Mathematics Commons^™

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.

An Investigation Of The Nature Of The Coefficients Of Entire Function, Marie Ann Philips

Mathematics & Statistics ETDs

The purpose of this study is to investigate the nature of the coefficients of certain power series. In particular, it is desired to know what characteristics the coefficients must possess in order that the series shall represent an entire function.

A Study Of Certain Substitution Groups, Merle Mitchell

Mathematics & Statistics ETDs

This thesis purposes to study a certain group of movements which can be expressed as substitutions. The groups of movements which send a square into itself is to be studied as a group of eight substitutions on the vertices for the purpose of leading up to the real problem of this paper. From the octic group, it is natural to proceed to a study of the movements which send a cube into itself. In particular, it is the aim of this thesis to discover the group of the cube and to analyze some of its properties. There are twenty-eight rotations …

Studies Arising From A Problem In The Calculus Of Variations, John Gonzalez

Mathematics & Statistics ETDs

In mathematics, generalization is progress; so much so that oftentimes one loses sight of the fact that generalization is the result of arduous work in the consideration of the particular. In no other branch of mathematics is this better exemplified than in the Calculus of Variations. The beginning of a systematic development of the theory of the Calculus of Variations really started with the two Bernoulli brothers (1654-1748) in their discussion of the brachistochrone problem in 1696. The method devised by them were sufficiently powerful in the attack of a large number of problems. Euler (1707-85) further elaborated the geometrical …

Upon The Asymptotic Representation Of Certain Entire Functions In Distant Portions Of The Plane, Abraham Franck

Mathematics & Statistics ETDs

The purpose of this paper is to study two particular entire functions which satisfy the conditions set up in a theorem due to Newsom. It is to be hoped that this report may be preliminary to the invention of a method which will lend itself toward the solution of certain general problems.

New Formulae For The Determination Of The Yield Of A Bond, Marvin Roberts

Mathematics & Statistics ETDs

A written contract to pay a certain amount of money on a specified redemption date, and to pay equal periodical dividends, is called a bond from a mathematical standpoint. The principal mentioned in the contract is its face value, or par value. The amount redeemed, or the redemption value, is denoted by C, the dividends by D, and the principal by F. A bond is redeemed at a par if C and F are the same, and at a premium if C is greater than F. The divided rate, or bond rate, is the interest rate named in the bond. …

The Evolution Of The Concept Of Axiom, William Fred Jones

Mathematics & Statistics ETDs

The field of knowledge known as mathematics is composed of the totality of mathematical systems. A mathematical system consists of a body of propositions known as the axioms. The concern of this paper is with the axioms; in fact, with the change which has taken place during the centuries in the ideas of mathematicians about the axioms.

Upon The Asymptotic Representation Of Entire Functions Where The General Coefficient Is The Product Of Two Gamma Functions, James R. Ellis

Mathematics & Statistics ETDs

The essential purpose of this paper is to obtain further information in regard to the asymptotic representation of a power series.

Some Applications Of The Principles Of Isomorphism And Variation To The Teaching Of Geometry, Ralph Mock

Mathematics & Statistics ETDs

In summary, it should be stressed that the numerous examples of this paper are important only in so much as they illustrate the use of the devices and concepts emphasized in the study. It is our premise that plane geometry, as usually taught, does not possess the value which it might have. Certain changes in content as well as in presentation would materially improve the course. This study, then, presents suggestions for improving the ordinary course in two directions. First, by presenting logical propositions from the students' experiences which are partially isomorphic to the theorems of plane geometry, it is …

The Efficiency Of Approximation Formulae For Determining The Rate Of Interest In Amortization Schedules, Wade Ellis

Mathematics & Statistics ETDs

The problem of this study is to determine the relative efficiency of the more important formulae for approximating the rate of interest involved in an amortization plan when the amount of the debt, the amount of the periodic payment, and the number of periods are known. By efficiency this meant the degree of accuracy obtainable, and the time required for solution.

Graphical Representations Of Singular Solutions Of Differential Equations, Kathryn Lois Pitman

Bachelors’ Theses

The first men to detect singular solutions of differential equations were Leibniz, Brook Taylor and Clairaut. The direct method of attack used by each man in attaining these solutions is not known, but a short history of each man and what he has contributed to mathematics can be given. Gottfried Wilhelm von Leibniz (1646-1716) was born in Leipsic, Germany, and was the son of a professor of law in a nearby university. He was well-educated in law himself, expecting to follow in the profession of his father. But not being under the necessity of earning his living, he enrolled at …