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.

Geometric Algebra and Einstein’s Electron

This thesis entitled Geometric algebra and einsteins electron: Deterministic field theories .The work in this thesis clarifies an important part of Koga’s theory.Koga also developed a theory of the electron incorporating its gravitational field, using his substitutes for Einstein’s equation.The third chapter deals with the application of geometric algebra to Koga’s approach of the Dirac equation. In chapter 4 we study some aspects of the work of mendel sachs (35,36,37,).Sachs stated aim is to show how quantum mechanics is a limiting case of a general relativistic unified field theory.Chapter 5 contains a critical study and comparison of the work of Koga and Sachs. In particular, we conclude that the incorporation of Mach’s principle is not necessary in Sachs’s treatment of the Dirac equation.

Studies on magnetic monopole solutions of non-abelian gauge theories and related problems

In 1931 Dirac studied the motion of an electron in the field of a magnetic monopole and found that the quantization of electric charge can be explained by postulating the mere existence of a magnetic monopole. Since 1974 there has been a resurgence of interest in magnetic monopole due to the work of ‘t’ Hooft and Polyakov who independently observed that monopoles can exist as finite energy topologically stable solutions to certain spontaneously broken gauge theories. The thesis, “Studies on Magnetic Monopole Solutions of Non-abelian Gauge Theories and Related Problems”, reports a systematic investigation of classical solutions of non-abelian gauge theories with special emphasis on magnetic monopoles and dyons which possess both electric and magnetic charges. The formation of bound states of a dyon with fermions and bosons is also studied in detail. The thesis opens with an account of a new derivation of a relationship between the magnetic charge of a dyon and the topology of the gauge fields associated with it. Although this formula has been reported earlier in the literature, the present method has two distinct advantages. In the first place, it does not depend either on the mechanism of symmetry breaking or on the nature of the residual symmetry group. Secondly, the results can be generalized to finite temperature monopoles.

Fluid mechanics-non-linear waves studies on korteweg-de vries equations

In this thesis the author has presented qualitative studies of certain Kdv equations with variable coefficients. The well-known KdV equation is a model for waves propagating on the surface of shallow water of constant depth. This model is considered as fitting into waves reaching the shore. Renewed attempts have led to the derivation of KdV type equations in which the coefficients are not constants. Johnson's equation is one such equation. The researcher has used this model to study the interaction of waves. It has been found that three-wave interaction is possible, there is transfer of energy between the waves and the energy is not conserved during interaction.

On Queueinginventory Models – product form solution; reservation, Cancellation and common life time

Queueing theory is the mathematical study of ‘queue’ or ‘waiting lines’ where an item from inventory is provided to the customer on completion of service. A typical queueing system consists of a queue and a server. Customers arrive in the system from outside and join the queue in a certain way. The server picks up customers and serves them according to certain service discipline. Customers leave the system immediately after their service is completed. For queueing systems, queue length, waiting time and busy period are of primary interest to applications. The theory permits the derivation and calculation of several performance measures including the average waiting time in the queue or the system, mean queue length, traffic intensity, the expected number waiting or receiving service, mean busy period, distribution of queue length, and the probability of encountering the system in certain states, such as empty, full, having an available server or having to wait a certain time to be served.