Physical Sciences and Mathematics Commons^™

Linear Estimation: The Kalman-Bucy Filter, William Douglas Schindel

Graduate Theses - Mathematics

The problem of linear dynamic estimation, its solution as developed by Kalman and Bucy, and interpretations, properties and illustrations of that solution are discussed. The central problem considered is the estimation of the system state vector X, describing a linear dynamic system governed by

dx/dt = F(t)X(t) + G(t)U(t)

Y(t) = H(t)X(t) + V(t)

for observations of Y (system output), where V is a random observation-corrupting process, and U is a random system driving process.

An extension of the Kalman-Bucy filter to estimation in the absence of priori knowledge of the random process U and V is developed and illustrated.

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 …

A New Test For Normality, Richard Leroy Roller

All Master's Theses

This paper presents a new test for normality which is based on a complete characterization of the normal distribution. Motivation for the test is given in terms of a proof of this characterization. The test is derived and evaluated by computer-simulated sampling from alternative distributions. The empirical powers of the test generated from such samplings are tabled and compared to nine commonly used tests. Evaluation of the proposed test is discussed and further avenues of investigation are suggested.

A Comparative Investigation Of The Effects Of Frequent Testing Upon Achievement In Secondary Advanced Algebra, John Thomas Fullerton

All Master's Theses

Relatively speaking, few studies have concerned themselves with the problem of frequent testing, and as Keys pointed out, empirical evidence, uncomplicated by differences in the amount of testing material employed, on the effects of frequent testing is, at best, scarce (14:427). Also many studies used tests and test results for direct instruction, thus introducing additional variables. Furthermore, the choice of subjects and disciplines has been limited, the better part being taken from college psychology and sociology classes or high school science classes. This investigation was not an attempt to modify previous experiments, nor was it an attempt to identify which …

Orthogonality In Normed Spaces, Martin R. Mccarthy

All Master's Theses

This paper presents three definitions of orthogonality in normed spaces. Each definition is shown equivalent to the inner product being zero when restricted to an inner product space. The definitions arise from such properties in two space as the diagonals of a rectangle being equal and the Pythagorean Theorem. The third definition shows that the idea of an inner product can be generalized under certain conditions.

Relationships Between Reversible And Connected Automata, Robert Michael Johnson

All Master's Theses

The present investigation explores some of the relationships among special classes of automata defined by Bavel and Muller (1:231-240), Trauth (6:170-175), and Cutlip (2).

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.

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.

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 …

Calculus And The Computer: A Conservative Approach, Melvin Henriksen

All HMC Faculty Publications and Research

This paper describes a program for making the use of numerical methods an integral part of the freshman college course in single variable calculus.

An Elementary Mathematics Curriculum Study To Determine If Achievement And Attitude Can Be Influenced By A Textbook Adoption, Elsie M. Railey

All Master's Theses

There is on the market a wide range of contemporary mathematics textbooks available. Textbooks approach mathematics differently and there is a variation in terms of the amount of time allocated to a topic, the development of elementary concepts and laws of arithmetic, and the amount of drill and repetition. The sequential development of the texts follows closely, but the scope and content differ significantly. Specifically, it is the purpose of this study to determine if there is a significant difference between series, as opposed to those in another mathematics series, in the variables of attitude and achievement. The two textbooks …

On The Theory Of Quaternions, Earle David Smith

All Master's Theses

Ordered triplets serve to describe space geometrically just as ordered pairs serve to describe the plane. A multiplication can be defined on pairs consistent with the complex numbers. However, as this paper will show, one cannot define a multiplication on triplets which is consistent with the complex numbers.

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 …

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 …

On Semigroup Rings, Lawrence Paul Runyan

All Master's Theses

Some of the properties of semigroup rings are described, illustrated and proved in this study. In particular, the central problem focuses on how various properties of the semigroup and ring are reflected in the resulting semigroup ring.

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.

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.

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.

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 …

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) …

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 …

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.

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.

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.

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.

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.

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 …

Period Relations For Picard Integrals Defined On A Special Class Of Kaehler Manifolds., Joseph Clement Wilson

LSU Historical Dissertations and Theses

No abstract provided.

The Spieker Circle And Certain Related Configurations, Berthola E. Lumzy

Electronic Thesis and Dissertation

No abstract provided.

A Necessary And Sufficient Condition That A Set Be Homeomorphic To A Plane Region Bounded By A Finite Number Of Nonintersecting Circles., Robert Lloyd Broussard

LSU Historical Dissertations and Theses

No abstract provided.