Physical Sciences and Mathematics Commons^™

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.

Extensions Of The Sigma And Tau Functions, Meredith Woods Potter

Masters Theses

No abstract provided.

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

Masters Theses

No abstract provided.

A Category Of Banach Spaces, Kenneth Leroy Pothoven

Masters Theses

No abstract provided.

A Class Of Linear Transformations Which Can Be Written As The Product Of Projections, John B. Hawkins, William J. Kammerer

John B. Hawkins

No abstract provided.

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 …

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 …

Plane Protective Geometry, Lana Sue Legrand

Honors Theses

The following study was based on the text A Modern Introduction to Geometries by Annita Tuller, Associate Professor of Mathematics at Hunter College. The study consisted of problem solving at the end of each topic studied. Therefore, this paper contains a brief summary of the topics covered followed by the problems solved with theta respective drawings. No attempted is made to include all of the theorems, axioms, or definitions necessary to solve the problems but page references are given to refer to the text.

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, …

The Development Of The Calculus, Janie Ferguson

Honors Theses

The Greeks made the first step in the inquiry of the infinitely small quantities by an attempt to determine the area of curves. The method of exhaustions they used for this purpose consisted of making the curve a limiting area, to which the circumscribed and inscribed polygons continually approached by increasing the number of their sides. The area obtained was considered to be the area of the curve. The method of integration is somewhat similar, to the extent that it involves finding the limits of sums. Zeno of Elea (c. 450 B.C.) was one of the first to work with …

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, …

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.

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.

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 …

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

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Paul Feyerabend's Telegram, Rudolf Kaehr

Rudolf Kaehr

6-page telegram from Paul Feyerabend (London) to Rolf Kaehr (Westberlin) Telegram 1 I am ill. Please let the seminar continue in my absence. Inform Prof Landmann and Prof Huebner, cancel the hotel reservation and read the following final message to my class on tuesday 1pm: I am sorry that I cannot give what Telegram 2 would have been my last lecture to you. In this lecture I would have elaborated on Verons argument and would have tried to show that it also excludes consience, self expression, identification. Turning back to the empiricist methodology and demand for theoretical unification I would …

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.

Nomography, Scotty Andrews

Honors Theses

No abstract provided.

Groups, Janie Ferguson

Honors Theses

This paper explores abstract algebra groups.

Industrial Mathematicians, Mary Beth Mcgee

Honors Theses

What is an industrial, or professional, mathematician? What does he do? Generally, there are two kinds: workers in pure mathematics and workers in applied math.

The pure mathematician likes to play with mathematical laws and principles just to see what will happen. They have mathematical curiosity; they are not especially interested in whether anyone ever finds any use for the result or not. They have the fun of working their problems, and that is the only reward they ask. There is a large group of men and women getting paid good salaries for having such fun; they are the pure …

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 …

Right Alternative Rings, Irvin Roy Hentzel

Irvin Roy Hentzel

No abstract provided.