Characterization of Probability Distributions Using the Residual Entropy Function

The present study on the characterization of probability distributions using the residual entropy function. The concept of entropy is extensively used in literature as a quantitative measure of uncertainty associated with a random phenomenon. The commonly used life time models in reliability Theory are exponential distribution, Pareto distribution, Beta distribution, Weibull distribution and gamma distribution. Several characterization theorems are obtained for the above models using reliability concepts such as failure rate, mean residual life function, vitality function, variance residual life function etc. Most of the works on characterization of distributions in the reliability context centers around the failure rate or the residual life function. The important aspect of interest in the study of entropy is that of locating distributions for which the shannon’s entropy is maximum subject to certain restrictions on the underlying random variable. The geometric vitality function and examine its properties. It is established that the geometric vitality function determines the distribution uniquely. The problem of averaging the residual entropy function is examined, and also the truncated form version of entropies of higher order are defined. In this study it is established that the residual entropy function determines the distribution uniquely and that the constancy of the same is characteristics to the geometric distribution

A fibre optic evanescent wave sensor for monitoring the rate of pulsed laser deposition of metal thin films

A novel sensing technique for the in situ monitoring of the rate of pulsed laser deposition (PLD) of metal thin films has been developed. This optical fibre based sensor works on the principle of the evanescent wave penetration of waveguide modes into the uncladded portion of a multimode fibre. The utility of this optical fibre sensor is demonstrated in the case of PLD of silver thin films obtained by a Q-switched Nd:YAG laser which is used to irradiate a silver target at the required conditions for the preparation of thin films. This paper describes the performance and characteristics of the sensor and shows how the device can be used as an effective tool for the monitoring of the deposition rate of silver thin films. The fibre optic sensor is very simple, inexpensive and highly sensitive compared with existing techniques for thin film deposition rate measurements

A fibre optic evanescent wave sensor for monitoring the rate of pulsed laser deposition of metal thin films

A novel sensing technique for the in situ monitoring of the rate of pulsed laser deposition (PLD) of metal thin films has been developed. This optical fibre based sensor works on the principle of the evanescent wave penetration of waveguide modes into the uncladded portion of a multimode fibre. The utility of this optical fibre sensor is demonstrated in the case of PLD of silver thin films obtained by a Q-switched Nd:YAG laser which is used to irradiate a silver target at the required conditions for the preparation of thin films. This paper describes the performance and characteristics of the sensor and shows how the device can be used as an effective tool for the monitoring of the deposition rate of silver thin films. The fibre optic sensor is very simple, inexpensive and highly sensitive compared with existing techniques for thin film deposition rate measurements.

Influence of personality factors on the consumption of personal care products

This research was undertaken with the primary objective of explaining differences in consumption of personal care products using personality variables. Several streams of research reported were reviewed and a conceptual model was developed. Theories on the relationship between self concept and behaviour was reviewed and the need to use individual difference variables to conceptualize and measure the salient dimensions of the self were emphasized. Theories relating to social comparison, eating disorders, role of idealized media images in shaping the self-concept, evidence on cosmetic surgery and persuasibility were reviewed in the study. These came from diverse fields like social psychology, use of cosmetics, women studies, media studies, self-concept literature in psychology and consumer research, and marketing. From the review three basic dimensions, namely self-evaluation, self-awareness and persuasibility were identified and they were posited to be related to consumption. Several personality variables from these conceptual domains were identified and factor analysis confirmed the expected structure fitting the basic theoretical dimensions. Demographic variables like gender and income were also considered.It was found that self-awareness measured by the variable public self-consciousness explain differences in consumption of personal care products. The relationship between public self-consciousness and consumption was found to be most conspicuous in cases of poor self-, evaluation measured by self-esteem. Susceptibility to advertising also was found to explain differences in consumption.From the research, it may be concluded that personality variables are useful for explaining consumption and they must be used together to explain and understand the process. There may not be obvious and conspicuous links between individual measures and behaviour in marketing. However, when used in proper combination and with the help oftheoretical models personality offers considerable explanatory power as illustrated in the seventy five percent accuracy rate of prediction obtained in binary logistic regression.

An optical fibre based evanescent wave sensor to monitor the deposition rate of thin films

A novel fibre optic sensor for the in situ measurement of the rate of deposition of thin films has been developed. Evanescent wave in the uncladded portion of a multimode fibre is utilised for this sensor development. In the present paper we demonstrate how this sensor is useful for the monitoring of the deposition rate of polypyrrole thin films, deposited by an AC plasma polymerisation method. This technique is simple, accurate and highly sensitive compared with existing techniques.

Evanescent wave sensor to monitor the etching rate of an optical fibre

The design and development of an evanescent wave sensor to determine the etching rate of the core of an optical fibre is discussed in this paper. The working of the device is based on the principle of propagation and loss of the evanescent wave in the cladding region of the fibre. The fraction of light intensity creeping out of the core of an uncladded fibre is a function of the core radius. As this radius decreases, the evanescent wave coupling to the medium surrounding the core enhances. This results in a decrease of the transmitted light intensity through the fibre. This technique is useful to design and fabricate optical fibres with different core geometries.

Recurrence Quantification Analysis of System Signals for Detecting Tool and Chatter in Turning

In this thesis, the applications of the recurrence quantification analysis in metal cutting operation in a lathe, with specific objective to detect tool wear and chatter, are presented.This study is based on the discovery that process dynamics in a lathe is low dimensional chaotic. It implies that the machine dynamics is controllable using principles of chaos theory. This understanding is to revolutionize the feature extraction methodologies used in condition monitoring systems as conventional linear methods or models are incapable of capturing the critical and strange behaviors associated with the metal cutting process.As sensor based approaches provide an automated and cost effective way to monitor and control, an efficient feature extraction methodology based on nonlinear time series analysis is much more demanding. The task here is more complex when the information has to be deduced solely from sensor signals since traditional methods do not address the issue of how to treat noise present in real-world processes and its non-stationarity. In an effort to get over these two issues to the maximum possible, this thesis adopts the recurrence quantification analysis methodology in the study since this feature extraction technique is found to be robust against noise and stationarity in the signals.The work consists of two different sets of experiments in a lathe; set-I and set-2. The experiment, set-I, study the influence of tool wear on the RQA variables whereas the set-2 is carried out to identify the sensitive RQA variables to machine tool chatter followed by its validation in actual cutting. To obtain the bounds of the spectrum of the significant RQA variable values, in set-i, a fresh tool and a worn tool are used for cutting. The first part of the set-2 experiments uses a stepped shaft in order to create chatter at a known location. And the second part uses a conical section having a uniform taper along the axis for creating chatter to onset at some distance from the smaller end by gradually increasing the depth of cut while keeping the spindle speed and feed rate constant.The study concludes by revealing the dependence of certain RQA variables; percent determinism, percent recurrence and entropy, to tool wear and chatter unambiguously. The performances of the results establish this methodology to be viable for detection of tool wear and chatter in metal cutting operation in a lathe. The key reason is that the dynamics of the system under study have been nonlinear and the recurrence quantification analysis can characterize them adequately.This work establishes that principles and practice of machining can be considerably benefited and advanced from using nonlinear dynamics and chaos theory.

Geodynamics of the Andaman - Sumatra - Java Trench - Arc System Based on Gravity and Seismotectonic Study

This work aims to study the variation in subduction zone geometry along and across the arc and the fault pattern within the subducting plate. Depth of penetration as well as the dip of the Benioff zone varies considerably along the arc which corresponds to the curvature of the fold- thrust belt which varies from concave to convex in different sectors of the arc. The entire arc is divided into 27 segments and depth sections thus prepared are utilized to investigate the average dip of the Benioff zone in the different parts of the entire arc, penetration depth of the subducting lithosphere, the subduction zone geometry underlying the trench, the arctrench gap, etc.The study also describes how different seismogenic sources are identified in the region, estimation of moment release rate and deformation pattern. The region is divided into broad seismogenic belts. Based on these previous studies and seismicity Pattern, we identified several broad distinct seismogenic belts/sources. These are l) the Outer arc region consisting of Andaman-Nicobar islands 2) the back-arc Andaman Sea 3)The Sumatran fault zone(SFZ)4)Java onshore region termed as Jave Fault Zone(JFZ)5)Sumatran fore arc silver plate consisting of Mentawai fault(MFZ)6) The offshore java fore arc region 7)The Sunda Strait region.As the Seismicity is variable,it is difficult to demarcate individual seismogenic sources.Hence, we employed a moving window method having a window length of 3—4° and with 50% overlapping starting from one end to the other. We succeeded in defining 4 sources each in the Andaman fore arc and Back arc region, 9 such sources (moving windows) in the Sumatran Fault zone (SFZ), 9 sources in the offshore SFZ region and 7 sources in the offshore Java region. Because of the low seismicity along JFZ, it is separated into three seismogenic sources namely West Java, Central Java and East Java. The Sunda strait is considered as a single seismogenic source.The deformation rates for each of the seismogenic zones have been computed. A detailed error analysis of velocity tensors using Monte—Carlo simulation method has been carried out in order to obtain uncertainties. The eigen values and the respective eigen vectors of the velocity tensor are computed to analyze the actual deformation pattem for different zones. The results obtained have been discussed in the light of regional tectonics, and their implications in terms of geodynamics have been enumerated.ln the light of recent major earthquakes (26th December 2004 and 28th March 2005 events) and the ongoing seismic activity, we have recalculated the variation in the crustal deformation rates prior and after these earthquakes in Andaman—Sumatra region including the data up to 2005 and the significant results has been presented.ln this chapter, the down going lithosphere along the subduction zone is modeled using the free air gravity data by taking into consideration the thickness of the crustal layer, the thickness of the subducting slab, sediment thickness, presence of volcanism, the proximity of the continental crust etc. Here a systematic and detailed gravity interpretation constrained by seismicity and seismic data in the Andaman arc and the Andaman Sea region in order to delineate the crustal structure and density heterogeneities a Io nagnd across the arc and its correlation with the seismogenic behaviour is presented.

Apptication of Biofloc Technology (BFI) in Ihe nunery rearing and farming of giant freshwater prawn, Macrobrachillm rosenbergii (de Man)

This thesis Entitled Application of Biofloc technology (BFT) In the Nursery Rearing and Farming of Giant Freshwater Prawn,Macrobrachium Rosenbergii(De Man). Aquaculture, rearing plants and animals under controlled conditions is growing with an annual growth rate of 8.3% in the period 1970-2008 (FAO, 2010). This trend of growth is essential for the supply of protein-rich food for ever increasing world population. But growth and development of aquaculture should be in sustainable manner, preferably without jeopardizing the aquatic environment.In the present study, the application of BFT in the nursery rearing and farming ofgiant freshwater prawn, M. rosenbergii, is attempted. The result of the study is organised into eight chapters. In the first chapter, the subject is adequately introduced. Various types of aquaculture practices followed, development and status of Indian aquaculture, present status of freshwater pravm culture, BF T and its use for the sustainable aquaculture systems, theory of BFT based aquaculture practices, hypothesis, objective and outline of the thesis are described. An extensive review of literature on studies carried out so far on biofloc based aquaculture are given in chapter 2. The third chapter deals with the application of BFT in the primary nursery phase of freshwater prawn. Several workers suggested the need for an intermediate nursery phase in the culture system of freshwater prawn for the successful production. Thirty day experiment was conducted to study the effect of BFT on the water quality, and animal welfare under the various stocking densities. The study concluded that stocking finfishes in biofloc-based monoculture system of freshwater prawns has the potential of increasing total yield. Prawns having a higher commercial value than finfishes besides ensuring economic sustainability. Results showed that prawn yield and survival was better in catla dominated tanks. Based on the results of the study, it is recommended to incorporate 25% rohu and 75% catla in the biofloc-based culture system of giant freshwater prawns. The results of the present study also recommend to stock relatively larger catla for biofloc-based culture system. Fish production was also higher in the 100% catla tank. When catla was added in higher percentages it should ensured that the hiding objects in the culture ponds shall be used in order to reduce the chance of cannibalism among prawns. rohu and catla equally have the ability to harvest the biofloc, catla consumes the planktonic contributes in the floc whereas rohu grazed on the bacterial consortium suspended in the water column. In Chapter 8, recommendations and future research perspectives in the field of biofloc based aquaculture is presented.

Studies on nonlinear dynamics of certain reaction systems

The nonlinear dynamics of certain important reaction systems are discussed and analysed in this thesis. The interest in the theoretical and the experimental studies of chemical reactions showing oscillatory dynamics and associated properties is increasing very rapidly. An attempt is made to study some nonlinear phenomena exhibited by the well known chemical oscillator, the BelousovZhabotinskii reaction whose mathematical properties are much in common with the properties of biological oscillators. While extremely complex, this reaction is still much simpler than biological systems at least from the modelling point of view. A suitable model [19] for the system is analysed and the researcher has studied the limit cycle behaviour of the system, for different values of the stoichiometric parameter f, by keeping the value of the reaction rate (k6) fixed at k6 = l. The more complicated three-variable model is stiff in nature.

Some bivariate life time models in discrete time"

The term reliability of an equipment or device is often meant to indicate the probability that it carries out the functions expected of it adequately or without failure and within specified performance limits at a given age for a desired mission time when put to use under the designated application and operating environmental stress. A broad classification of the approaches employed in relation to reliability studies can be made as probabilistic and deterministic, where the main interest in the former is to device tools and methods to identify the random mechanism governing the failure process through a proper statistical frame work, while the latter addresses the question of finding the causes of failure and steps to reduce individual failures thereby enhancing reliability. In the probabilistic attitude to which the present study subscribes to, the concept of life distribution, a mathematical idealisation that describes the failure times, is fundamental and a basic question a reliability analyst has to settle is the form of the life distribution. It is for no other reason that a major share of the literature on the mathematical theory of reliability is focussed on methods of arriving at reasonable models of failure times and in showing the failure patterns that induce such models. The application of the methodology of life time distributions is not confined to the assesment of endurance of equipments and systems only, but ranges over a wide variety of scientific investigations where the word life time may not refer to the length of life in the literal sense, but can be concieved in its most general form as a non-negative random variable. Thus the tools developed in connection with modelling life time data have found applications in other areas of research such as actuarial science, engineering, biomedical sciences, economics, extreme value theory etc.

Effect of Feeding Rate in Polymer Extrusion ”

Starve feeding of single screw extruder was described as an important means of improving the performance characteristics of the extruder. In addition to such improvement with versatility, the starve feeding technique also may affect the mechanical properties of the extrudate since the heat transfer an(l mixing characteristics in the starve fed and Hood fed extruders are not the same. Since the material is more loosely packed in the channels of the starve fed extruder, there may be greater bed mobility and uniformity. Further, the. thermal an(l shear induced degradation are also less since possibilities of developing local high temperatures are less compared to a densely compacted extruder bed. This study has been undertaken mainly to explore the effect of feeding rate on the mechanical properties of rubber and plastic extrudates since the effect of feeding rate has not been analysed from this angle so far.

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto 11 and beta distributions. Further, we generalize the identities for fire Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in file context of lengthbiased models are also explored

Characterizations of some continuous distributions using partial moments

Inthis paper,we define partial moments for a univariate continuous random variable. A recurrence relationship for the Pearson curve using the partial moments is established. The interrelationship between the partial moments and other reliability measures such as failure rate, mean residual life function are proved. We also prove some characterization theorems using the partial moments in the context of length biased models and equilibrium distributions

Characterizations of distributions using log odds rate

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties.