Physical Sciences and Mathematics Commons^™

Completeness And Related Topics In A Quasi-Uniform Space, John Warnock Carlson

Doctoral Dissertations

"Completions and a strong completion of a quasi-uniform space are constructed and examined. It is shown that the trivial completion of a T₀ space is T₀ . Examples are given to show that a T₁ space need not have a T₁ strong completion and a T₂ space need not have a T₂ completion. The nontrivial completion constructed is shown to be T₁ if the space is T₁ and the quasi-uniform structure is the Pervin structure. It is shown that a space can be uniformizable and admit a strongly complete quasi-uniform structure and not admit a complete uniform structure. Several counter-examples …

Search Algorithms For The Simple Plant Location Problem, John Bruce Prater

Doctoral Dissertations

"Two algorithms are developed, one exact, one approximate, for finding solutions to the simple plant location problem. Theorems are proved which give sufficient conditions for the inclusion of a plant in the optimal solution. The exact algorithm which is developed is similar to the Branch and Bound method. The approximate technique consists of a directed search through the solution tree for the problem, followed by terminal iterations. The terminal iterations are justified by empirical results obtained from a preliminary version of the technique and a theorem which is proved. Statistics from the results of applying the algorithm to a large …

Characterizations Of Some Functors Of Categories Of Banach Spaces, Kenneth L. Pothoven

Dissertations

No abstract provided.

Analysis Of Heat Transfer In A Two-Layer Circular Cylinder:Constant Flux On Outer Surface And Zero Flux On Inner Surface, Mary Elena Franklin

Mathematics & Statistics ETDs

The one-dimensional time-dependent equation of heat conduction is solved analytically for an infinite two-layer circular cylinder whose core may be either hollow or solid. On the outer surface of the cylinder, which has no heat loss due to convection, a constant heat flux from an external source of heating is applied uniformly. The layers are in perfect thermal contact, and there is no heat loss at their interface. At the smaller radius of the inner layer is a perfect insulator so that the heat flux on the inner surface of the two-layer cylinder is zero. The temperature is uniform initially …

On The Derivative Of Bounded Functions, Wimberly C. Royster

Mathematics Faculty Publications

No abstract provided.

A Combinational Analysis Of Finite Minimal Uniform Covers, Gustavus J. Simmons

Mathematics & Statistics ETDs

No abstract provided.

The Fresnel Integrals, Jean Therese Powers

Master's Essays (1922 - )

In the study of complex analysis, and in particular in the area of complex integration, there arise a series of integrals whose evaluation require more than an thing else, a great deal of mathematical ingenuity. Among these classical integrals are two known as the Fresnel Integrals and it is the purpose of this paper to discuss one method of evaluation of this pair of functions.

On The Theory Of Quaternions, Earle David Smith

All Master's Theses

Ordered triplets serve to describe space geometrically just as ordered pairs serve to describe the plane. A multiplication can be defined on pairs consistent with the complex numbers. However, as this paper will show, one cannot define a multiplication on triplets which is consistent with the complex numbers.

Semi-Groups And A Class Of Singular Perturbation Problems, Andrew Y. Schoene

Mathematics & Statistics ETDs

No abstract provided.

Bayesian Inference For Decision Making, Ming-Yih Kao

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

In recent years, Bayesian inference has become very popular in applied statistics. This study will present the fundamental concept of Bayesian inference and the basic techniques of application to statistical quality control, marketing research, and other related fields.

Stochastic Processes Model And Its Application In Operations Research, Chun Yuan Hsu

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

Just as the probability theory is regarded as the study of mathematical models of random phenomena, the theory of stochastic processes plays an important role in the investigation of random phenomena depending on time. A random phenomenon that arises through a process which is developing in time and controlled by some probability law is called a stochastic process. Thus, stochastic processes can be referred to as the dynamic part of the probability theory. We will now give a formal definition of a stochastic process.

Let T be a set which is called the index set (thought of as time), then, …

Computer Programs For Incomplete Block Designs, Fred Miller

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

In most disciplines where research is involved, there exists an occasional problem of having minimal facilities and/or funds for conducting experiments. This often necessitates the use of designs known as incomplete block designs.

Since the calculations needed to provide an appropriate statistical analysis are somewhat tedious, particularJ..y in the larger designs, it is advantageous to have computer programs to do the necessary calculations.

There are several computer programs at Utah State University written in Fortran II language with Forcom subroutines that perform the analyses for incomplete block designs. These programs, for the most part, were authored by Justus Seely and …

A Study Of The Exponential Distirbutions And Their Applications, Michael Chang-Yu Wang

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

The exponential distribution is a widely known distribution i n statistical theory. It can be regarded as the continuous analogue of the Poisson distribution, discussed by S. D. Poisson in 1837. The Poisson is a limiting form of the Binomial distribution which can be t race d back as early as 1700, discussed by James Bernoulli. A paper by Marsden and Barratt (1911) on the radioactive disintegration of thorium gives a typical frequency distribution which follows the exponential law (8, p. 89). The exponential distribution has achieved importance recently in connection with the theory of stochastic process and has found …

The Beginnings Of Mathematics, Gail Ray

Honors Theses

Our first conceptions of number and form date back to times as far removed as the Old Stone Age. Little progress was made in understanding numerical values and space relations until the transition occurred from the mere gathering of food to its actual production, from hunting and fishing to agriculture. With this fundamental change, a revolution in which the passive attitude of man toward nature turned into an active one, we enter the New Stone Age. The tempo of technical improvement was enormously accelerated.

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 …

Analysis Of Contingency Tables, James Joseph Biundo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two methods of analyzing multi-dimensional frequency data are detailed.

The Second Order Exponential (SOE) model is applicable for dichotomous classifications. The distribution has two sets of parameters, ϴ_i's and ϴ_j's. The ϴ_i's are interpreted as the log of the odds of the marginal probabilities if no two factor relationships exist. Or if all ϴ_ij are not zero, then the ϴ_i's are analogous to a main effect in a 2^m factorial analysis, (m = number of factors or classifications). The ϴ_if's may be interpreted as a measure and direction …

A Concept Of Buoyancy In Topological Spaces, With Applications To The Foundations Of Real Variables, Elwyn David Cutler

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Buoyancy Theorem states that a compact set is buoyant if every point of the compact set has a neighborhood whose intersection with the compact set is buoyant. In this paper, the Buoyancy Theorem is used to prove several standard results involving compact sets. The proof of such a result may be a direct application of the Buoyancy Theorem or the proof may rely on a certain compactness argument which follows from the Buoyancy Theorem. The last application in this paper is such an example.

The method used is to, first of all, define a buoyancy on the compact set; …

An Elementary Proof Of The Prime Number Theorem, James G. Huard

Honors College

No abstract provided.

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 …

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 …

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 …

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

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Paul Feyerabend, Against Method (Typoscript 1969), Rudolf Kaehr

Rudolf Kaehr

Facsimile of Paul Feyerabend's AGAINST METHOD Original typoscript of Against Methods from 1968 with handwritten corrections. Last sentence, p. 116: "We must take care that it does not lose its ability to make such a choice."

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.

A History Of Mathematics Through The Time Of Greek Geometry, Janet Moffett

Honors Theses

The concept of numbers and the process of counting developed long before the time of recorded history. The manner of its development is not known for certain but is largely conjectural. It is presumed that man, even in most primitive times, had some number sense, at least to the extent of recognizing "more" or "less" when objects were added or taken away from a small group. As civilization progressed it became necessary for man to count. He needed to know the number of sheep he owned, the number of people in his tribe, etc. The most logical method was to …

Selections From "Mathematics: Our Great Heritage" Edited By William L. Schaaf, Mary Beth Mcgee

Honors Theses

This paper reviews and summarizes several essays within the text, Mathematics: Our Great Heritage edited by William L. Schaaf.

Mathematical Philosophy, Janie Ferguson

Honors Theses

The purpose of Mathematical Philosophy by Cassius J. Keyser is to delve into some of the more essential and significant relations between mathematics and philosophy. To see this relation, one must gain insight into the nature of mathematics as a distinctive type of thought. The standard of excellence in the quality of thinking to which mathematicians are accustomed is called "logical rigor;" clarity and precision are essentials. The demands of logic, however, cannot be fully satisfied even in mathematics, but it meets the requirements much more nearly than any other discipline. Thus, the amount of mathematical training essential to education …

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 …

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 …

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 …