Physical Sciences and Mathematics Commons^™

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 …

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

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

Masters Theses

No abstract provided.

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 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 …

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.

An Investigation Of The Range Of A Boolean Function, Norman H. Eggert, Jr.

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this section is to define a boolean algebra and to determine some of the important properties of it.

A boolean algebra is a set B with two binary operations, join and meet, denoted by + and juxtaposition respectively, and a unary operation, complementation, denoted by ', which satisfy the following axioms:

(1) for all a,b ∑ B (that is, for all a,b elements of B) a + b = b + a and a b = b a, (the commutative laws),

(2) for all a,b,c ∑ B, a + b c =(a + b) (a + b) …

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 …

Anti-Associative Systems, Dick R. Rogers

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A set of elements with a binary operation is called a system, or, more explicitly, a mathematical system. [2] The following discussion will involve systems with only one operation. This operation will be denoted by "⋅" and will sometimes be referred to as a product.

An Investigation Of The Properties Of Join Geometry, Louis John Giegerich Jr.

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper presents a proof that the classical geometry as stated by Karol Borsuk [1] follows from the join geometry of Walter Prenowitz [2].

The approach taken is to assume the axioms of Prenowitz. Using these as the foundation, the theory of join geometry is then developed to include such ideas as 'convex set', 'linear set', the important concept of 'dimension', and finally the relation of 'betweenness'. The development is in the form of definitions with the important extensions given in the form of theorems.

With a firm foundation of theorems in the join geometry, the axioms of classical geometry …

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 …

Stochastic Processes And Models In Textile Research., J. Sudarshan Rao Dr.

Doctoral Theses

This thesis is concerned with the application of the theory of stationary stochastic processes and of stochastic models to some important theoretical problems of textile technology. We shall study in this work these problems in detail using the theory of stationary stochastic processes and give a satisfactory explanation of the phenomenon of "drafting waves."

Convolution Properties Of Distributions On Topological Groups., S. R. S. Varadhan Dr.

Doctoral Theses

The collection of probability distributions on the real line which is a semigroup under the convolution operation and topological space under weak convergence has attracted, during the last quarter of a century, the attention of such great mathematicians as Khintchine, Kolmogorov, Bawly, Levy and others. Their results constitute a deep analysis of the factorization problems on the one hand and the asymptotic behavior of infinite convolutions on the other. However, a complete and systematic investigation of these problems is not available in considerable generality. The aim of the present thesis is to investigate the topological and algebraic properties and the …

On Compactness And Related Concepts, Willard Robert Boland

Dissertations, Theses, and Masters Projects

No abstract provided.

On Convolution Of Arithmetic Functions, Nathaniel Riddick Withers

Dissertations, Theses, and Masters Projects

No abstract provided.

A Stochastic Model For Programming The Supply Of A Strategic Material, Herman Karreman

About Harlan D. Mills

No abstract provided.

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 …

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.

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.

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

Masters Theses

No abstract provided.

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 …

Distribution Theory Of Some Classification Statistics., S. John Dr.

Doctoral Theses

This thesis eives the distri bution theory of four clae aifioation statistics. Sone parta of it were published a few years ago. The relevant publicationa are listed nt the end.What the author knows of related work by other authors is set out in the Introductions little material of this nature is given elsewhere in the theats. If a result is not explicitly credited to another author, it may be taken to nean that the author believes it to be hia worik.It will be noticed that three (U, R and 2) of the four statistics receive less a pace than the …

A Random Walk Production-Inventory Policy: Rationale And Implementation, Daniel Orr

About Harlan D. Mills

No abstract provided.

Some Problems Of Ergodic Theory And Information Theory., K. R. Parthasarathy Dr.

Doctoral Theses

The subject of ergodic theory which is the mathematical outgrowth of the gas problem in statistical machines and the subject of information theory which in the mathematical outgrowth of the problem of information transmission through communication channels have many interesting dual features. In ergodic theory we study collectively and individually the measure preserving transformations of a first measure space, where as in information theory we do the same with the set of all measured in variant under a fixed measurable transformation of a measurable space. The object of this thesis it to study some of the dual relations between the …

Some Problems Of Estimation In Sampling From Finite Populations., M. Murthy Dr.

Doctoral Theses

In this thesis the results of the research work done by the author in the field of sample surveys are presented. Scheme problems of estimation in sampling from finite populations were taken up for reset arch. A brief summary of this thesis is given below.In chapter 1, the author has developed a generalized theory of getting unbiased estimator for a certain class of parameters in sampling from finite population. The class of parameters considered are those which can be expressed as the sum of single-valued set functions defined over a class of sets of units belonging to a finite population. …

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).

Some Contributions To The Theory Of Sampling., Pramod Kumar Pathak Dr.

Doctoral Theses

The work Presented here had originated from a pioneering paper by Basu1 and is essentially an extension of his ideas to different problem in sample surveys. The whole word mainly consists in deriving estimators uniformly better than those usually adopted in with replacement schemes.in with replacement sampling schemes, the 'order-statistic' (distinct sample unite arranged in an ascending order of their unit-indices) forms a sufficient statistic. Therefore, if any estimator (e.g., say of the population man) does not depend on the 'order-statistic', it can be uniformly improved by the use of the Rao-blalckwell theorem. The author has not hesitated to use …

On The Estimation Of Parameters When The Observations Are Subject To Measurement Error, Paul D. Minton, Vanamamalai Seshadri

Journal of the Graduate Research Center

Maximum likelihood estimation of parameters is considered in the situation where a measurement x is taken to mean "x + d." The maximum likelihood estimator for the parameter of the exponential distribution is found for this case and compared with the usual estimator.

A Geometrically Characterized Reference Frame For The Study Of Cartan Hypersurfaces In N-Dimensional Projective Space, W. Dale Maness

Journal of the Graduate Research Center

In the projective differential geometry of ordinary space a problem of fundamental importance is that of obtaining a covariantly determined reference frame for the definition of local point coordinates and associated power series developments for the equations of curves and surfaces. Much of the celebrated memoir [1] of G. M. Green was devoted to this problem for a surface or 2-dimensional Cartan variety. However, the complete geometric characterization of the reference frame used by Green was not completed until sixteen years later by Bell [2]. In this paper, an extension of Green's "relation R" is given for a linear (n-2)-space …