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.

Excitation wavelength dependence of energy transfer in dye mixture doped polymer optical fibre preforms

Dependence of energy transfer parameters on excitation wavelength has been investigated in poly (methyl methacrylate) (PMMA) optical fibre preforms doped with C 540:Rh B dye mixture by studying the fluorescence intensity and the lifetime variations. A fluorescence spectrophotometer was used to record the excitation spectra of the samples for the emission wavelengths 495 and 580 nm. The fluorescence emission from the polymer rods was studied at four specific excitation wavelengths viz; 445, 465, 488 and 532 nm. The fluorescence lifetime of the donor molecule was experimentally measured in polymer matrix by time correlated single photon counting technique. The energy transfer rate constants and transfer efficiencies were calculated and their dependence on the acceptor concentration was analysed for three excitation wavelengths. It was found that any change in the excitation wavelength leads to significant variations in the quenching characteristics, which in turn affect the calculated energy transfer parameters.

Energy-Efficient Cluster based Routing Schemes for Static and Mobile Sensor Networks

The theme of the thesis is centred around one important aspect of wireless sensor networks; the energy-efficiency.The limited energy source of the sensor nodes calls for design of energy-efficient routing protocols. The schemes for protocol design should try to minimize the number of communications among the nodes to save energy. Cluster based techniques were found energy-efficient. In this method clusters are formed and data from different nodes are collected under a cluster head belonging to each clusters and then forwarded it to the base station.Appropriate cluster head selection process and generation of desirable distribution of the clusters can reduce energy consumption of the network and prolong the network lifetime. In this work two such schemes were developed for static wireless sensor networks.In the first scheme, the energy wastage due to cluster rebuilding incorporating all the nodes were addressed. A tree based scheme is presented to alleviate this problem by rebuilding only sub clusters of the network. An analytical model of energy consumption of proposed scheme is developed and the scheme is compared with existing cluster based scheme. The simulation study proved the energy savings observed.The second scheme concentrated to build load-balanced energy efficient clusters to prolong the lifetime of the network. A voting based approach to utilise the neighbor node information in the cluster head selection process is proposed. The number of nodes joining a cluster is restricted to have equal sized optimum clusters. Multi-hop communication among the cluster heads is also introduced to reduce the energy consumption. The simulation study has shown that the scheme results in balanced clusters and the network achieves reduction in energy consumption.The main conclusion from the study was the routing scheme should pay attention on successful data delivery from node to base station in addition to the energy-efficiency. The cluster based protocols are extended from static scenario to mobile scenario by various authors. None of the proposals addresses cluster head election appropriately in view of mobility. An elegant scheme for electing cluster heads is presented to meet the challenge of handling cluster durability when all the nodes in the network are moving. The scheme has been simulated and compared with a similar approach.The proliferation of sensor networks enables users with large set of sensor information to utilise them in various applications. The sensor network programming is inherently difficult due to various reasons. There must be an elegant way to collect the data gathered by sensor networks with out worrying about the underlying structure of the network. The final work presented addresses a way to collect data from a sensor network and present it to the users in a flexible way.A service oriented architecture based application is built and data collection task is presented as a web service. This will enable composition of sensor data from different sensor networks to build interesting applications. The main objective of the thesis was to design energy-efficient routing schemes for both static as well as mobile sensor networks. A progressive approach was followed to achieve this goal.

Phenylethynylarene Based Donor-Acceptor Systems: Design, Synthesis and Photophysical Studies

This thesis Entitled phenylethynylarene based Donor-Acceptor systems:Desigh,Synthesis and Photophysical studies. A strategy for the design of donor-acceptor dyads, wherein decay of the charge separated (CS) state to low lying local triplet levels could possibly be prevented, is proposed. In order to examine this strategy, a linked donor-acceptor dyad BPEPPT with bis(phenylethYlly/)pyrene (BPEP) as the light absorber and acceptor and phenothiazine (PT) as donor was designed and photoinduced electron transfer in the dyad investigated. Absorption spectra of the dyad can be obtained by adding contributions due 10 the BPEP and PT moieties indicating that the constituents do not interact in the ground stale. Fluorescence of the BPEP moiety was efficiently quenched by the PT donor and this was attributed to electron lransfer from PT to BPEP. Picosecond transient absorption studies suggested formation of a charge separated state directly from the singlet excited state of BPEP. Nanosecond flash photolysis experiments gave long-ived transient absorptions assignable to PT radical cation and BPEP radical anion. These assignments were confirmed by oxygen quenching studies and secondary electron transfer experiments. Based on the available data, energy level diagram for BPEP-PT was constructed. The long lifetime of the charge separated state was attributed to the inverted region effects. The CS state did not undergo decay to low lying BPEP triplet indicating the success of our strategy

Modelling and Analysis of Bivariate Lifetime Data using Reversed Hazard Rates

Department of Statistics, Cochin University of Science and Technology

‘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