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Full-Text Articles in Physical Sciences and Mathematics
Contributions To Methodology Of Construction Of Consistent Index Number., Dodla Sai Prasada Rao Dr.
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.
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.
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.
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.
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.
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.
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.
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 …