Applied Mathematics Commons^™

A Study Of Certain Conservative Sets For Parameters In The Linear Statistical Model, Roger Alan Chapin

Masters Theses

"In the case of the linear statistical model, it has been shown that under certain conditions the confidence intervals obtained by considering the parameters one at a time are conservative when used as a joint confidence region, using the product of confidences as the confidence. However, nothing had been known of how conservative they are. This research provides accurate estimates of the true confidence for these cases.

Also, it has not yet been proved that they are indeed conservative for all cases. It is thought that they are, and the results of this research support this conjecture"--Abstract, page ii.

How To Measure The Capacity Of Farm Dams, G Gauntlett

Journal of the Department of Agriculture, Western Australia, Series 4

AT some time or another nearly every farmer needs to be able to measure the capacity of an ordinary farm dam of the "excavated earth tank" type and many requests are made for a method of calculating this volume.

This article describes how this can be done.

Latent Class Analysis And Information Retrieval, George Loyd Jensen

Masters Theses

"Information retrieval may be defined roughly as a procedure to either locate or physically retrieve a document or documents containing information on a given topic with a high degree of reliability. Information retrieval is one of the newest fields in computing science. Being so new there are many unexplored areas. The research that has been done has not been standardized beyond the point of the effort which has been slanted toward solving the "Library Problem" ... Several different information retrieval methods have been suggested and some research done on them to try and solve the "Library Problem". Of these methods …

Comparison Of Methods To Select A Probability Model, Howard Lyndal Colburn

Masters Theses

"A comparison is made between the estimates of the parameters in a gamma distribution obtained by the method of moments with those obtained by a numerical approximation to the maximum likelihood estimates. The estimates obtained by the numerical approximation had a smaller mean squared error from the true value than the estimates obtained by the method of moments. Modifications to tests of fit are made in order to develop methods to select a distribution from a set of possible distributions for a population with an unknown distribution. These selection methods are compared in their ability to make correct selections. Although …

Linear And Quadratic Programming With More Than One Objective Function, William John Lodholz

Masters Theses

"A computational procedure is presented for determining optimal solutions to the linear and quadratic programming problem when there is more than one objective function subject to linear constraints. In general a unique solution does not exist and a set of "best" or "efficient" points is determined and presented in graphical or tabular form. To solve the mathematical programming problems the simplex method is used for linear objective functions and Wolfe's method is used for quadratic objective functions"--Abstract, page ii.

Tschebyscheff Fitting With Polynomials And Nonlinear Functions, George F. Luffel

Masters Theses

"It is the purpose of this study to survey the properties of the Tschebyscheff polynomials with particular reference to how they are employed as approximants and interpolants. The survey is extended to include the process known as "Tschebyscheff Approximation" or "Tschebyscheff Fitting" of a function by functions other than polynomials. One such fitting technique which will be of particular interest in this study is that of fitting f(x) by the function ab^x + c where a, b, c are real and b ≠ 1. In addition to a survey of the properties of the Tschebyscheff polynomials and of Tschebyscheff …

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.

A Method To Give The Best Linear Combination Of Order Statistics To Estimate The Mean Of Any Symmetric Population, Robert M. Smith

Masters Theses

“This paper gives a distribution for the ratio of two non-independent normally distributed random variables. The random variables involved are jointly distributed as the bivariate normal with means zero and variance- covariance matrix V.

The sample mean and one-half the sum of the smallest and largest sample observations from the symmetrically truncated Cauchy density function are compared as estimates of the mean of this density function. The reason for this comparison is to determine which of these two estimators gives the best estimate of the mean.

A method to empirically determine the best linear combination of order statistics for any …

The Effect Of Matrix Condition In The Solution Of A System Of Linear Algebraic Equations., Herbert R. Alcorn

Masters Theses

"The solution of a system of linear non-homogeneous equations may contain errors which originate from many sources. A system of linear equations in which small changes in the coefficients cause large changes in the solution is unstable and the coefficient matrix is ill- conditioned .

The purpose of this study is to define several measures of matrix condition and to test them by correlation with a measure of the actual errors introduced into a system of equations.

The study indicates that three of the five measures of condition tested were reliable indices of the magnitude of error to expect in …

Estimation And Tabulation Of Bias Coefficients For Regression Analysis In Incompletely Specified Linear Models., Harry Kerry Edwards

Masters Theses

"There is often some uncertainty as to the exact number of predictors to include in the specification of the linear model when the theory of regression analysis is applied to specific data. To aid the experimenter in defining the correct number of predictors, a bias function that estimates the deviation of a linear model from the true model has been defined.

The writer has derived an accurate, economical, numerical method for calculating the bias function associated with an incompletely specified linear model and has tabulated bias function coefficients for a reasonable number of doubtful predictors"--Abstract, page ii.

A Study Of Methods For Estimating Parameters In The Model Y(T) = A₁E-P₁T + A₂E-P₂T + Ε, Gerald Nicholas Haas

Masters Theses

“In this study, methods for estimating the unknown parameters A₁, A₂, p₁, and p₂ in the model
y(t) = A₁e^-p₁t + A₂e^-p₁t + ϵ
where ϵ ~ N(0, σ) are investigated. In the model investigated, A₁, A₂, p₁, and p₂ are positive.

Four methods, one non-iterative method and three iterative methods, for estimating parameters in this model are investigated. The non-iterative method is known as Prony's Method. The three iterative methods are (1) the Modified Gauss …

Some Properties Of Certain Sets Of Coprime Integers, Roger C. Entringer

Mathematics & Statistics ETDs

The set P(n) of all primes equal to or less than n has the obvious property that it contains exactly one multiple of each prime equal to or less than n. We use this partial description of P(n) as a basis for the following

Definition 1.1. An increasing sequence {a₁,...,a_k} of integers greater than 1 is a coprime chain if it contains exactly one multiple of each prime equal to or less than a_k.

Convergence Functions And Their Related Topologies, Darrell C. Kent

Mathematics & Statistics ETDs

A convergence function is a correspondence between the filters on a given set S and the subsets of S which specifies which filters converge to which points of S. This concept is defined to include types of convergence which are more general than that defined by specifying a topology on S. Thus a convergence function may be regarded as a generalization of a topology.

Topological Groups, Nicolas Anthony Thireos

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A topological group is an abstract group which is also a topological space and in which the group operation are continuous. In group theory the algebraic binary operation of passage to a limit is studied in a similar manner. The two fundamental mathematical concepts of binary operation and passage to a limit are united and interrelated in the concept of topological group.

The concept of topological groups arose from the study of continuous transformations. However, topological groups can be studied quite independently from continuous transformations and the latter can be presented as applications of topological groups. The first person to …

Investigation Of The Properties Of The Iterations Of A Homeomorphism On A Metric Space, Murray B. Peterson, Jr.

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Considerable study has been made concerning the properties of the iterations of a homeomorphism on a metric space. Much of this material is scattered throughout the literature and understood solely by a specialist. The main object of this paper is to put into readable form proofs of theorems found in G.T. Whyburn's "Analytic Topology" pertaining to this topic in topology. Properties of the decomposition space of point-orbits induced by the iterations of a homeomorphism will compose a major part of the study. Some theorems will be established through series of lemmas required to fill in much of the detail lacking …

Investigation Of Measures Of Ill-Conditioning, Thomas D. Calton

Masters Theses

“The object of investigation in this study is that of ill-conditioning in the solution of a system of linear equations. Ill-conditioning arises when the solution is very sensitive to small changes in the coefficients of the unknowns.

A study is made in this paper of the various proposed measures of ill-conditioning for the purpose of finding the most practical method or measure for determining whether a system is ill-conditioned.

The problem of near-singular or ill-conditioned systems is of great importance in the solution of linear systems because of the extensive use made of them in practical situations. Solution of a …

A Modified Algorithm For Henrici's Solution Of Y' ' = F (X,Y), Frank Garnett Walters

Masters Theses

"The purpose of the present study is to discuss the boundary value problems leading to equations exemplified by the four equations previously mentioned and to write a program for an I.B.M. computer in Fortran II language as a contribution to the numerical solution of an important class of linear and nonlinear differential equations"--Introduction, page 4.

On The Initial Value Problem For The Quasi-Linear Parabolic Partial Differential Equation, Henry Hermes

Mathematics & Statistics ETDs

In this paper we consider second order parabolic partial differential equations on the infinite strip. We confine our attention to the quasi-linear equations, and in particular, the problem

(0-1) u͙(t,x) = f(u)u_xx(t.x) , (t,x) ε(0,T)x(-∞,∞) ≡ D_{T, T>0}

u(0,x) = u₀(x) , x ε (-∞,∞).

Existence, uniqueness and properties of the solution are discussed. These results can be immediately generalized to problems where the differential equation is of the form u͙(t,x) = f(t,x,u)u _xx(t,x).

Select On Fleece Weight And Cull The Low Producers, W L. Mcgarry

Journal of the Department of Agriculture, Western Australia, Series 4

EFFICIENT calling of maiden ewes before they join the breeding flock is an essential part of any policy of flock improvement.

Removal of the low wool producers should be one of the first considerations when culling the flock.

A Generalization Of The Rayleigh Distribution, Ruth H. Lemon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This papers is divided into numbered sections. The equations are numbered anew in each section, and equation numbers are always enclosed in parentheses. Merely the equation number is given when referring to an equation in the same section as the references; otherwise the section number is prefixed. Thus equation (4) refers to the fourth equation of the same section as the reference, and equation (2.2) refers to the second equation of the second section.

A Numerical Treatment Of One-Dimensional Non-Steady Compressible Flows, Paul J. Kazek

Mathematics & Statistics ETDs

The problem that will be considered here will be the flow in a cylinder filled with a homogeneous ideal gas, bounded on one end by a vacuum and/or a rigid wall with the motion initiated by a piston on the other end. First, the basic Lagrangian differential equations will be derived along with other necessary thermodynamical relations. A scheme of difference equations will be presented and the viscosity term discussed as well as a method for insuring stability of the difference equations during the calculations

A Statistical Technique For Predicting A Two Dimensional Vector With Application, Richard E. Vogel

Mathematics & Statistics ETDs

The problem of multiple regression analysis where the dependent and independent variables are components of a two dimensional vector is discussed, and a complete statistical development of the solution of estimators for the parameters in the model given. The theory regarding predictions and confidence statements about such predictions is also developed. A computer code was written for the IBM 704 computer which solves the above problem and a description of the code appears in the appendix.

The statistical model was applied to a meteorological problem in wind forecasting at the Eniwetok Proving Ground, and prediction equations were developed and evaluated.

Facts And Figures For The Man On The Land, J A. Mallett

Journal of the Department of Agriculture, Western Australia, Series 4

FARM or station life calls for the exercise of so many different skills that the farmer or pastoralist is usually an accomplished handyman.

For those whose schooldays are far behind them however, the most difficult part of many tasks is that of dealing with the calculations involved, and it is hoped that these facts and figures will serve as a handy aid to those whose mathematical ability has not kept pace with their manual and technical skill.

Studies On The Sampling Methodology Of Peas For Yield And Quality, Pratapsinha Chintamani Pendse

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Pea¹ growers have much at stake in getting high yields of peas of prime quality. The income accruing from a pea crop grown for processors is determined by the yield as well as quality. Therefore the farmers' efforts are directed toward growing such a crop.

Research workers are interested in knowing the yield of peas with known tenderometer values which will indicate the quality of peas. Present methods of field harvesting are costly and time consuming which tend to limit the number of varieties that can be satisfactorily evaluated for trial.

A comparison of sampling techniques with present harvesting …

Beta And Gamma Distributions, Calvin Rogers

Mathematics & Statistics ETDs

The purpose of this paper is to exhibit the main properties of Gamma and Beta distributions and show their relation to certain well known distributions.

In chapter II the Gamma and Beta distributions are defined in terms of Gamma and Beta functions. The moments of these distributions are calculated, and the moment generating function and cumulant generating function for the Gamma distribution are obtained. The curves are classified with respect to parameter values and the curves are graphically illustrated in Figures 1, 2, and 3. The exponential distribution, as a special case of interest, is shown to be a Gamma …

The Use Of Kamke's Transformation In Approximating The Zeros Of Orthogonal Polynomials, Robert L. Daniels

Mathematics & Statistics ETDs

The importance of the classical orthogonal polynomials has long been acknowledged. It has not been possible, however, to represent them in such a way that all of their important properties are immediately evident. In particular, the location of the zeros of these polynomials is of considerable interest.

This thesis is primarily concerned with a different technique in which Kamke's transformation is applied to the differential equations frequently used to define these polynomials. The resulting trigonometric differential equations cannot be explicitly solved either, but certain characteristics of these solutions facilitate the derivation of approximations to the zeroes of the solutions.

The Numerical Treatment Of A Simple Hydrodynamical Shock By The Von Neumann-Richtmyer Method, Charles F. Sprague Iii

Mathematics & Statistics ETDs

When the differential equations describing the flow of compressible fluids are derived under the assumptions that (1) forces in the fluid are due only to variations in pressure and (2) that the entropy of any volume element remains constant, it can be shown mathematically that these differential equations cannot have continuous solutions under all circumstances. If we adopt the notion of “shock discontinuities” in these solutions, the differential equations describing the flow in continuous regions together with conditions expressing the laws of conservation across the discontinuities suffice to completely determine the flow. An alternative procedure is to use a method, …

Algebraic Relations For Property-Composition Curves Of Binary Mixtures, Louis Frank

Journal of the Arkansas Academy of Science

No abstract provided.

Estimates Of Error In Numerical Integration, Dorothy M. Hoover

Journal of the Arkansas Academy of Science

No abstract provided.