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Articles 421 - 450 of 466
Full-Text Articles in Mathematics
On A General Class Of Unbiased Ratio, Product, Ratio-Cum-Product And Regression Type Estimators., N. S. Sastry Dr.
On A General Class Of Unbiased Ratio, Product, Ratio-Cum-Product And Regression Type Estimators., N. S. Sastry Dr.
Doctoral Theses
Probability enmpling methods ha ve extenaive a pplication in la rge- eca le agricultural and socio economic surve ys, Sampling is ale used in one or more stages of a census and sometimes as a mubstitute for a complete Census. Over the pa st four deca de s, confidence in the use of san pling and a ppreciation for the technique have stee dily grown thanks to the pi onee ring efforts of Neyman, Hansen, Hurwit z, Maha lanobis, Sukha tme, Cochran, Yate s and others.2. It is well known that the principa i problem of the theory of sampling …
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 …
On Some Problems Of Sequenting And Grouping., T. S. Arthanari Dr.
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 …
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 …
Study Of Dynamic Programming And Gambling Systems., N. D. Prabhakar Dr.
Study Of Dynamic Programming And Gambling Systems., N. D. Prabhakar Dr.
Doctoral Theses
The body of methods known as Dynamic Programming (d.p.) was developed by Bellman and was successfully applied by him to solve practical problems in diverse fields (see 12] and the pa pers cited there.). These methods revolved around an intuitively appealing principle which Bellman called the principle of optimatity. A general formulation of d.p. problem was given by Blackwell (3, s] which is narrower in scope than Bollman's but includes many important applications i12) and offers a proper framework for asking the many inte- resting and mathematically sophisticated questions that arise in d.p.. Strauch, Brown, Maitra, Furukawa, Dantas, Hinderer etc., …
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 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 …
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) …
Biometrics Of Bilateral Symmetry In Plants., T. Davis Dr.
Biometrics Of Bilateral Symmetry In Plants., T. Davis Dr.
Doctoral Theses
During the past ten deendes, observation rolating to ayune try, asymmatry, dis-oyame try, radlal symmetry, rotatiÉ”nal Bymne try, bilateral aymme try and ambidextry in the fields of bo tany, Boology, geology, chemiatry, eryatellography, physics, astronomy, engineering, mathematics, sunio, poetry and art vere recorded by various scientists. The prevent treatise is a sua- mary of an elaborato study on bilaterai syame try or microrinage symse try occurring in vari us plant organs. Unlike moet of the earlior reports, the problem here has been takled unified on a quantitative basis, thereby ereating situations where sophisti-cated techniques of statietios could be effectively employed. …
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 …
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.
Statistical Study Of Tongue Pigmentation In Man., Dabeeru Chandrasekhara Rao Dr.
Statistical Study Of Tongue Pigmentation In Man., Dabeeru Chandrasekhara Rao Dr.
Doctoral Theses
Tongue pigmentation in man:The 'partioular' type of dark apots and patohes on the surface of the tongue, as investigated in the prosent thesis, wae first not ioed in human populations by Davis [5], who called it 'tongue piementation'. It is to be emphasized that not all colour piements come under this 'particular' type. There are some pathological conditione giving rise to transient discolouration of the tongue. This aspeot will be disouesed a little later. Such tongue pigmentation does not seem to have been reported for any population, human or otherwise.Tongue pigmentation be usually found on the upper surface or borders …
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 …
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 …
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 …
Some External Problems And Charecterization In The Theory Of Graphs., Ramachandra Rao Dr.
Some External Problems And Charecterization In The Theory Of Graphs., Ramachandra Rao Dr.
Doctoral Theses
Graph theory has become such a well known and widely applied subject that it is not nocessary to give a general Introduetion to it. Instead ve eive helov a summary of the results of the thesis chapterwise.The study of extremal problems in Graph theory was started by Turan who deternined the minimum independence number of a graph on n vertices vith m edges. More recently Harary determined the maxinum conneetivity of a graph on n vortices vith m edges.In a paper concerning the degrees of the vertices of a graphy laktnd posed the following two problems : dotermin the maximum …
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 …
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 …
Some Contributions To The Design And Analysis Of Experiments With Special Reference To Weighing Designs,Partially Balanced Designs And Designs For Two Way Elimination Of Heterogensity., M. Bhaskar Rao Dr.
Doctoral Theses
Thie dissertation containe the authors vurious contributions to the design and analysia of experimenta. The min topios covered in this theeia are veighing designe, partially balanced designa and designs for tuo-vay elimination of hoterogeneity. Some of the material of the chaptere 2, 3, 4, 5 (marked vith asteriska in the theais) has beon conpiled from the authors publiahed papers. [9],[10].[13],[12],[13].[14].Chapters I and II deal with chemioal balanoe velghing designs. Yates [11] and Hotelling [36] obeerved that the veichta of the objeeta ean be more accurately determined by voighing thon in groupe. I a wodghing operations are made to veighp objecta, …
Studies In The Theory Of Graphs., R. P. Gupta Dr.
Studies In The Theory Of Graphs., R. P. Gupta Dr.
Doctoral Theses
No abstract provided.
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 …
Biometrical Genetics Of Insecticide Resistance:A Quantal Response Character., N Singh Dr.
Biometrical Genetics Of Insecticide Resistance:A Quantal Response Character., N Singh Dr.
Doctoral Theses
Geneses of the Froblems1.1.1 Resistence -A poblem in the fields of publio hosl th, agriculture, and endmel husbandry Discovery of the synthetic insecticides of residual toxcicity and their availability for civilian use after the World Mar I had presented a bright proapeot of freedom from insect bome diseases, Lindted fleld trials of chlorinated hydrocarbon insecticides in the sphere of ublic heal th had resulted in decline of the veotor/post pepulations by 'erdsia! and oonsaquentay the incidonce of vector borne diseases recorded drameatic falls. Inspired by such good results different combries and World Heoalth Organi zntion (WED) embarked upon the adventuro …
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.