impreciseness is not apparently of a probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces.

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

Development of Hierarchical Clustering Techniques for Gridded Data from Mixed Data Sequences

Knowledge discovery in databases is the non-trivial process of identifying valid, novel potentially useful and ultimately understandable patterns from data. The term Data mining refers to the process which does the exploratory analysis on the data and builds some model on the data. To infer patterns from data, data mining involves different approaches like association rule mining, classification techniques or clustering techniques. Among the many data mining techniques, clustering plays a major role, since it helps to group the related data for assessing properties and drawing conclusions. Most of the clustering algorithms act on a dataset with uniform format, since the similarity or dissimilarity between the data points is a significant factor in finding out the clusters. If a dataset consists of mixed attributes, i.e. a combination of numerical and categorical variables, a preferred approach is to convert different formats into a uniform format. The research study explores the various techniques to convert the mixed data sets to a numerical equivalent, so as to make it equipped for applying the statistical and similar algorithms. The results of clustering mixed category data after conversion to numeric data type have been demonstrated using a crime data set. The thesis also proposes an extension to the well known algorithm for handling mixed data types, to deal with data sets having only categorical data. The proposed conversion has been validated on a data set corresponding to breast cancer. Moreover, another issue with the clustering process is the visualization of output. Different geometric techniques like scatter plot, or projection plots are available, but none of the techniques display the result projecting the whole database but rather demonstrate attribute-pair wise analysis

A New Gridding Technique for High Density Microarray Images Using Intensity Projection Profile of Best Sub Image

As the technologies for the fabrication of high quality microarray advances rapidly, quantification of microarray data becomes a major task. Gridding is the first step in the analysis of microarray images for locating the subarrays and individual spots within each subarray. For accurate gridding of high-density microarray images, in the presence of contamination and background noise, precise calculation of parameters is essential. This paper presents an accurate fully automatic gridding method for locating suarrays and individual spots using the intensity projection profile of the most suitable subimage. The method is capable of processing the image without any user intervention and does not demand any input parameters as many other commercial and academic packages. According to results obtained, the accuracy of our algorithm is between 95-100% for microarray images with coefficient of variation less than two. Experimental results show that the method is capable of gridding microarray images with irregular spots, varying surface intensity distribution and with more than 50% contamination