Physical Sciences and Mathematics Commons^™

A Survey Of The Applications Of Difference Equations, Roberta Lanice Harkey

Mathematics & Statistics ETDs

In asserting that people in other fields often tend to be afraid to use mathematics, F.K. Mechta, an economist, expressed an uncertainty which contributes to the hesitancy to use mathematics. “Mathematics is tricky, it maintains silence, does its work quietly; and when we do not understand its ways and misinterpret its message, it just smiles. It never loses its temper, never laughs; we can observe a suppressed smile on its lips. Such is mathematics.” It is the purpose of this paper to conduct a brief survey of the applications of difference equations. The use of these equations is often rather …

Embedding A Ring Into A Ring With Identity, Richard F. Maruszewski Jr.

Master's Essays (1922 - )

The presentation of this paper is divided into three sections. The first or these sections is composed of proofs of different ways of embedding rings into rings with identity The material in this section, which constitutes pages 1 - 10 , is quite different from the material in the last two sections. Because of this difference I followed a different method of presentation in the first section. The method used is to present a lecture outline, that is to produce the material just as I would in class. The last two sections ·are presented in a more narrative fashion. In …

Tests Of Independence In Contingency Tables, Su-Feng Wongbhan

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

This report is a survey of the literature for a combination of different tests for both two-way and multi-way tests of independence in contingency tables. The derivation of the commonly used chi-square statistic for the tests will be shown immediately below, then followed by the summary of the different tests which will be the contents of this report.

Reduction And Summarization Of Forage Production Data From Pasture And Range Lands, Julian Leigh Wilkinson Jr.

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

In an attempt to control and properly manage our vast pasture and range lands there have been many problems that the scientist has been confronted with. Among these has been the problem of reducing the great quantity of collected data from the ranges and pasture lands into a form suitable for scientific analysis. In the past this reduction process has been accomplished by slow, painstaking hand calculation methods, thus making it virtually impossible for the scientist to analyze and propose corrective measures at the time they are needed. However, with the advent of high speed computing equipment this need no …

The Development Of The Slide Rule, Robert Bray

Honors Theses

Although the slide rule has been used extensively in business, industry, and science only in recent years, it is not a modern invention. Since the slide rule is a mechanical device whereby the logarithms of numbers may be manipulated, the slide rule of today was made possible over three and one-half centuries ago by John Napier, Baron of Merchiston in Scotland. In 1594, Napier privately communicated his results to Tycho Brake, a Danish astronomer, but did not publicly announce his system of logarithms until 1614. Napier set forth his purpose.

Bayesian Inference, Sing-Chou Wu

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

Bayes' original paper "Essay Towards Solving a Problem in the Doctrine of Change" was published in Philosophical Transactions of the Royal Society, 1763. Over 200 years, Bayes' Concepts have survived numerous critical onslaughts. Even though Bayesian Inference is still regarded as being somewhat unorthodox, it is becoming more generally accepted each year by statisticians and other scientists.

It is the purpose of this paper to provide a bird's-eye view of Bayesian Inference with emphasis on the comparison of Bayesian approaches and conventional approaches. This paper is written for those who have had about one year's background in mathematical statistics.

Some …

A Logistic System Simulation Model Encompassing Poisson Processes And Normal Or Weibull Life, Willard A. Hansen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis describes a computer simulation model for determining effective spares stock levels for recoverable items at Air Force bases and depots. The simulation model is based on the following fundamental inventory theory; whenever a demand arises, it is satisfied from stock on hand, and the quantity equal to that demand is recorded immediately; when a demand exceeds stock on hand, the excess demand is backordered immediately and when item life expires procurement action is initiated at depot level. The resulting product of the model cam be used as a guide for the optimum distribution of available spares or as …

A Density For A Generalized Likelihood-Ratio Test When The Sample Size Is A Random Varible, Raymond H. Neville

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many articles, books, papers, and abstracts have been published, which describe the analysis and design of experiments. R. A. Fisher's (1951) book, The Design of Experiments, is referred to by D. J. Finney (1960) as the classic for experimental designs. Some of the more outstanding books and publications in this area are those by Cochran and Cox (1957), Cox (1958), Davis et al., (1954), Federer (1955). Quenouille (1953). and Kempthorne (1952).

Review Of Reliability Techniques, Eugene Richard Doherty

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In the development of any product to perform a specific function the first concern of the engineer is to design for satisfactory operation. Engineers originally approached the reliability problem by using excessive safety factors to be assured the structure or material would withstand the calculated loads and stresses. The engineer also learned from operating or testing the equipment until failures occurred and then redesigning as mistakes became apparent. These methods were time consuming and often resulted in bulky over designed products. These approaches became impractical with the advent of new technological advancements. The accelerated industrial development of aircraft, missiles, and …

Probable Circular Error (Cep) Of Ballistic Missiles, James Edward Moran Jr.

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The survival of our nation, during a nuclear exchange, depends upon an effective national defense structure. The prime weapon system in this defense structure is the ballistic missile. Although many factors enter into an evaluation of the effectiveness of a ballistic missile, one of the most important measure is accuracy. Without an accurate weapon system we have no weapon system.

The Department of Defense has places emphasis on using a method of accuracy evaluation called "Probably Circular Error (CEP)." Probably Circular Error is defined as "The radius of a circle, centered at the intended target, within which 50% of the …

A Monte Carlo Study Of Non-Linear Regression Theory, Ya-Ming Liu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Multiple regression provides the capability of using non-linear functions to fit various curvilinear surfaces. These non-linear functions are, however, linear in the parameters. Non-linear term of the variables such as X², X³, ln X, X, YX are incorporated in a linear model. For example:

Y = b₀ + b₁ x₁ + b₂ x₁² + b₃ lnx₂ + ϵ

Many practical situations require the fitting of mathematical functions which are non-linear in the parameters and perhaps the variables. For example:

Y = b, e^b₂X + ϵ

Intuitionist Logic, Dennis R. Ferman

Electronic Theses & Dissertations

This thesis deals with the somewhat controversial topic of Intuitionist logic and mathematics. Since the writer's objective in this case is to explain this theory, the point of view expressed herein will tend toward that of the intuitionist's, with emphasis given to the positive aspects of the theory.

For those who might wonder whether the material covered in this thesis is really logic, mathematical philosophy, or foundations of mathematics; there is no exact answer. These three concepts tend to be artificial since the boundaries between them, if any, are rather vague. The writer does feel though, that this material should …

Equivalence Classes Of Fundamental Sequences Of Rational Numbers, M. Marlene Greatens

Master's Essays (1922 - )

No abstract provided.

On The Solution To Partial Differential Equations By Means Of Bergman's Integral Operator, George R. Young

Dissertations, Theses, and Masters Projects

No abstract provided.

Fourier Transforms In Euclidean K Space, Terry A. Straeter

Dissertations, Theses, and Masters Projects

No abstract provided.

Comparative Definitions Of The Derivative, Richard Francis Barry

Dissertations, Theses, and Masters Projects

No abstract provided.

On The Inversion Of A Hilbert Type Matrix, William Trench, Perry Scheinok

William F. Trench

We consider the inversion of finite and infinite matrices related to Hilbert matrices.

On The Univalence Of A Certain Integral, Wimberly C. Royster

Mathematics Faculty Publications

No abstract provided.

Rounding Errors In Algebraic Processes, J. H. Wilkinson

The Harlan D. Mills Collection

No abstract provided.

Decision Problems, Lowell Anderson

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

From an intuitive point of view the notion of effective procedure consists of a set of rules or instructions that enables one, in a finite number of steps and in a purely mechanical way, to answer yes or no to any one of a given class of questions. This procedure requires no intelligence to carry out the instructions and, in fact, it is con­ceivable that some mechanical contrivance may be constructed to carry out these instructions. Should such an effective procedure exist, that answers either yes or no, then the group of problems in question is said to be effectively …

Axiomatic Set Theory, Ronald P. Smit

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

An analysis of the well known paradoxes found in intuitive set theory has led to the reconstruction of set theory by axiomatic means. This exposition is devoted to Zermelo-Fraenkel set theory with some changes made by Suppes.

The first order predicate calculus is presupposed. In addition to the usual quantifiers admitted, a unique existential quantifier is used. The primitive notions of the set theory are the empty set and the two place membership predicate.

Fredholm Solution Of Linear Integral Equations, Dewey F. Furness

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

An integral equation of the form

ζ(x) - λ∫ K(x, s) ζ(s) ds = f(x) a ≤ x ≤ b

is called a Fredholm equation. By the method of successive approximations a solution can be obtained if the parameter λ is sufficiently small. If the kernel, K (x, s), is degenerate then a solution can be obtained by reducing it to a system of linear algebraic equations. In the general case the kernel is represented as an infinite Fourier Series. With this representation the solution is obtained by combining the two methods mentioned. The solution is the solution of two …

Laplace, Finite Fourier Sine And Cosine, Transformations, Jan Eugene Wynn

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

The Laplace and finite Fourier sine transforms can be used to solve certain boundary value problems. Also the Laplace transform is a useful took in solving some integral and integrodifferential equations. This report is composed of transform solutions of seventeen such applied problems, while the author's first report is focused towards the theoretical aspect of these transforms.

Several different types of problems are solved in this report. Among these are Bessel's classical differential equation of index n, two electrical circuit problems, a beam problem, a vibrating string problem, a heat flow problem, and a temperature gradient problem.

One of the …

Error Structure Of Randomized Design Under Background Correlation With A Missing Value, Tseng-Chi Chang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The analysis of variance technique is probably the most popular statistical technique used for testing hypotheses and estimating parameters. Eisenhart (12) presents two classes of problems solvable by the analysis of variance and the assumption underlying each class. Cochran (9) lists the assumptions and also discusses the consequences when these assumptions are not met. It is evident that if all the assumptions are not satisfied, the confidence placed in any result obtained in this manner is adversly affected to varying degrees according to the extent of the violation.

Barypact Topological Spaces, Bradley Y. Maughan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Recently, Kimber [3] has discovered a general class of topological spaces, the members of which are termed barypact spaces, that includes the compact topological spaces. This class is distinct from the set of all compact topological spaces, but its members possess many of the useful properties associates with compactness. As a consequence, several standard compactness theorems become special cases of corresponding theorems in a more general setting and the techniques of proof applied to these extensions provide new, and sometimes remarkably simple, proofs of the very theorems they generalize. The purpose of this paper is to extend to this …

Boolean Space, Tzeng-Hsiang Sun

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

M. H. A. Stone showed in 1937 and subsequently that many interesting and important results of general topology involve latices and Boolean rings. This type of result forms the substance of this thesis.

Theorem 4, page 11, states that for any r ≠ 0 in a Boolean ring, there exists a homomorphism h into I₂ , (the field of integers modulo 2), such that h(r) = 1.

Theorem 3, page 6, states that any subring of a characteristic ring of a Boolean space X is the whole ring if it has the two points property (that is, given x, …

The Space Of Minimal Prime Ideals Of A Commutative Ring, Melvin Henriksen, Meyer Jerison

All HMC Faculty Publications and Research

The present paper is devoted to the space of minimal prime ideals of a more-or-less arbitrary commutative ring. Rings C(X) of continuous functions on topological spaces X appear only in §5 where they serve largely to provide significant examples.

On The Recovery Of Linear Group Information In One And Two Way Designs., K. R. Shah Dr.

Doctoral Theses

This thesis is being submitted to the Indian Statistical Insti tute in support of the authors application for the degree of Doctor of Philosophy. The thesis embodies research oarried out by the author during the period 1960-1963 under the supervision of Dr. J. Roy, Professor of Statistics at the Indian Statistical Institute, Calcutta.Some aspects of recovery of inter-group information are exmined in this thesis, The main results are concermed with the variance of the combined inter and int r-block estimntors in incomplete block designs , recovery of inter-row and inter-column information in two-wy designs laid out in row9 and columns, …

Genetic Studies Of The Andhra Pradesh Population., Krishna Rao Dronamraju Dr.

Doctoral Theses

An understanding of the social structure and nating systene of a population 1s essential for genetie investigat lons. The inhabitanta of the coastal districts of Andhra Pradesh are of special intereat to a population genetieist because of the high rate of inbreeding that is practiced there. This population 1s specially suited for evaluating the genetic effects of inbreeding on the progeny of consanguineous parents. In most populations of the world the Inbreeding levels are much lover than in Andhra Pradesh and vhere they are slightly higher, as in some Japanese islande, the populat iona are cmprised of only a fev …

Mathematics For Management, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.