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Generalized Inverses Of Special Types Of Matrices., Rao Vara Prasada Pullepu Sree Satya Narayana Dr.
Generalized Inverses Of Special Types Of Matrices., Rao Vara Prasada Pullepu Sree Satya Narayana Dr.
Doctoral Theses
Inverses, in the regular sense of the term, do not exist for singular square matrices and rectangular matrices. however for such matrices there exist matrices which satisfy many important properties similar to those of inverses of nonsingular matrices and for many purposes, can be used in the same way as regular inverses. These matrices are named generalised inverses (g-inverses) to distinguish then from the inverses of nonsingular matricos. Only since 1955 this field of study af generalized inverse was: invostigated systenatically and was expiorcd for nany beautiful and interesting results and applications though the concept of generalizod inverse was first …
Studies In Probability Theory., Ramanathan Subramaniam Dr.
Studies In Probability Theory., Ramanathan Subramaniam Dr.
Doctoral Theses
This thesis consists of four chapters.The inpetus for the work in Chapter 1 comes from the concept of 'conditional atom' introduced by ileveu (191. Here, using conditional atoms we generalize the concept of nenatomicity of measures. (We confine ourselves to probability measures). We obtain generalizations of results on non atomic measures in [1), [3] and of Liapounoff's theorem. The results in Chapter 2 have their origins in a paper by Boylan [7]. To study 'e quiconvergence of martingales' Boylan introduced in [7] a metric on the space of complete sub d-algebras of a probability space. A little later, Never showed …
Studies In The Theory Of Measurable Maltifunctions., Sheshi Mohan Srivastava Dr.
Studies In The Theory Of Measurable Maltifunctions., Sheshi Mohan Srivastava Dr.
Doctoral Theses
During the last fifteen years a large number of papers have been devoted to the study of elosed set valued multifunetions. The studies were notivated by both the theoretical and spplica- tional interests that such multifunetions have. From the appli- cational point of view it is worth noting that such multifune- tions arise in varlous problems of control theory, dynanie progra- aning etc. The theoretieal'aspects of these studies belong properly to classieal deseriptive set theory. Classionl deserip- tive set theory asks que stions about how sets are constructed and about other definability properties of sets. The results on closed set …
Invariant Subspaces Of Vector Valued Function Spaces On Bohr Groups., Somesh Chandra Bagchi Dr.
Invariant Subspaces Of Vector Valued Function Spaces On Bohr Groups., Somesh Chandra Bagchi Dr.
Doctoral Theses
The theory of invariant subspaces of various Cunclion-spaces of complox-valued and vector-valued functions on the circle group 13 well known through the 'Loctures on Invariant Subspaces' by Helson ([4]), Replacin; Line circle croup by a Bohr group B (that is, a compact ahelian group whose dual is a subgroup of tho ronl. line R, dense in the topology of R), Helson and Lowdenalager initiated the study of invariant subspaces of L2,(B) in (6]. They discovered that after suitable normalisation, the simply invariant subspaces of L2(B) arcinonc-to-one correspondence with a certain class of functions on R x B, which are called …
Maximal And Minimal Topologies., Asit Baran Raha Dr.
Maximal And Minimal Topologies., Asit Baran Raha Dr.
Doctoral Theses
Given a topological property Ï€ and a pon-void set X, let Ï€(X) denote the set of topologies on X with property Ï€. 7 (X) is obviously partially ordered by inclusion, A topologi- cal space (X,T) is minimal if T is a minimal element in T (X). (X, T) is said to be maximal Ï€ if T1 1s a maximalelement in Ï€(X), The study of maximal and minimal topological space is, as a matter of fact, a study of maximal Ï€ and minimal Ï€ spaces. Topological spaces closely related to minimal T sp aces are T-closed and KatetoV T spaces, (X,T) …
Studies In Boolean Algebras And Measure Theory., K. P. S. Bhaskara Rao Dr.
Studies In Boolean Algebras And Measure Theory., K. P. S. Bhaskara Rao Dr.
Doctoral Theses
This Thesis is divided into six chapters the first three chapters constituting studies in Boolean algebras and the last three chapters constituting studies in measure theory. We give below a sketch of the main problems treated in this Thesis.A De composition theorem due to Sobczyk and Hammer (28] implies that strongly continuous charges on Boolean algebras play a role similar to that of nonatomic measures on Boolean g-algebras. CHAPTER 1. Rudin [25] and Knowles [14] gave necessary and sufficient conditions for the Boral o-ficld of a compact Hausdorff space to admit a nonatomic measure. But there are no necessary and …
Contributions To Measure Theory., Merepalli Bhaskara Rao Dr.
Contributions To Measure Theory., Merepalli Bhaskara Rao Dr.
Doctoral Theses
This thesis 1s devoted to a study of measures vith emplas sis on nonatonie nea sures. Me briefrly desoribe here the work carried out in various chapters. In Chapter 1, we study various aspects of nonatomic nea sures based on some characterisations obtained early in the Chapter. In Chapter 2, the problem - when a mixture of nonatoftic mea sures is nonatomic - is exanined. An example and rive sufficient conditions are given. In Chapter 3, we examine when a mixture of 1nvariant non-ergorlie mesures is non-ergodic. An example and three sufficient eonditions are given. In Chapter 4, we study …
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 …
Studies In Borel Structures., Bhamidi Visweswara Rao Dr.
Studies In Borel Structures., Bhamidi Visweswara Rao Dr.
Doctoral Theses
It ts the nurposo of this chapter to collect together the problons that were acattored throughout the provious two chapters. This chaptor has sovon scctions. The first threo soc tions doal with the probloms that arc raised in or have c onnec tion witl: the topic of chaptor 1. The last tihree sectiona dcal with thc ne of chapter 2. Soction 4 stands mid- vay betweon bo tli, We ahall nunber the problomsi sorially and the nunber appears in bracko to. Wherover posaible wo shall includo somo dincuscion abcut the problcn involvod. There are no now rocults in thin chapter …
Theory Of Equitable Quality Level And Errors- Areas Under The Operating Characteristic Curves Of Lot Acceptance Sampling Plans., M. T. Subramanya Dr.
Theory Of Equitable Quality Level And Errors- Areas Under The Operating Characteristic Curves Of Lot Acceptance Sampling Plans., M. T. Subramanya Dr.
Doctoral Theses
This monograph deals with the theory of Equitable Quality Level and error-areas under the operating characte- ristic curves of lot acceptance sampling plans. A brief sumnary of the contents is given in Sections 1.2b (pages 15-16) and 2.9 (pages 107-111). A fairly good idea of the topics considored in this monograph can be obtained from the detailod list of contents given in pagos iv- xi.Most of the results given in the monograph are new and have not been published anywhe re. They are based on author's own research work and are contained in his doctoral dissertation.Most of the work connected …
Contribution To The Ergodic Theory., S. Natarajan Dr.
Contribution To The Ergodic Theory., S. Natarajan Dr.
Doctoral Theses
Ergodic theory is chiefly concerned with the study of transformations on a measure space which preserve the measure. Interesting classes of such transformations are the classes of ergodic, weakly mixing and mixing transformations. The bulk of this thesis is devoted to the study of a closely related family of transformations called the we akly stable transformations; these are more general than the weakly mäxing transformations.This thesis is divided into three parts. Part I contains preliminary ideas, notations and some results on the invertibility and continuity properties of transition functions (Chapters 1 and 2). In Chapter 3 we collect known results …
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 …
Contributions To The Theory Of Sampling Strategies., T. J. Rao Dr.
Contributions To The Theory Of Sampling Strategies., T. J. Rao Dr.
Doctoral Theses
Sample survny an a tochnique for collantion of data haa been w1dely accepted since quite a long time and it is only during the thirties and forties that a more syetem matic development has taken place owing to the most signi- ficant and rcmarkable works of Cochran, Hansen, Hurwitz, Mahalanobie, Neyman, Sukhatme, Yates and othera. Daring thin period, there were many important advances and tremendous progress in this field was achieved in India under the direction of Professor P. C. Mahal anobis. Besides the theoretical developments, streen was laid on the practical techniques and large-scale sample aurveys played a major …
Threshold Order Of A Switching Function And Stochastic Dependence Of Inputs., T. Krishnan Dr.
Threshold Order Of A Switching Function And Stochastic Dependence Of Inputs., T. Krishnan Dr.
Doctoral Theses
This Ä‘insertation is being submitted to the Indian Statiatical Inatitute, in support of the author's application for the degree of Doctor of Philosophy. This diasertation enbodien the work carried out by the author at the Indian Statistieal Institute under the aupervision of frofensor C. R. Rso. le is grate ful to Professor Rao for his constant encouragenent and inspi- ration and for the facilities provided at the Institute.The main part of the results of Chapter 5 have already been ublished (20). Zhe resulte of Chapters 2 and 3 and of Chapter 4 &e being reviewed for publie cation. ReferRes of …
Probabilistic Aspects Of Rings Of Operators., A. R. Padmanabhan Dr.
Probabilistic Aspects Of Rings Of Operators., A. R. Padmanabhan Dr.
Doctoral Theses
This theeis is submittod to the Irdian Statistical Institute in suppert bf the' author'a annlication for the degrée of Doctor of Philncophy. The thes is cmbodtee the research carried ut by thie author under the u pervision of Dr. J/S thurarn at the ind ian Sttiotivel Inatitute, Calcutta.Thia theain consis ts of three chapters. The first chapter dcals wri th convergence in mearur in ringe (of operatore) and allied reaul ts, the nee7:d, is devoted to a study of stnbility und mixing ir rims, and the last chapter is concerned wi tn aom: dominated convergenc the orema in ringo.
Minimax Theorems And Product Solutions., T. Parthasarathy Dr.
Minimax Theorems And Product Solutions., T. Parthasarathy Dr.
Doctoral Theses
It was John von-leumann who laid the foundationa of a miathematical theory of games of strategy . The climax of the pioneering period of de velopment oame in 1944 with the publication of The Theory of Gamea And Economic Behaviour by John von-Neumann and Oscar Morgenstern. Tha field of game theory ja now well established and widely diffused through the mathematical world- thanke to the auccese of thẻ volumes entitled Contributione to the theory of games and Advances in game theory . These volumes conprise a collection of contributions to the theory of games and answer some questions raised explicitly …
Solutions Of Some Balanced Doubly Balanced And Partially Balanced Statistical Designs., Chilakamarri Ramanujacharyulu Dr.
Solutions Of Some Balanced Doubly Balanced And Partially Balanced Statistical Designs., Chilakamarri Ramanujacharyulu Dr.
Doctoral Theses
The theory and methods of con struction of statistical designs have connections with Modern algebraic systems, theory of numbers, arithmetic theory of quadratic forms, information theory and construction of codes. The properties of finite linear spaces have been used for the construction of (i) complete set of mutually orthogonal latin squares (Bose and Nair, 1941) (ii) balanced incomplete block designs (Bose 1939) (iii) partially balanced incomplete block designs (Bose and Nair 1939) (iv) designs where some effects of treatments are confounded (Bose, 1947). Primrose (1951) studied quadric surfaces and used them in the construction of balanced incomplete block designs. Roychoudhuri …
Extensions Of The Theory Of Positive Operators And Their Relationship To Minimax Games., T. E.S. Raghavan Dr.
Extensions Of The Theory Of Positive Operators And Their Relationship To Minimax Games., T. E.S. Raghavan Dr.
Doctoral Theses
The theory of positive matrices (matrioco with non- negative entries) nnd the the ory of positive operetors are used extensively in the study of vibrationa of mechanical eysteme l16], stochaatic proceuses (36] nd mathematical economics ((9] and L20].) It is well known from the claseical theoreme of Perron and Frobenius ((13), [14) and (25] that any non-eingul ar squere matrix with non-negative entries has a positive cigenvalue which ts maximal in modulus among al1 the eigenvalues of the matrix. Further for this positive eigenvalue, it has a non-null eigenvector with all components non-negative. If the matrix is also irroduc lble11) …
External Graph Theoretic Problems With Applications To Communication Networks., Ramachandra Muthy Dr.
External Graph Theoretic Problems With Applications To Communication Networks., Ramachandra Muthy Dr.
Doctoral Theses
Graphs havre now become recognized models for a wide variety of situations. Whenever we have a collection of è´¸bjects with a binary relation defined on them graphs serve as excellopt toola to study the combinatoria properties of the collection with respect to the binary relation. D. Konig was the firat person to recognize the usefulness of graph theoretic modols. He conceived of a unified study of grapha under an abstract set up. His book was a pioneering work in this field.The graph theoretic problems embodied in this thesis have been motivated, by situations arising in communicationhave been motivated, by situations …
Contributions To Stratified Sampling And Some Related Problems., V. K. Sethi Dr.
Contributions To Stratified Sampling And Some Related Problems., V. K. Sethi Dr.
Doctoral Theses
In this thesis I have presented some of my results on problems connected with stratified sampling. Most of the results have already been published in various journals or have been submitted for publication. The thesis includes some extension of the published results and a much greater amount of evidence to support some conjectures than could be accomodated in papers submitted to journals.A major portion of the thesis in contained in Part I. This part deals with the problem of optimum stratification and the use of simple rules to approximate optimum stratification. In this thesis attention has been confined to Normal …
Convolution Properties Of Distributions On Topological Groups., S. R. S. Varadhan Dr.
Convolution Properties Of Distributions On Topological Groups., S. R. S. Varadhan Dr.
Doctoral Theses
The collection of probability distributions on the real line which is a semigroup under the convolution operation and topological space under weak convergence has attracted, during the last quarter of a century, the attention of such great mathematicians as Khintchine, Kolmogorov, Bawly, Levy and others. Their results constitute a deep analysis of the factorization problems on the one hand and the asymptotic behavior of infinite convolutions on the other. However, a complete and systematic investigation of these problems is not available in considerable generality. The aim of the present thesis is to investigate the topological and algebraic properties and the …
Distribution Theory Of Some Classification Statistics., S. John Dr.
Distribution Theory Of Some Classification Statistics., S. John Dr.
Doctoral Theses
This thesis eives the distri bution theory of four clae aifioation statistics. Sone parta of it were published a few years ago. The relevant publicationa are listed nt the end.What the author knows of related work by other authors is set out in the Introductions little material of this nature is given elsewhere in the theats. If a result is not explicitly credited to another author, it may be taken to nean that the author believes it to be hia worik.It will be noticed that three (U, R and 2) of the four statistics receive less a pace than the …
Some Problems Of Estimation In Sampling From Finite Populations., M. Murthy Dr.
Some Problems Of Estimation In Sampling From Finite Populations., M. Murthy Dr.
Doctoral Theses
In this thesis the results of the research work done by the author in the field of sample surveys are presented. Scheme problems of estimation in sampling from finite populations were taken up for reset arch. A brief summary of this thesis is given below.In chapter 1, the author has developed a generalized theory of getting unbiased estimator for a certain class of parameters in sampling from finite population. The class of parameters considered are those which can be expressed as the sum of single-valued set functions defined over a class of sets of units belonging to a finite population. …
Some Contributions To The Theory Of Sampling., Pramod Kumar Pathak Dr.
Some Contributions To The Theory Of Sampling., Pramod Kumar Pathak Dr.
Doctoral Theses
The work Presented here had originated from a pioneering paper by Basu1 and is essentially an extension of his ideas to different problem in sample surveys. The whole word mainly consists in deriving estimators uniformly better than those usually adopted in with replacement schemes.in with replacement sampling schemes, the 'order-statistic' (distinct sample unite arranged in an ascending order of their unit-indices) forms a sufficient statistic. Therefore, if any estimator (e.g., say of the population man) does not depend on the 'order-statistic', it can be uniformly improved by the use of the Rao-blalckwell theorem. The author has not hesitated to use …