Physical Sciences and Mathematics Commons^™

Flow-Shop Scheduling Problems., N. R. Achuthan Dr.

Doctoral Theses

Researchers attention was drawn to the study of schodulirg problems through mathemtical modelling, probably for the first time, when Johnson (1954) publishod his famous paper in mval research logistic quarterly. Thercafter, mny authors have contimued to contribute to the growth of the theory of scheduling. A vast colloctim of papers related to this area is rogularly published by journals like mamgement science, operations research, operational research quarterly, naval research logistic quarterly, opsearch etc.. A good grasp of the litermture in this arca can be had from the books by Conway et al. (1967), Baker (1974) and Rinnooy Kan (1976).This thesis …

Asymptotic Theory Of Extimation When The Limit Of The Log-Likelihood Ratios Is Mixed Normal., P. Jeganathan Dr.

Doctoral Theses

In one of his fundamental papers Le Can (1960) introduced what is now called locally asymptotically normal (LAN) families of distributions and obtained several basic results regarding the asymptotic theory of estimation and testing. Roughly speaking, a sequence of families is said to satisfy the LAN condition if the corresponding sequence of appropriately normalised log-likelihood function is locally approximated with probability tending to one by the sum of two expressions, the first one being a sequence of rand om linear functions of the normalised parameter and the second one being a non-random quadratic form of the normalised parameter, and the …

Extended Particles And The Interpretation Of Quantum Mechanics., C. K. Raju Dr.

Doctoral Theses

A now fornulation of the problen of junotion condiiions 1a given, It is pointed out that, if the existing the ory of relativity ie to be consistent with the existence of natter in the form of particles, thon the cannot be continuously aifferentiable everywhere, The mathonatical part of the problem of Junction conditiona is solved by using nonatandard analysis to define prod uo ta and compoaitions vith distributiona, The definitiona are auch that o ontimaed belief in the equations of relativity is justified, As an application, the equations of IRotion for the apherically-synne tric surface layor, at the Schwerzachild-Minkowsici junction, …

Abo Blood-Group Gene Frequencies In The Indian Sub-Continent: A Statistical Study Of Patterns Of Variation., Partha Pratim Majumder Dr.

Doctoral Theses

The main objective of this thesia is to diascover patterns of variation botwoen geographácal regions and socio- religious groups in the Indian sub-continant in respect of the distribution of ABO ganea controlling the O-A-B-AB blood group syston through a comprehensive, unified statistical analysia of all the relevant data avallable táll 1977.The posaibility of uning the 0-A-B-AB blood groupe as a marker for population genctic studias was first discovereda by Dr. and Mra, Hirachteld in 1919. The data collected by tham from amy personnel bolonging to various populatian groupa ahowed clear-cut di frerences and ganerated a lot of interost emong anthropologista, …

Contractual Arrangements In Agriculture : Some Theory And Empirical Evidence., Chandrasekhar Pant Dr.

Doctoral Theses

Tenancy in agriculture is an arrangement between the landowner and tenant in which the tenant paye to the landowner a certain mutually greed sun (or stare) of produce in return for the right to cul ti vate and appropriate the output produced on rentedend. There are different types of tenaney arrangements and often these differences relate to the form of payment of rent. Two of the more prevalent tendancy arrangements are share cropping (or cropshering) sand fixed-rent tendany, Under sh-re- cropping, the rent is a contructed percentage of the output produced on rented land while in a fixed-rent contract the …

Studies In Multipartite Self-Complementary Graphs., T. Gangopadhyay Dr.

Doctoral Theses

The class of self-complenentary egraphs has been extensively etudied by nany people, among others by C.R.J. Clephan, S.B, Rao, G, Ringel and H. Sache, and nany problems have been solved for this class, such as the Haniltonian problen and the characterisati on of potentially and forcibly self-complenentary dogree sequences (see [1], [2], [12), [13), [14, [15)). Thus self-complenentary graphs form an interesting class and this has been generalised by Hebbare [8] into the class of multipartite self-conplementary graphs.An r-partite self-complenentary graph is an r-partite graph G which is isomorphic to its r-partite complement where H has the sane vertex set …

Some Asymptotic Properties Of Maximum Likelihood Procedures., Kasala Subramaniam Dr.

Doctoral Theses

This thesis consists of two parts dealing with maximum likeli. hood procedures in two different frameworks. In the first part (Chapters 1,2 and 3) we consider inference about a parameter which is discrete or separated in the sense that no f(x, e) can be obtained as a "limit" of ff(x,e1)}, + e. (A precise definition of what is meant by & "limit" is given in Chapter 1). In the second part (Chapters 4 and 5) we consider the usual eÅŸtimetion problem of what may be called in constrast to Part I, a contimuous parameter. We assume, we have an exponential …

On Some Non Uniform Rates Of Convergence To Normality With Applications., Ratan Dasgupta Dr.

Doctoral Theses

We obtain non-uniform rates of convergence to normality of the partial sums in a triangular array of random variables, where variables in each array are independently distributed. Section 2 of this chapter generalizes the results of Michel (1976) mainly in the direction of considering a triangular array of rand om variables. A slight generality in the moment assumptions is also made. The later extension is quite in spirit with Katzs (1963) extension of the classical Berry-Esseen theorem. Since by Tomkins theorem (see Tomkins (1971) or Stout (1974)) the laws of the iterated logarithm are directly related to the zone where …

Some Problems On Econometric Regression Analysis., Maitreyi Chaudhuri Dr.

Doctoral Theses

Very often in eoonometrio enslysis one adopts the classical lineer regression model. The classical linear regression model is given by If, in addition, e is assumed to be normally Ä‘istributed, the model is called classical normal1 linear regression mode1.Ordinary least squares (0LS) methods of estimation and hypothesis testing are besed on this ndal, d eveluton copy of CV POFO But the assumptions on É›is and- xs may not be fulfilled in reality; or, in other words, the model may not be correctly specified. Cne class of problems arises when some of the regressors are omitted from the equation and/or scme …

Geological Depletion And Locational Advantage In The Analysis Of Mineral Extraction Programmes., Sudhir Dattatray Chitale Dr.

Doctoral Theses

The aim of the study is to evolve optimal pro- duction and linkage plans, to meet and oxogenously specified, spatially distributed time profile of damands from a set of spatially dispersed coking coal bearing geological blocks. The plans are optimal in the sense of minimun discounted present value of the sun of production, washing and transport costa.Pocussing our attention on a geological block consisting of many coal seams, we work with it as if it was operated as one production conplex. Geological depletion in ea ch block is formalised by estimat ing a Block Level Cumulative Cest Function (BLCCF) based …

On The Asymptotic Theory Of Quantiles And L-Statistics., Kesar Singh Dr.

Doctoral Theses

Let {Xi} be a sequence of r.v.s. nth stage we At the define e.d.f. as Fn (x) = (# Xi, ≤ x :≤ i ≤ n)/n and the ttn sample quantile as Qnt = inf {x : Fn (x) ≥ t} for t > 0 and = en(0+) for t=0. Most of the techniques of studying the process Qnt: 0 ≤ t≤ 1} consist of relating {Qnt} with some suitable linear statistics. The following are some of the commonly used methods for studying quantiles :(i) The Direct Methods In The Independent Case. Here, one can actually find the exact dis tribution …

A Study Of Admissibility Through Exterior Boundary Value Problem., C. Srinivasan Dr.

Doctoral Theses

The study of admissible decision procedures began in late forties when Wald introduced the concept to characterize the minimal complete class of decision procedures. Starting with the pioneering work of Abraham Wald, there has been considerable contribution to this area over the last three decades. However, most of the articles in this field dealt with specific decision procedures arid studied their admissibility. It was Stein [11 who first characterized, admissible decision procedures. Farrell ([2], (3]) generalized the result of Stein. In spite of the works of Stein and Farrell the problem of deciding whether a given decision procedure is admissible …

Employment And Output Objectives In Project Selection., Basudeb Sen Dr.

Doctoral Theses

Alarmingly high and increasing rates of unemployment among the fast growing labour force has, in the recent years, becmne a serious threat to the social, political and economic envirorment in developing countries like India. Despite planned efforts at economic development, the percentage of unemployed in the labour force is estimated to have increased fron 9.0 per cent in 1962 to 1o.4 per cent in 1971 and 11.0 per cent in 1972 Dutt and Sundharam (1975) 7. Eradication of unemployme nt through creation of large-scale job opportuni ti es has come to establish itself as a major objective of the country. …

Some Combinatorial Arrangements And Incomplete Block Designs Through Them., Anis Chandra Mukherjee Dr.

Doctoral Theses

The use and importance, in Statistical Experimental, of Incomplete Block Designs, particularly, Balanced Incomplete Block (BIB) Designs, Doubly Balanced Incomplete Block (DBIB) Designs and Partially Balanced Inçomplete Block (PBIB) Designs are well known. Several combinational arrangements, including the incidence matrices of these Incomplete Block Designs and association matrices associated with PBIB Designs are known to be of use in Design of Experiments. In this thesis, we consider the construction problems pertaining to some of these combinational arrangements and take up the problem of construction of BIB, DBIB and FBIB Designs through them. The combinational arrangements studied in the thesis have, …

On Some Problems Of Sequenting And Grouping., T. S. Arthanari Dr.

Doctoral Theses

The problems of sequencing arise in almost all walks of life. Theory of scheduling deals with such problems. Usually, these probl ems are stated in the literature in terms of jobs, machines, operations, penalties, due dates et cetera, that is, in the language of machine shops. The real life problems of In machine - shop job sequencing are of a complex nature. general, we consider processing n items on a certain group of machines, so as to optimize certain objective, subject to various cons traints on precedence, machine availability, due date and so on. The job sequencing problems are includ …

Contributions To Methodology Of Construction Of Consistent Index Number., Dodla Sai Prasada Rao Dr.

Doctoral Theses

International variation in national product is a subject of considerable interest, and any meaningful comparison of national product or per capita national income has to be in termo of a common currency. An intertemporal comparison for the same country at two points of time is mote meaningful in real terms, or in other words when the currency unit is adjusted for change in the general price level between the two points of time. In the same manner, the level of output or of consumption of a group of persons belonging to a region or to a particular socio-economio group can …

Some Contribution To The Theory Applications And Computations Of Generalized Inverses Of Matrices., Pochiraju Bhimasankaram Dr.

Doctoral Theses

The origin of the concept of a generalized inverse dates back to as early as 1920 when Moore defined the generalized inverse of matrix which is equivalent toDefinition 1 (Moore) : Let A be a m >< n matrix over the field of complex numbers. Then a is the generalized Inverse of A if AG is the orthogonal projection operator projecting arbitrary vectors onto the column space of A and GA is the orthogonal projection operator projecting arbitrary sectors onto, the column space of G.Mod re (1935) discussed this concept and its properties in some detail. Tsong (1949a, 1949b, 1956) discussed about generalized 1nverses of operators in more general spaces and Bjerhammer (1951) discussed the generalized inverse of a matrix in connection with an application to geodetic calculations. Unaware of the work of Hoore and others, Penrose (1955) defined a generalized inverse of a matrix as follows :Definition 2 (Penrosel) : Let A be a m *n -matrix over the field of complex numbers. Then G is a generalized inverse of a if (i) AFA= A; (ii) GAG=G; (iii) (AG)*=AG and (iv) (GA)*-GA.Penrose (1955,1956) showed that for every matrix there exists a unique generalized inverse, discussed several of its important properties, gave applications to solution of matrix equations and suggested a practical method of computation of the generalised inverse.As was pointed out by Rado (1956) Moo res definition of generalized inverse is equivalent to that of Penrose, Such generalized inverse is called the Moore-Penrose inverse and A is used to denote the Moore-Penrose inverse of A.Rao (1955), unaware of the earlier or contemporary Work, constructed a pseudo-inverse of a matrix which he used in some least squares computations, In a paper in 1962, he defined a generalized inverse (g-inverse) as follows, proved some interesting properties and gave applications of g-inverses to Mathomatical Statistics.Definition 3 (Rao) : Lot A be am x n matrix, Then a n >< m matrix. Then a n >< m matrix G is a g-inverse of A if x = Gy is a solution of the linear system Ax = y whenever it is consistent.A g-inverse if u matrix (in the sense of Rao) is in general not unique, As 1s easily observed (from definitions 2 and 4) the class of all g-inverses of a matrix A contains A*. Rạo (1965, 1967) developed a calculus of g-inverses, classified the g-inverses according to their use and according to the proporties they possess similar to those of the inverse of a nonsingular matrix and suggested further applications to Mathematical Statistics. Mitra (1968a, 1968b) gave an equivalem definition of a g-inverse, developed further calculus of z-inverses, used g-invorses to solve some matrix equations of interest and explored the possibilities of some new classes of g-inverses with applications. In a series of papers, and a monograph Mitra and Rao (1968, 1970) pursued the research on generalized inverses of matrix's and their applications to various scientific disciplines.

Optimum Estimators And Strategies In Survey Sampling., M. K. Ramakrishnan Dr.

Doctoral Theses

This thesis consists of nine chapters. In the first chapter we give the basic concepts and definitions and also a broad review of the literature related to the problems considered in this thesis. The second and third chapters are devoted to a detailed modified comparison of sampling with and without replacement, for the case of equal and unequal probability sampling respectively. In the fourth and fifth chapters we discuss the criteria of hyper-admissibility and linear suf2iciency for the choice of an optimum estimator for a given sampling design. The succeeding three chapters have as their main objective the central problem …

Contributions To The Theory Of Directed And Undirected Graphs., Siddani Bhaskara Rao Dr.

Doctoral Theses

Graph thoory has becone such a well Imown and widely applicd subject with nuncrous applications in operations rescarch, coding thoory, gone thoory, physical and so oial sciences (to montion only a few), that it is not neccasary to give a goneral introduction to 1t. Instead wo give below a Burnary of the reaults containod in thia thosis chapterwisc.This thesis contains five chapters which are, morc or loss, indopendent of cach. other. In Chaptcr 1, we study the existence of locally restricted graphs, that is graphs having a proscribod property with given dogrecs. In Section 1.1, wc obtain necossary and sufficient …

Some Statistical Considerations On Population Structure, Genetic Correlation And Human Multiple Births., Ranajit Chakraborty Dr.

Doctoral Theses

Siree the reiiecovery of Mentel'a works tamsrds tha beglaning of this contury the mnetiolete did not confine their atudies only at fanilial level. The atudy of penetie entities at poyulation level also bocune equally important for understending the mol.ani an of inharitanec. Thda branch of urderotanding the neoahantes of herodity, knowa sa Population Geneties, has by noe bacane no eli incm that a discunoion of say part of it drea not nead ny geneeal introtuetion. In view of shia faot, we irstead speni sone time to get into the problans diseussus in this thesia.Bastcally wa atudy theeo problene in this …

Some Contributions To The Analysis Of Circular Data., J. S. Rao Dr.

Doctoral Theses

In many diverae scientifie fields, one cones serose experimente where the basie variable unter obaervation ia a direction. We ahall be conoerned, throughout this theais, only with diraations in two-dimensions and wo refer to such a collection of directione an 'circular data or dimenstionl data. In order to make a statintical analyaie of circular data, the first prerequisite is to put thom in a quantitative form. One way of doing thie is to represent the directiona anglea no aaured d thre apeet to eone mui tably choscn sero direation. Al ternately, einee a direetion han no nagni- tude, it can …

Contribution To Linear Quaternionic Analysis., K. Viswanath Dr.

Doctoral Theses

Several articles have appeared in recent years which discuss linear transformations on finite-dimensional vector spaces over the quaternions in terms of matrices, but the general infinite -dimensional situation does not seen to have received much attention. In particular, very little is known about linear transformations on quaternionic Hilbert spaces apart from the obvious theory of Hermitian operators. There are hardly any discussion of this subject, apart from the brief treatment of Finkelstein, Jauch, Schiminovitch and Speiser in their fundamental paper on the foundations of quaternion quantum mechanics (1962), which gives spectral theorems for unitary operators and skew hermitian operators and …

Some Stochastic Models In Reliability., R. Natarajan Dr.

Doctoral Theses

The work presented in this thesis was carried out under the supervision of Dr. J. Sethuraman, Research & Training School, Indian Statistical Institute, Calcutta, and is devoted to the study of some stochastic models of standby and parallel redundant systems. Some of the reliability characteristics studied are the expected time to system failure, the long-run availability, expected number of system failures in a given interval of time, interval reliability etc. These reliability characteristics will be useful in the better design of systems and making management decisions in improving system reliability.The investigations carried out in this thesis are presented in four …

Design Optimization Using Model Estimation Programming, Richard Kay Brimhall

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Model estimation programming provides a method for obtaining extreme solutions subject to constraints. Functions which are continuous with continuous first and second derivatives in the neighborhood of the solution are approximated using quadratic polynomials (termed estimating functions) derived from computed or experimental data points. Using the estimating functions, an approximation problem is solved by a numerical adaptation of the method of Lagrange. The method is not limited by the concavity of the objective function.

Beginning with an initial array of data observations, an initial approximate solution is obtained. Using this approximate solution as a new datum point, the coefficients for …