Applied Mathematics Commons^™

A Survey Of The Applications Of Difference Equations, Roberta Lanice Harkey

Mathematics & Statistics ETDs

In asserting that people in other fields often tend to be afraid to use mathematics, F.K. Mechta, an economist, expressed an uncertainty which contributes to the hesitancy to use mathematics. “Mathematics is tricky, it maintains silence, does its work quietly; and when we do not understand its ways and misinterpret its message, it just smiles. It never loses its temper, never laughs; we can observe a suppressed smile on its lips. Such is mathematics.” It is the purpose of this paper to conduct a brief survey of the applications of difference equations. The use of these equations is often rather …

Reduction And Summarization Of Forage Production Data From Pasture And Range Lands, Julian Leigh Wilkinson Jr.

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

In an attempt to control and properly manage our vast pasture and range lands there have been many problems that the scientist has been confronted with. Among these has been the problem of reducing the great quantity of collected data from the ranges and pasture lands into a form suitable for scientific analysis. In the past this reduction process has been accomplished by slow, painstaking hand calculation methods, thus making it virtually impossible for the scientist to analyze and propose corrective measures at the time they are needed. However, with the advent of high speed computing equipment this need no …

Bayesian Inference, Sing-Chou Wu

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

Bayes' original paper "Essay Towards Solving a Problem in the Doctrine of Change" was published in Philosophical Transactions of the Royal Society, 1763. Over 200 years, Bayes' Concepts have survived numerous critical onslaughts. Even though Bayesian Inference is still regarded as being somewhat unorthodox, it is becoming more generally accepted each year by statisticians and other scientists.

It is the purpose of this paper to provide a bird's-eye view of Bayesian Inference with emphasis on the comparison of Bayesian approaches and conventional approaches. This paper is written for those who have had about one year's background in mathematical statistics.

Some …

A Logistic System Simulation Model Encompassing Poisson Processes And Normal Or Weibull Life, Willard A. Hansen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis describes a computer simulation model for determining effective spares stock levels for recoverable items at Air Force bases and depots. The simulation model is based on the following fundamental inventory theory; whenever a demand arises, it is satisfied from stock on hand, and the quantity equal to that demand is recorded immediately; when a demand exceeds stock on hand, the excess demand is backordered immediately and when item life expires procurement action is initiated at depot level. The resulting product of the model cam be used as a guide for the optimum distribution of available spares or as …

Tests Of Independence In Contingency Tables, Su-Feng Wongbhan

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

This report is a survey of the literature for a combination of different tests for both two-way and multi-way tests of independence in contingency tables. The derivation of the commonly used chi-square statistic for the tests will be shown immediately below, then followed by the summary of the different tests which will be the contents of this report.

Review Of Reliability Techniques, Eugene Richard Doherty

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In the development of any product to perform a specific function the first concern of the engineer is to design for satisfactory operation. Engineers originally approached the reliability problem by using excessive safety factors to be assured the structure or material would withstand the calculated loads and stresses. The engineer also learned from operating or testing the equipment until failures occurred and then redesigning as mistakes became apparent. These methods were time consuming and often resulted in bulky over designed products. These approaches became impractical with the advent of new technological advancements. The accelerated industrial development of aircraft, missiles, and …

Degeneration Of The Solutions Of Certain Well Posed Systems Of Partial Differential Equations Depending On A Small Parameter, Larry Bobisud

Mathematics & Statistics ETDs

Let be a system of N partial differential equations, where α is a multi­index, p is a positive number, the B_α are N x N matrices of constants, A(ϵ) is an N X N diagonal matrix with N-m ϵ's followed by m ones (1 ≤ m ≤ N-1), and For each ϵ > 0 V_ϵ is to satisfy V(0, x) = f(x). Under sufficiently strong assumptions on (1), this problem can be solved for each sufficiently small ϵ > 0 provided f has a sufficient number of L₁ and continuous derivatives. Let M₁ denote the upper left (N …

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, …

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 …

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 …

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.

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 …

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).

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.

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, …

Estimates For The Zeros Of Ultraspherical Polynomials, Frank B. Correia

Mathematics & Statistics ETDs

In this work an attempt is made to develop a new method for estimating the zeros of the Ultraspherical Polynomials. This method presupposes knowledge of the differential equation that these polynomials satisfy. However the method is applicable to a much wider class of functions since it may also be applied to estimating the zeros of the solutions of any homogeneous linear differential equation of the second order which satisfies certain initial conditions.

The Spieker Circle And Certain Related Configurations, Berthola Elmo Lumzy

Electronic Theses and Dissertations

This thesis, presented to the Department of Mathematics at Xavier University in partial fulfillment of requirements for the degree of Master of Arts in 1952, examines the Spieker circle, a circle inscribed in the median triangle of a given triangle, and extends its defining properties to related geometric configurations. Lumzy first establishes a series of analogies between the Spieker circle and the nine-point circle, demonstrating parallel relationships involving radius, center, harmonic conjugates, and homothetic centers relative to the incenter, median point, and Nagel point of a triangle.

The thesis then proves that the Spieker circle is inscribed in two congruent …

The Variation Problems Of Weierstrass-Bliss And Radon, Douglas M. Gragg

Mathematics & Statistics ETDs

Problems of the Calculus of Variations are generalizations of the familiar minimum problems treated in the differential calculus. The relationships between the ordinary minimum problems of the calculus and the generalizations dealt with in the Calculus of Variations is possibly best seen by examining the general Hilbert-Moore minimum problem, and the special examples of such problems formulated in the table below.

Inverse Problems Of Hamel-Type., Robert G. Schrandt

Mathematics & Statistics ETDs

The formulation and discussion of the simplest (fixed) end point direct problem of the calculus of Variation is a necessary preliminary to attack on the inverse problems considered in Chapters II and III of this thesis. Since the plane problem is already comprehensively treated in the literature, only enough of its theory is developed here to render intelligible to the reader the inverse problems studied in the sequel.

The Darboux Inverse Problem In The Calculus Of Variations, Frank O. Lane

Mathematics & Statistics ETDs

The simplest non-parametric problem of the calculus of variation, the so-called direct problem of the plane, is the problem of finding that arc C_o of a family of admissible arcs y=y (x) joining two fixed pointed (x₁ , y₁ ), (x_1, y₂) in the x,y-plane such that along the C_o the integral takes on a minimum value.

An Investigation Of The Meaning Of Α3 As A Measure Of Skewness, John W. Coy

Mathematics & Statistics ETDs

The purpose of this study is the interpretation of α₃ by means of a relatively simple formula which will predict the amount of shift in the effective limits of the Type III curve for a given change in the skewness. The methods used are chiefly empirical.