Digital Commons Network^™

Studies In The Theory Of Graphs., R. P. Gupta Dr.

Doctoral Theses

No abstract provided.

Rings Of Continuous Functions On Open Convex Subsets Of R, Lyle E. Pursell

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Inferences On The Parameters Of The Weibull Distribution, Darrel Ray Thoman

Doctoral Dissertations

"For the most part, solutions to the problems of making inferences about the parameters in the Weibull distribution have been limited to providing simple estimators of the parameters. Little has been known about the properties of the estimators. In this paper the small and moderate sample size properties of the maximum likelihood estimators are studied and their superiority is established. The problem of making further inferences which are based on the maximum likelihood estimates of the parameters is then considered. The inferences that are presented can be divided into those based on a single sample and those based on two …

A Description And An Analysis Of The Results Of Using Cadet Teaching As A Method Of Improving The Multiplication Proficiency Of A Selected Sample Of Fourth And Seventh Grade Students, Richard Mark Anderson

Dissertations and Theses @ UNI

The purpose of this study is to describe and analyze the results of using cadet teaching as a method of improving the multiplication proficiency of fourth grade students from Price Laboratory School and seventh grade students from Holmes Junior High who have difficulty with multiplication. A multiplication test designed by the investigator was administered to sixty fourth grade students and forty-four seventh grade students. As a result of this test, sixteen fourth grade students and sixteen seventh grade students were identified as having difficulty with multiplication. Eight of the fourth grade students and eight of the seventh grade students were …

Topic From Galois Theory, Pai-Yuan Chang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Galois theory constitutes an excellent introduction group theory and field theory and provides a strong motivation for the introduction of the basic concepts of abstract algebra. This paper explains the basic theory and describes how it is applied to prove the unsolvability "by radicals" of equations of degree n >= 5.

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 …

An Examination Of The Romberg Method For Numerical Integration, Water James Halpin

Mathematics & Statistics ETDs

INTRODUCTION

This paper will amount to an inquiry into the mathematical structure and properties of a matrix of approximate integration formulas due to Werner Romberg 1 which have found considerable favor in numerical analysis during the past decade. Like other devices for approximate integration the Romberg method has its origin in the exhaustion techniques developed by the Greeks for determining the areas of figures enclosed by lines in the plane. It is particularly closely associated with the scheme employed by Archimedes2 (circa 250 B.C.) for approximating the value of [3.14]. This involves a doubling process which is essentially the basis …

On Some Categories Of Partially Ordered Sets With Residuated Mappings, Gary D. Crown

Mathematics & Statistics ETDs

Croisot [1] was apparently first to examine some of the properties of residuated mappings. It is the purpose of this paper to show that certain constructions currently useful in homological algebra can be made in a suitable category of partially ordered sets with residuated mappings. In Section 1 we note some elementary properties of residuated mappings all of which are well known cf. Janowitz [4]. In Section 2 we notice some properties of various categories of partially ordered sets with residuated mappings. In Section 3 we prove that the category of complete lattices with residuated mappings has enough injectives and …

Ua66/10/1 Sixty Years Of Math At Western, Robert Bueker

WKU Administration Documents

A brief history of the WKU Mathematics department from 1906-1967.

Air Force Rotc At The University Of Richmond, 1951-1957, Robert J. Dandridge

Honors Theses

In the summer of 1950, after the seriousness of the Korean conflict had become evident, a special committee appointed three years earlier by the Executive Committee of the Board of Trustees was reactivated for the purpose of considering "the feasibility of applying for a Reserve Office Training Corps unit" for the University of Richmond. This special committee, called the ROTC Committee, after thorough study, rendered a unanimous recommendation to the Board that a unit of Army ROTC be applied for. The application was completed and mailed to the Department of the Army. Approval of the application was not long in …

A Study Of Lommel Functions, Robert Glenn Mayo

Masters Theses

No abstract provided.

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.

The Approximation Of Eigenvalues And Eigenfunctions Of Convolution Kernels, Adelbert Lee Roark

Mathematics & Statistics ETDs

No abstract provided.

Lattice Topologies, Alan A. Bishop

Masters Theses

No abstract provided.

A Theorem On Repeating Decimals, William G. Leavitt

Department of Mathematics: Faculty Publications

It is well known that a real number is rational if and only if its decimal expansion is a repeating decimal. For example, 2/7 = .285714285714 . . . . Many students also know that if n/m is a rational number reduced to lowest terms (that is, n and m relatively prime), then the number of repeated digits (we call this the length of period) depends only on m. Thus all fractions with denominator 7 have length of period 6. A sharp-eyed student may also notice that when the period (that is, the repeating digits) for 2/7 is split …

A Study Of Cotorsion Groups, Arlo D. Davis

Masters Theses

No abstract provided.

Completion And Compactification Functors For Cauchy Spaces, James Francis Ramaley

Mathematics & Statistics ETDs

The subject of this thesis is topological but the approach is categorical. We consider the approach as important as the subject itself and so we try to indicate whenever we have a categorically defined concept. In fact, we are led by this approach to make definitions and constructions so that certain relationships are categorical in nature. Our coreflective completion functor of Chapter IV is one example of this approach.

We wish here to give a brief outline of the historical develop­ment of convergence theory and how category theory has come to play a role in this development...

Convergence Relations On Universal Algebras., Allan Matlock Weber Carstens

Mathematics & Statistics ETDs

In this paper we derive some first results on convergence algebras, which are universal algebras with a convergence structure. The first concept was defined some time ago and a unified study of it is available in [4]. Convergence functions were first defined in [7] and have been studied in further works by Kent and others. Kent also investigated the results of imposing a convergence structure on an algebraic structure, in the special case of convergence groups [8]. Our results on loops and quasigroups extend some of his.

Convergence Rates For The Law Of The Iterated Logarithm And For Probabilities Of Moderate Deviations., James Avery Davis

Mathematics & Statistics ETDs

Let {Xn:n=1,2,…} be a sequence of independent identically distributed random variables with common distribution function F(x). If {an} is a monotonic increasing sequence and Sn=sigmak=1 n Xk, then under certain conditions

P[ Is n I > a n J or P[ sup I> 1) k > n I 8'J< 8it

A Best Running Test For Symmetry And Distribution Free Tests For Symmetry, David Lloyd Burdick

Mathematics & Statistics ETDs

A sequential test of a statistical hypothesis H₀ versus H₁ is said to be a running test if there is a positive probability that the test will not stop if H₀ is true. Tests of this nature were introduced for testing the Bernoulli case by D. A. Darling and Herbert Robbins [1]; an earlier paper of Roger Farrell [2] deals implicitly with the asymptotic expected sample size of such tests for testing the hypothesis Ѳ = 0 in the parameterized family of generalized density functions h(Ѳ)e^ϴxdµ. Herbert Robbins, in a lecture given at the Sandia …

Linear Coordinate Systems And Statistical Independence And Vector Spaces And Linear Statistical Models, James B. Mcdonald

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The object of this report is an investigation of statistical independence and linear coordinate systems. It is hoped that this report will give some background for an ultimate investigation of independence and non­linear coordinate systems using tensor analysis.

An additional basic objective is to obtain explicit algebraic expressions for different types of linear trans- formations.

The first concepts to be covered are arbitrary linear transformations, various ways of looking at linear transformations, and the effects of a linear transformation on a vector of normally distributed random variables.

Next orthogonal transformations to independence, and then oblique transformations to independence will be …

Topics In Semigroups, Merlin Ray Jenson

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The semigroup theories of fundamental importance were discovered in 1928 with the publication of a paper by A. K. Suschkewitsch. The paper is included in the only book published prior to 1961 dealing primarily with the algebraic theory of semigroups. The book written by the above author and published in 1937 is entitles "The Theory of Generalized Groups."

Since 1940 the number of papers on semigroups has increased to approximately 30 per year. Thus we find ourselves in the midst of a new and expanding area of mathematics. Our interest centers around the structure of semigroups and their representation by …

An Exposition On Bayesian Inference, John Laffoon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Bayesian approach to probability and statistics is described, a brief history of Bayesianism is related, differences between Bayesian and Frequentist schools of statistics are defined, protential applications are investigated, and a literature survey is presented in the form of a machine-sort card file.

Bayesian thought is increasing in favor among statisticians because of its ability to attack problems that are unassailable from the Frequentist approach. It should become more popular among practitioners because of the flexibility it allows experimenters and the ease with which prior knowledge can be combined with experimental data.

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 …

A New Family Of Partially Balanced Incomplete Block Designs With Some Latin Square Design Properties, Dale M. Mesner

Department of Mathematics: Faculty Publications

An extensive family of two-class PBIB designs is defined in Section 1and given the title of NL designs. Several analogies of NL designs with Latin square type designs are discussed in Sections 1 and 2. Some of these designs have already appeared in scattered contexts. Section 3 gives a construction based on finite geometry for an infinite class of XL designs, and others can be constructed by methods to be taken up elsewhere. An extension to designs with more than two associate classes is indicated in Section 4.

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 …

On Reduction Of Order Of A System Of Linear Nonhomogeneous Ordinary Differential Equations, Otis D. Shouse

Masters Theses

No abstract provided.

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 …

Tolerance Regions For A Joint Exponential Distribution, Lee J. Bain

Mathematics and Statistics Faculty Research & Creative Works

The evaluation of the reliability of a system of components, when the components are assumed to follow a joint exponential distribution, is considered. The approach used is to develop tolerance regions for the joint exponential distribution or to estimate the probability content of the appropriate specification region. Copyright © 1968 by The Institute of Electrical and Electronics Engineers, Inc.