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.

Electron Donating Property and Catalytic Activity of Perovskite-type Mixed Oxides (ABO3 ) Consisting of Rare Earth and 3d Transition Metals

The catalytic activity of Perovskite-type mixed oxides (LaCo03 . PrCo03 and SmCo03 ) for the reduction of cyclohexanone to cyclohexanol with 2-propanol (Meerwein-Ponndorf-Verley reduction) has been studied. The data have been correlated with the surface electron donor properties of these mixed oxides.

Protection of property and criminal law - A study with special reference to intellectual property

Theoretically speaking, property is extension of the personality of the individual. It serves the purpose of satisfying the self of the individual in the society. Various theories have been attempted to explain its origin and development. However, it is the socialist theory of property which finds acceptance in many societies today. A proper definition of the concept of property has notbeen given in the statutes governing protection of property or in the Indian Constitution. While deciding cases under the Indian Penal Code, the courts have however, been interpreting the term 'property' in a manner facilitating its accommodation within the contours of the socialist theory of property, though there was no attempt for any formal theorization. An examination of the decisions under the Penal Code provisions and Constituent Assembly Debates has reinforced the above view that our courts as well as legislature have adopted the socialist concept of property. Because of the importance of the theory of property in the general scheme of this study, it was thought appropriate toinclude a chapter on the theory of property as reflected in our constitution.