Digital Commons Network^™

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.

A Study Of The Use Of Laboratory Methods To Promote Student Discovery In Tenth-Grade Geometry, Russell Franklin Hein

Dissertations and Theses @ UNI

In recent years there has been a trend toward the use of discovery methods in the teaching of mathematics. This trend has been especially noticeable in the teaching of geometry since this subject deals with various plane and solid figures which contain many relationships for the students to discover. There has also been increased interest in the use of audio-visual materials for the presentation of geometric topics. This has been particularly evident in the use of models for solid or three-dimensional geometry. The use of such models has not only enabled the students to more readily grasp the desired relationships …

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

Mathematics Faculty Publications

No abstract provided.

Rings With A Not Necessarily Transitive Order Relation, Lawrence Arnold Machtinger

Retrospective Theses and Dissertations

The main objective of this paper is the study of rings with a relation which has all the properties of an order relation on a ring except, perhaps, for one: transitivity. Consequently, many of the results presented here are generalizations of well-known facts about transitively ordered rings; and most, but not all, of the conclusions of this paper are applicable to such rings.

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 …

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 …

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 …

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.

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 …

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.

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.

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 …

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, …

A Note On The Parameters Of Pbib Association Schemes, Dale M. Mesner

Department of Mathematics: Faculty Publications

In an m-class partially balanced incomplete block (PBIB) design [3], any two distinct treatments are related as first, second, . . . ,or mth associates in accordance with certain rules, and the resulting classification of pairs of treatments is called an association scheme [1], [4]. Parameters, including v, n_i, pⁱ_jk, which depend only on the association relation between treatments and are common to all designs having a given association scheme, are called association scheme parameters. Other parameters, including b, r, k, λ_i, depend, in addition, on the arrangement of the treatments …

Minimal Projective Extensions Of Compact Spaces, Melvin Henriksen, Meyer Jerison

All HMC Faculty Publications and Research

A compact space E is called projective if for each mapping ψ of E into a compact space X, and each continuous mapping τ of a compact space Y onto X, there is a continuous mapping φ of E into Y such that ψ = τ o φ.

Modules Over Commutative Rings, William G. Leavitt

Department of Mathematics: Faculty Publications

The following is another short proof of the fact that for a commutative ring with unit R, any finitely based R-module is "dimensional" in the sense that all of its bases have the same number of elements.

THEOREM. Let R be a commutative ring with unit. If M is a unitary R-module with a basis of n elements, then all bases of M contain exactly n elements.

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 …

Variation Of Human Stature In India., N. T. Mathew Dr.

Doctoral Theses

This is the first investigation on a large-sc le (1,47,066 measurements) of human stature in India based on deta from all pers of the country. Work done hitherto has been on much smaller serics which can in no way be considered representative of the country as a whole. In the present study certain inte- resting ond inportant results have been obtained which we shall now summarise. lany of the comparisons between meaningful groups involve smell differences which would require falrly large samples to establish with statistical signific- ance. This consideration will apply not only to stature but to other hody …

On The Optimal Search Problem, Wallace E. Franck Jr.

Mathematics & Statistics ETDs

Suppose a searcher is at a given point on a line and wishes to locate an object which is known to be somewhere on the line. Suppose further that there is a probabilistic law which governs the location of the object on the line. The searcher can only locate the object by traveling to the point where it is. He desires to formulate a search plan which will minimize the average distance traveled before locating the object. The only initial choice he has is as to which direction to go. Then he must decide how far to go before turning …

A Development Of The Number System, Janet R. Olsen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper is based on Landau's book "Foundations of Analysis" which constitutes a development of the number system founded on the Peano axioms for natural numbers.

Simulation Of Mathematical Models In Genetic Analysis, Dinesh Govindal Patel

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In recent years a new field of statistics has become of importance in many branches of experimental science. This is the Monte Carlo Method, so called because it is based on simulation of stochastic processes. By stochastic process, it is meant some possible physical process in the real world that has some random or stochastic element in its structure. This is the subject which may appropriately be called the dynamic part of statistics or the statistics of "change," in contrast with the static statistical problems which have so far been the more systematically studied. Many obvious examples of such processes …

A Property Of The Mean Stieltjes Integral, J. A. Dyer

Journal of the Graduate Research Center

The purpose of this note is to consider the following problem. Suppose [a,b] is an interval, f a function in [a,b] and g a function which has a derivative in [a,b].

Experimental Design Models, J. Leroy Folks

Journal of the Graduate Research Center

If we were to assume a linear relationship between x and y described by the model y = a + βx + e it is unlikely that we would consider writing the model as y = a + bx + cx + e. It is even more unlikely that we would apply the least squares principle by minimizing Σe2 with respect to a, b, and c. Yet a similar thing happens in experimental design. In fact, it is common practice to use less than full-rank models where the parameters are not defined and, in cases where they are defined, to …

Some Information - Theoretical And Empirical Techniques In Statistical Inference, Chaitanya Swarup

Mathematics & Statistics ETDs

This study is divided into two seemingly disjoint parts -- one containing EMPIRICAL (Bayesian and Non-Bayesian) approach and the second containing INFORMATION-THEORETICAL techniques in problems of statistical estimation and tests of hypotheses. But in the end, both approaches have been brought together for solving ENCODING problems of COMMUNICATION THEORY to unify the whole dissertation.

Averages Of Continuous Functions On Countable Spaces, Melvin Henriksen, John R. Isbell

All HMC Faculty Publications and Research

Let X = {x1, x2, ...} be a countably infinite topological space; then the space C*(X) of all bounded real-valued continuous functions f may be regarded as a space of sequences (f(x1), f(x2), ...). It is well known [7, p. 54] that no regular (Toeplitz) matrix can sum all bounded sequences. On the other hand, if (x1, x2, ...) converges in X (to x_m), then every regular matrix sums all f in C*(X) (to f(x_m)).

The main result of this paper is that if a regular matrix sums all f in C*(X) then it sums f …

A Parameter Perturbation Procedure For Obtaining A Solution To Systems Of Nonlinear Equations., James Carlton Helm

Masters Theses

"For simultaneous nonlinear equations the convergence of the known functional iterative procedures is dependent upon a good initial approximation to the desired roots. In this paper the restriction on the choice of the initial approximation has been circumvented by dividing each problem into a number of subsidiary problems in accordance with a parameter perturbation procedure. The study presents a discussion of the algorithm and the conditions for convergence. The discussion, also, includes the problems which were solved using the parameter perturbation procedure"--Abstract, p. ii

A Study Of Stability Of Numerical Solution For Parabolic Partial Differential Equations., Tsang-Chi Huang

Masters Theses

"Parabolic partial differential equations hold a very important position in science and technology since they are encountered frequently in the solution of diffusion and heat-conduction problems. Theoretically, it is possible to solve many of these equations by analytical methods, but the modern development of mathematics has revealed that there are numerous difficulties in obtaining the solution. Numerical solutions for most applied problems of a parabolic partial differential equation type are practically necessary, thus methods for numerical solution or approximate solution became more important. Since numerical results are required for most applied problems of a parabolic partial differential equation type a …

Minimization Of Boolean Functions., Don Laroy Rogier

Masters Theses

"A systematic computational procedure is presented for simplifying a Boolean function. The procedure is an extension of the methods presented by W. V. Quine and E. J. McCluskey. Jr. Specific attention is given to the combined use of linear programming and dominance arguments to find a minimum sum of products for large cyclic prime implicant tables"--Abstract, p. ii