Digital Commons Network^™

Lattice-Ordered Rings And Function Rings, Melvin Henriksen, John R. Isbell

All HMC Faculty Publications and Research

This paper treats the structure of those lattice-ordered rings which are subdirect sums of totally ordered rings -- the f-rings of Birkhoff and Pierce [4]. Broadly, it splits into two parts, concerned respectively with identical equations and with ideal structure; but there is an important overlap at the beginning.

On The Structure Of A Class Of Archimedean Lattice-Ordered Algebras, Melvin Henriksen, D. G. Johnson

All HMC Faculty Publications and Research

By a Φ-algebra A, we mean an Archimedean lattice-ordered algebra over the real field R which has an identity element 1 that is a weak order unit. The Φ-algebras constitute the class of the title. It is shown that every ф-algebra is isomorphic to an algebra of continuous functions on a compact space X into the two-point compactification of the real line R, each of which is real-valued on an (open) everywhere dense subset of X. Under more restrictive assumptions on A, ropresentations of this sort have long been known. An (incomplete) history of them …

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 Uniform Right Ideals Of A Ring Of Matrices, Gerald Joseph Janusz

Bachelors’ Theses

The concept of uniform right ideals plays an important part in the structure tbeory of prime rings and semi-prime rings as developed by Goldie in [1] and (=[2]. Very few examples of uniform right ideals appear in the literature, however. In section one, we obtain the form of these right ideals in a matrix ring, I_n, where I is a right Ore domain with identity. The existence of the identity involves some loss of generality, but greatly simplifies the approach used in this paper.

Pfaffian Differential Expressions And Equations, K. Raman Unni

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

It is needless to point out the necessity and the importance of the study of Pfaffian differential expressions and equations. While it is interesting to consider from the pure mathematical point of view, their applications in many branches of applied mathematics are well known. To mention a few, one may observe that they arise in connection with line integrals (example, determination of work). They provide a more rational formulation of the foundations of thermodynamics as developed by the Greek mathematician Caratheodory. They also arise in the problem of determining the orthogonal trajectories. In many branches of engineering and other physical …

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 Determination Of The Earth's Gravity Field In Spheroidal Coordinates, M. Spencer Hamilton Jr.

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The earth's gravity field G * at a point P in the region surrounding the earth's surface is defined as the force acting on a unit mass concentrated at P. This is a force resulting from two components: (1) G₁ due to the gravitational attraction of the earth's mass, and (2) G₂ due to the earth's rotation.

As a result of Newton's law of gravitation, G₁ can be written in integral form as follows:

G₁ = k ( (_V ( rdm/r³

where r = PQ, r = |r|, Q is a point which ranges …

A Note On Hausdorff Separation, Edwin Halfar

Department of Mathematics: Faculty Publications

The examples usually given as instances of topological spaces that have T₁-separation but not T₂-separation (Hausdorff) also have the property that some compact subset is not closed. This with the classic result concerning closedness of compact subsets of a Hausdorff space suggests the question of the equivalence of Hausdorff separation and the condition that the class of compact subsets be a subclass of the class of the closed subsets of a given space. The following is a simple result of this type and may be of some use in an introductory course in point set topology. …

The Estimation Of Parameters In Regression Functions Subject To Certain Restraints, Paul D. Minton, Alfred E. Crofts Jr.

Journal of the Graduate Research Center

We consider two types of problems in maximum likelihood estimation of parameters of linear functions subject to certain restraints. One is a family of lines with equal slopes or intercepts; the other is a pair of lines constrained to meet at a predetermined point. In the case of normally distributed errors with equal variances within each set, the solutions are identical with least squares solutions. In addition to linear functions, non-linear functions which are transformable to linearity may be treated under these methods.

A Formula For A Class Of Steady State Solutions, Don E. Edmondson

Journal of the Graduate Research Center

An integral representation formula is developed to cope with the problem of determining and studying the steady state solutions of a class of differential equations. The class of differential equations studied is y' + yf = g, where f and g are continuous functions admitting period T > 0. The formula then defines a function admitting period T and serves to allow an analysis of the differential equation above. Theorem I delineates some of the properties of the function and Theorem II provides answers to the steady state questions. An application is made to a capacitance circuit problem.

Some Applications Of The Weierstrass Mean Value Theorem, V. F. Cowling, Wimberly C. Royster

Mathematics Faculty Publications

No abstract provided.

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.

Coefficient Problems For Functions Regular In An Ellipse, Wimberly C. Royster

Mathematics Faculty Publications

No abstract provided.

Four Dimensional Graphs Of Complex Functions, Malcom Lee Murrill

Master's Theses

Complex functions of a single complex variable involve four unknowns, two independent and two dependent variables, and thus cannot be adequately represented in two- or three- dimensional space. Various geometric constructions in both two and three dimensions have been devised in the past, however, in attempts to illuminate complex function theory. The standard and most useful, of these representations is that developed by Gauss and Riemann employing two complex planes simultanesously. These show the correspondence between a particular curve or region in the object plane and its image, as mapped by a given transformation, in the image plane.

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 …

On Linear Associative Algebras Corresponding To Association Schemes Of Partially Balanced Designs, R. C. Bose, Dale M. Mesner

Department of Mathematics: Faculty Publications

Given v objects 1, 2, .. , v, a relation satisfying the following conditions is said to be an association scheme with m classes:
(a) Any two objects are either 1st, or 2nd, . . ,or mth associates, the relation of association being symmetrical, i.e., if the object α is the ith associate of the object β, then β is the ith associate of α.
(b) Each object a has n_i ith associates, the number n_i being independent of α.
(c) If any two objects α and β are ith associates, then …

Linear Programming In High School Mathematics, Vernon Earl Cotter

Dissertations and Theses @ UNI

"Modern mathematics," a term associated with experimental and revised programs for the teaching of mathematics, should be interpreted only in part as meaning new subject matter. It is true that modern mathematics is associated with such subject matter as the theory of sets and the revision of the definitions of 'relation' and 'function.' But it also connotes a new spirit, a new method of approach, and a new organization of material and problems. Also it may retain much of the traditional subject matter. Of course the order of presentation may be changed and traditional subject matter bounds may be disregarded …

On A Theorem Of Hölder, Donald W. Miller

Department of Mathematics: Faculty Publications

A well-known result, due to Hölder [1], is the following: The symmetric group S_n, has outer automorphisms if and only if n = 6. The classical proof of the existence of a class of outer automorphisms of S₆, as formulated by Burnside [2], rests in part on the theory of primitive groups and entails extensive computation. In this note we offer a direct method for constructing such automorphisms. The author is grateful to Professor R. H. Bruck for raising this problem and for subsequent helpful remarks.

Some Properties Of Compactifications, Melvin Henriksen, John R. Isbell

All HMC Faculty Publications and Research

A compactification of a topological space X is a compact (Hausdorff) space containing a dense subspace homeomorphic with X. Since only completely regular spaces have compactifications, all spaces mentioned here will be completely regular unless the contrary is assumed explicitly. This paper is a study of properties of the sets of points which may be added to a space in compactifying it.

Applications Of Eighth Grade Mathematics To The Ninth Grade General Shop Program In Iowa, Robert Vern Echelbarger

Dissertations and Theses @ UNI

As a student engages in the construction of a project in an industrial arts class, it is necessary for him to learn the uses of tools and materials. The extent of his learning is reflected in part by the tangible evidence of the completed project and increased skill in the mastery of tools. Just as a student must learn the uses of tools and materials, so must he learn the use of intangible tools such as mathematics, reading, writing, and speech. The mastery of these intangible tools is important for the general education of the student . Mathematics plays an …

A Comparative Study Of Two Approaches To The Teaching Of Area In The Junior High School, Margaret Patricia Green

Dissertations and Theses @ UNI

It was the purpose of this study to compare the amount of information learned and retained by the students through two approaches to teaching the topic of Area. One approach followed the material presented in a seventh grade arithmetic book; the other followed the material presented in a unit especially constructed for this experiment. The investigation was directed toward the question: Was there a difference between the two teaching methods as measured by the amount of information learned and retained by the students participating in this experiment?

A Proposal For Emphasizing Modern Mathematics In Elementary Algebra, Betty Sayre Grubb

Dissertations and Theses @ UNI

For the past fifty years educators and mathematicians have urged that we change our approach to mathematics. The need for change or modernization of teaching mathematics is at least as great now as it ever was. The body of mathematical content vital to the pursuit of both pure and applied mathematics is growing continually. At the same time the demand for people trained in mathematics, including its newer developments, is growing. The only solution would appear to be the integration of these new ideas, as extensively as possible by each teacher, into all levels of training in mathematics. This thesis …

Local Connectedness In The Stone-Cech Compactification, Melvin Henriksen, John R. Isbell

All HMC Faculty Publications and Research

This is a study of when and where the Stone-Čech compactification of a completely regular space may be locally connected. As to when, Banaschewski [1] has given strong necessary conditions for βX to be locally connected, and Wallace [19] has given necessary and sufficient conditions in case X is normal. We show below that Banaschewski's necessary conditions are also sufficient and may be restated as follows: βX is locally connected if and only if X is locally connected and pseudo-compact (Corollary 2.5). Moreover, the requirement that βX be locally connected is so strong that it implies that every completely regular …

Some Remarks On A Paper Of Aronszajn And Panitchpakdi, Melvin Henriksen

All HMC Faculty Publications and Research

In the paper of the title [1], a number of problems are posed. Negative solutions of two of them (Problems 2 and 3) are derived in a straightforward way from a paper of L. Gillman and the present author [2]. Motivation will not be supplied since it is given amply in [1], but enough definitions are given to keep the presentation reasonably self contained.

On Minimal Completely Regular Spaces Associated With A Given Ring Of Continuous Functions, Melvin Henriksen

All HMC Faculty Publications and Research

Let C(X) denote the ring of all continuous real-valued functions on a completely regular space X. If X and Y are completely regular spaces such that one is dense in the other, say X is dense in Y, and every f ε C(X) has a (unique) extension f E C(Y), then C(X) and C(Y) are said to be strictly isomorphic. In a recent paper [2], L. J. Heider asks if it is possible to associate with the completely regular space X a dense subspace μX minimal with respect to the property that C(μX) and C(X) are strictly isomorphic.

A Study In Predicting Success In Algebra, Leslie Milton Graham

Dissertations and Theses @ UNI

Students of Manson High School at Manson, Iowa, select either algebra or general mathematics, subject to the approval of the principal. Some of the students' achievement records are incomplete, thus handicapping the principal in guiding the students to make their choices. As a result, several students have chosen to try algebra and have failed, and sometimes they have become discouraged and have left high school. It occurred to the writer that, if a predicting device could be established to show the student his chances in mathematics, it possibly could spare the pupil's failing in algebra.

A Comparison Of The Accuracy Of Finite Difference Methods And Variational Methods In The Numerical Solution Of Partial Differential Equations, Robert F. Brodsky

Mathematics & Statistics ETDs

The purpose of this thesis is to investigate some of the numerical methods available to solve partial differential equations intractable to analytic solutions with a view towards: 1. Indicating where particular methods appear most applicable, from the standpoints of accuracy, easy of solution, minimum expenditure of effort; and 2. Indicating the accuracy to be expected in the use of two of the more powerful methods investigated as applied to a problem of elasticity.

On The Equivalence Of The Ring, Lattice, And Semigroup Of Continuous Functions, Melvin Henriksen

All HMC Faculty Publications and Research

A large number of papers have been published that are devoted to showing that certain algebraic objects obtained by defining operations on the set of all continuous real-valued functions on a suitably restricted topological space determine the space. We mention but a few of them in this article.

A Historical Survey Of Methods Of Solving Cubic Equations, Minna Burgess Connor

Master's Theses

It has been said that the labor-saving devices ot this modern age have been made possible by the untiring efforts of lazy men. While working with cubic equations, solving them according to the standard methods appearing in modern text-books on the theory of equations, it became apparent, that in many cases, the finding of solutions was a long and tedious process involving numerical calculations into which numerous errors could creep. Confessing to laziness, and having been told at an impressionable age that "any fool can do it the hard way but it takes a genius to find the easy …