Mathematics Commons^™

Heuristic Algorithms For The Generalized Vehicle Dispatch Problem, Leland Ray Miller

Doctoral Dissertations

"A heuristic algorithm, called the sweep algorithm, is developed for the vehicle dispatch problem with distance and load constraints for each vehicle. A mathematical development and a step procedure for the sweep algorithm is given. Also given are eight problems and their solutions derived by the sweep algorithm. The solutions for this algorithm are compared with solutions from other vehicle dispatch algorithms, and the sweep algorithm is found to give better results for almost every problem. Various modifications are also presented for the sweep algorithm. A mathematical formulation is given for the vehicle dispatch problem with arbitrary cost functions at …

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 …

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

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Manifold Phenomena In The Theory Of Polyhedra, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

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 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 …

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

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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 …

Tolerance Regions For A Joint Exponential Distribution, Lee J. Bain

Mathematics and Statistics Faculty Research & Creative Works

The evaluation of the reliability of a system of components, when the components are assumed to follow a joint exponential distribution, is considered. The approach used is to develop tolerance regions for the joint exponential distribution or to estimate the probability content of the appropriate specification region. Copyright © 1968 by The Institute of Electrical and Electronics Engineers, Inc.

Handlos And Baron Model: Short Contact Times, J. Patel, Robert M. Wellek

Chemical and Biochemical Engineering Faculty Research & Creative Works

No abstract provided.

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

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 …

A Study On Estimating Parameters Restricted By Linear Inequalities, William Lawrence May

Masters Theses

“A comparison of two methods for estimating parameters restricted by linear inequalities in linear statistical models was made.

The first method consisted of finding the least squares estimates of the parameters disregarding the restrictions, and then forcing those parameters that were outside of their allowable ranges to the nearest endpoints of those ranges.

The second method made use of quadratic programming to minimize the same sum of squares that the first method minimized while keeping the parameters inside or at the endpoints of their allowable ranges.

The quadratic programming gave better estimates of the parameters in the sense that the …

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 A Method For Selecting The Best Of Two Or More Mathematical Models, August J. Garver

Masters Theses

"A method for selecting the best in some sense of two or more mathematical models is investigated in this study. The method is that of using part of the data to estimate parameters and using the resulting equation to predict the additional data which are then compared with the existing data not used in estimating the parameters. In particular the effects produced on the method by the number and location of points used in estimating the parameters and the criterion for determining the best fit are investigated. It was concluded from the results of an empirical investigation that the success …

On A Numerical Solution Of Dirichlet Type Problems With Singularity On The Boundary., Randall Loran Yoakum

Masters Theses

No abstract provided.

A Numerical Study Of Van Der Pol's Nonlinear Differential Equation For Various Values Of The Parameter E., Charles C. Limbaugh

Masters Theses

"This paper briefly reviews the geometric concepts associated with nonlinear differential equations and then proceeds to a study of the homogeneous van der Pol equation. After studying the method of Kryloff and Bogoliuboff for small values of the parameter €, the author makes a numerical study of the equation using Hamrning's Method for the numerical solution. Several trajectories and the phase plane are shown for E = 0.1, 1.0, and 5.0. The author then studies one of the analytic theories, i.e., the method of Cartwright and Littlewood, and indicates some of the other analyses for large €"--Abstract, p. ii

A Study Of Methods For Estimating Parameters In Rational Polynomial Models, Thomas B. Baird

Masters Theses

“The use of rational polynomials for approximating surfaces is investigated in this study. In particular, methods for estimating parameters for a rational polynomial model were investigated.

A method is presented for finding initial estimates of the parameters. Two iterative methods are discussed for improving those estimates in an attempt to minimize the sum of the squares of the residuals. These two methods are (1) Scarborough’s Method for applying the theory of least squares to nonlinear models and (2) the Method of Steepest Descent.

Data from two functions were chosen and approximated as illustrations. Each set of data was used two …

Stability Properties Of Various Predictor Corrector Methods For Solving Ordinary Differential Equations Numerically., Charles Edward. Leslie

Masters Theses

No abstract provided.

A Study Of Methods For Determining Confidence Intervals For The Mean Of A Normal Distribution With Unknown Varience By Comparison Of Average Lengths, Karl Richard Kneile

Masters Theses

“The purpose of this thesis is to briefly review various properties which may be desirable for a system of confidence intervals; and to empirically determine whether the system of confidence intervals obtained from the Student’s t distribution will produce shorter average lengths than those obtained by other methods which may be used. It was concluded from the results of an empirical investigation that there was no significant difference between the average lengths of confidence intervals obtained from a family of distributions of which the Student’s t is a member"--Abstract, page ii.

Mathematical Techniques In The Solution Of Boundary Value Problems., Vincent Paul Pusateri

Masters Theses

"This study was undertaken to present a summary of mathematical techniques as applied to the solution of boundary value problems in partial differential equations.

The techniques that were presented can be considered to be some of the most popular in applied science.

The salient features of the study are that different techniques can present different analytical expressions for a solution to the same boundary value problem, and from the viewpoint of computation and accuracy one solution may prove more desirable than the other.

The study also indicates that in boundary conditions where finite discontinuities exists, a slight perturbation to remove …

A Numerical Approach To A Sturm-Liouville Type Problem With Variable Coefficients And Its Application To Heat Transfer And Temperature Prediction In The Lower Atmosphere., Troyce Don Jones

Masters Theses

No abstract provided.

An Investigation Of Lehmer's Method For Finding The Roots Of Polynomial Equations Using The Royal-Mcbee Lgp-30, James W. Joiner

Masters Theses

“The solution of the general polynomial equation f (x) = O, where f(x) = a_nxⁿ + a_n-1x^n-1 + … + a₁x = a_o, has received the attention of many mathematicians for hundreds of years and is at present in a very highly developed state. Even a cursory examination of the literature will reveal many volumes on this subject. However, this study is concerned primarily with the numerical methods for solving polynomial equations, hence the classical methods will be treated here only as they contribute to this field.

Virtually all of …

The Spinning Top, Aaron Jefferson Miles

Masters Theses

"Several mathematicians have solved the problems of motion of the top and gyroscope most completely, but none of them have considered in their solutions the effects of the supporting gimbal rings upon the motion or the effects of a variable rotor speed. It is the purpose of this paper to investigate the top equations by two well known methods; namely, by the method of Lagrange and by the method of Jacobi; considering in both the dynamics of the gimbal rings and varying rotor speed"--Introduction, page 3.