Digital Commons Network^™

Generation Of Random Numbers, Keith H. Eberhard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Subroutines are written to generate random numbers on the computer. Depending on the subroutine used, the generated random numbers follow the uniform, binomial, normal, chi-square, t, F, or gamma distribution. Each subroutine is tested using the chi-square goodness of fit test to verify that the random numbers generated by each subroutine follow the statistical distribution for which it is written. The interpretation of the test results indicates that each subroutine generates random numbers which closely approximates the theoretical distribution for which it is designed.

The approach used in the subroutine which generates gamma distributed random numbers involves the use of …

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 …

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 …

On Semigroups Of Functions On Topological Spaces, Troy L. Hicks, A. G. (Glen) Haddock

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

The Eigenvalue Set Of A Class Of Equimodular Matrices, Gerald L. Bradley

CMC Faculty Publications and Research

The paper is divided into four sections, the first of which is basically introductory and contains definitions, notational conventions, and well-known results. The second section contains a fundamental theorem on multilinear polynomials which forms the crux of all our mail results, and the final two sections are devoted to discussions of the combinatorial and boundary properties of Y(A), respectively.

Manifold Phenomena In The Theory Of Polyhedra, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Exact Test For Simple Correlation In Analysis Of Dispersion, James E. Dunn

Journal of the Arkansas Academy of Science

No abstract provided.

Characterizing Topologies By Continuous Selfmaps, Derald David Rothmann

Doctoral Dissertations

"Various topological spaces are examined in an effort to describe topological spaces from a knowledge of their class of continuous selfmaps or their class of autohomeomorphisms. Relationships between topologies and their continuous selfmaps are considered. Several examples of topological spaces are given and their corresponding classes of continuous selfmaps are described completely. The problem, given a set X and a topology U when does there exist a topology V either weaker or stronger than U such that the class of continuous selfmaps of (X,V) contains the class of continuous selfmaps of (X,U), is considered. M* and S** spaces are defined …

Statistical Inferences For Location And Scale Parameter Distributions, Robert Henry Dumonceaux

Doctoral Dissertations

"The problem of discriminating between two location and scale parameter distributions is investigated. A general test based on a ratio of likelihoods is presented. A test based on a Pearson Goodness of Fit statistic is also considered. Tables are given for discriminating between the normal and exponential, the normal and double exponential, the normal and extreme value, and also between the normal and logistic. For location and scale parameter distributions, two-sided tolerance limits are shown to always be obtainable by Monte Carlo simulation. A method for obtaining confidence intervals on the reliability at a fixed time t is also given. …

Statistical Inferences For The Generalized Gamma Distribution, Harold Walter Hager

Doctoral Dissertations

"Procedures for handling statistical problems with nuisance parameters are considered with special reference to problems in the three parameter generalized gamma distribution. Maximum likelihood estimation of the parameters of this density has been investigated. Properties of these estimates are established which make it possible to make inferences about the parameters. Discrimination between various models for life testing problems is discussed and the robustness of the Weibull model is advanced. The question of the existence of the maximum likelihood estimates of the parameters for all samples is raised. Empiric evidence is presented indicating that they may not exist for all small …

Statistical Inferences For The Cauchy Distribution Based On Maximum Likelihood Estimators, Gerald Nicholas Haas

Doctoral Dissertations

"Various estimators of the location and scale parameters in the Cauchy distribution are investigated, and the superiority of the maximum likelihood estimators is established. Tables based on maximum likelihood estimators are presented for use in making statistical inferences for the Cauchy distribution. Those areas considered include confidence intervals, tests of hypothesis, power of the tests, and tolerance intervals. Both one- and two-sample problems are considered. Tables for testing the hypothesis of whether a sample came from a normal distribution or a Cauchy distribution are presented. The problems encountered in finding maximum likelihood estimators for the Cauchy parameters are discussed, and …

Formally Real Fields, Gail L. Carns

Mathematics & Statistics ETDs

This paper is concerned with the analysis of the set of orders on a formally real field using category and sheaf theory as tools. We topologize the set of orders in a way similar to that used in the prime spectrum of algebraic geometry and define a presheaf of groups using the notion of inverse limits. We then find necessary and sufficient conditions that these presheaves be sheaves. Next we notice that if F ⊆ Fⁱ respectively, fields, θ and θⁱ are the set of orders on F and Fⁱ respectively, and Γ and Γⁱ are …

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.

A Study Of A Graphical Valued Function Associated With An Extension Of Graphs, Douglas W. Nance

Masters Theses

No abstract provided.

Extensions Of The Sigma And Tau Functions, Meredith Woods Potter

Masters Theses

No abstract provided.

A Category Of Banach Spaces, Kenneth Leroy Pothoven

Masters Theses

No abstract provided.

Functional Relationships For Fredholm Integral Equations Arising From Pseudo-Transport Problems., Richard Crenshaw Allen Jr.

Mathematics & Statistics ETDs

In this dissertation we consider a class of integral equations of the general form

Ψ(z)=g(z) + ∫_y^x Y(z’)K(|z-z’|) Ψ(z’)dz’

Where K has an integral representation of the type

K(u)= ∫₀^∞ k(s’)e^-a(s’)uds’

With this integral equation, we associate the pseudo transport problem

(sgn s) ∂/∂z N(z,s) + a(s)N(z,s) = k(s)Y(z) ∫_-∞^∞ N(z,s’)ds’,

Y< =z< =x, |s| < ∞

with certain boundary conditions. (Equation (2) is a generalization or the equation for particle transport in a slab geometry). Equivalence between the problems (1) and (2) is established. Thus any results concerning the problem (2) produce corresponding results concerning the …

Propositions Equivalent To The Continuum Hypothesis, Bernard L. Bohl

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

Two sets A and B are said to have the same power if there exists a one-to-one correspondence between them. All sets which have the same power as the natural numbers are called countable and have power N₀. All sets which have the same power as the real numbers are said to have the power of the continuum will be denoted by 2^N₀, since 2^N₀ can be shown to be equal to c as will be indicated in the preliminary results.

Given an element a of a well-ordered set B, the set of …

Measure Theory And Lebesgue Integration, Evan S. Brossard

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

The Lebesgue integral is a generalization of the Riemann integral which extends the collection of functions which are integrable.

Lebesgue integration differs from Riemann integration in the way the approximations to the integral are taken. Riemann approximations use step functions which have a constant value on any given interval of the domain corres­ponding to some partition. Lebesgue approximations use what are called simple functions which, like the step functions, take on only a finite number of values. However, these values are not necessarily taken on by the function on intervals of the domain, but rather on arbitrary subsets of the …

Principal Component Factor Analysis, Herbert H. Jolliff

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

Factor analysis came into being around 1900 in the field f psychology to explain theories of human ability. Several methods of factor analysis exist; but according to Harman (1967) principal component factor analysis is unique in the mathematical sense, therefore, quite often the preferred method. The centroid method is computationally easier, and it gives close approximations to the principal component method on some data sets. An example of this is shown in Appendixes B and F by comparison.

Factor analysis is being used in many fields. A few of the fields are sociology, meteorology, political science, medicine, geography, business, economics, …

Computer Analysis Of Consumer Attitude And Consumption Data For Fluid Milk Products, James Reed Fisher

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

The American public, with a per capita disposable income currently at an all time high, has become a source of vital concern to dairy market researchers. The unique socio-economic structure of the present generation causes the dairy industry to be concerned with how the consumer view its products. Effective education and advertising programs must be developed to attract the taste and meet the demands of the consumer.

Two factors which greatly influence market research and advertising programs are the attitude of the consumer toward a given product and the relationship of attitude to the degree of actual milk consumption. To …

Tests Of Methods That Control Round-Off Error, Dale M. Rasmuson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Methods of controlling round-off error in one-step methods in the numerical solution of ordinary differential equations are compared. A new Algorithm called theoretical cumulative rounding is formulated. Round-off error bounds are obtained for single precision, and theoretical cumulative rounding. Limits of these bounds are obtained as the step length approaches zero. It is shown that the limit of the bound on the round-off error is unbounded for single precision and double precision, is constant for theoretical partial double precision, and is zero for theoretical cumulative rounding.

The limits of round-off bounds are not obtainable in actual practice. The round-off error …

Reliability And Maintainability Sampling Procedures For Life Cycle Cost Evaluation, Doyle H. Harris

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The intent of this thesis is to investigate, develop, and apply techniques to determine the reliability and maintainability of populations of items. These techniques are to be used in determining the total life-time operating costs of the populations so that those items with the lowest life-time costs can be bought. To do this, the author has explored current techniques for determining compliance to some minimum required Mean Time Between Failure (MTBF) in what is referred to as a Phase I testing. After the requirements of Phase I testing have been met, testing may be continued at the option of the …

Algebraic Properties Of Endomorphisms Of Abelian Groups And Rings, Johnnie George Slagle

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The main objective of the thesis was to extend the definition of an M-Group to what is called an M-Ring. From this extension a system called an expanded ring follows naturally. To facilitate the development of the expanded ring, chapter I is devoted to developing properties on systems that are not quite rings where many interesting examples are constructed. In chapter II the definition of an M-Ring is given and some of its properties are derived. In chapter III some of the properties of expanded rings are proved, and examples of expanded rings are given to show their existence.

The Fundamental Groups Of The Complements Of Some Solid Horned Spheres, Norman William Riebe

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the methods used for the construction of the classical Alexander horned sphere leads naturally to generalization to horned spheres of higher order. Let M₂, denote the Alexander horned sphere. This is a 2-horned sphere of order 2. Denote by M₃ and M₄, two 2-horned spheres of orders 3 and 4, respectively, constructed by such a generalization.

The fundamental groups of the complements of M₂, M₃, and M₄ are derived, and representations of these groups onto the Alternating Group, A₅, are found. The form of the presentations …

A Proof Of Newton's Power Sum Formulas, J. A. Eidswick

Department of Mathematics: Faculty Publications

For a polynomial P(z) = α₀ + α₁z + ... + α_nzⁿ = α_n (z – z₁) (z – z₂) ... (z – z_n), the power sums S_m = ∑ ⁿ _k=1 z^m _k, m = 1, 2, ... , can be calculated from the formulas ...

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, …

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 …

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 …