Digital Commons Network^™

On The Prime Ideals Of The Ring Of Entire Functions, Melvin Henriksen

All HMC Faculty Publications and Research

Let R be the ring of entire functions, and let K be the complex field. In an earlier paper [6], the author investigated the ideal structure of R, particular attention being paid to the maximal ideals. In 1946, Schilling [9, Lemma 5] stated that every prime ideal of R is maximal. Recently, I. Kaplansky pointed out to the author (in conversation) that this statement is false, and constructed a non maximal prime ideal of R (see Theorem 1(a), below). The purpose of the present paper is to investigate these nonmaximal prime ideals and their residue class fields. The author is …

On Rings Of Entire Functions Of Finite Order, Melvin Henriksen

All HMC Faculty Publications and Research

In an earlier paper, the author showed that if M is any maximal ideal of R, the residue class field R/M is isomorphic with the complex field K. In this paper, under some restrictions, this theorem is extended to the ring R_λ of all entire functions of order no greater than λ, and hence to R*.

Convexity And Starlikeness Of Analytic Functions, Wimberly C. Royster

Mathematics Faculty Publications

No abstract provided.

The Solution Of Boundary Value Problems By Use Of The Laplace Transformation As Compared With Classical Methods, Dan W. Stoddard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to present a study of different methods of solving certain boundary value problems. In particular it will be concerned with solutions by classical methods and by operational methods. Of the various operational methods that may be considered, the Laplace transformation appears to be the best⁽¹⁾ and will be used in this paper.

In the 1951 Encyclopedia Americana Annual is this report on the activities in applied mathematics for the previous year:

Progress was made on the general problem of finding the eigenvalues of matrices and systems of differential equations. Considerable effort was also …

What Is A Riemmian Manifold?, Frederick Griffin

Journal of the Arkansas Academy of Science

No abstract provided.

On The Ideal Structure Of The Ring Of Entire Functions, Melvin Henriksen

All HMC Faculty Publications and Research

Let R be the ring of entire functions, and let K be the complex field. The ring R consists of all functions from K to K differentiable everywhere (in the usual sense).

The algebraic structure of the ring of entire functions seems to have been investigated extensively first by O. Helmer [1].

The ideals of R are herein classified as in [2]: an ideal I is called fixed if every function in it vanishes at at least one common point; otherwise, I is called free. The structure of the fixed ideals was determined in [1]. The structure of the …

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 …

A Critical Analysis Of Several Product And Factoring Formulas, Herbert Wills

Masters Theses

No abstract provided.

The Expansion Of A Single-Valued Function Of Several Variables Having For Its Rangeadenumerable Set Of Real Numbers And For Its Domain Of Definitionaset Of Real Numbers, Nicholas Christ Scholomiti

Master's Theses

No abstract provided.

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.

The Diophantine Equation, Frederic C. Barnett

Mathematics & Statistics ETDs

In the first part of Chapter II of this thesis a study is made of these surfaces F_n. In the second part of Chapter II, several differential geometric properties of F_n are adduced, and again, an attack based on certain of these is shown to lead to the very theorem we seek to prove. Finally, we obtain three geometrical implications of the assumption that an integral triad exists on F_n suggesting new lines of attack on the theorem of Fermat.

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 Tangent Surface To A Circular Helix, David Alan Rux

Bachelors’ Theses

The circular helix is a space curve which may be defined as the curve generated by a point on an element of a circular cylinder as the point moves along the element and the element moves around the cylinder, both at a constant rate. The circular helix may also be defined as the curve, on the surface of a circular cylinder, which cuts each element of the cylinder under the same angle.

A Compilation Of Published Research In Elementary Arithmetic Since 1931, Alfred C. Birdsell

Master's Theses or Doctor of Nursing Practice

Many articles are published each year pertaining to elementary arithmetic. Some of these may very properly be designated "mere opinion” while others may very properly be classified as "research". Because of the large number of such articles appearing in print pertaining to some aspect of arithmetic, no doubt a service may be rendered to teachers of the subject by evaluating and classifying them as research or otherwise. From this situation grew the problem of this thesis, the title of which may be stated as follows: A Compilation of Published Research in Elementary Arithmetic Since 1931. Such a guide should be …

Fourier Series And Some Applications, Lawrence D. Marcotte

Master's Theses or Doctor of Nursing Practice

The object of the author in writing this thesis was to make a compilation of material necessary to work certain problems in mathematical physics with one use of Fourier series. Although whole books have been written on different aspects of this thesis, all had some intervening material which was too advanced for the average student. Any students interested in mathematics or physics cannot fail to see the importance of Fourier series. To mention a few applications, the series is used in finding the solution to various problems in heat distribution, electrical transmission, and aircraft construction.

A Test Of Richardson's Equation, Gerald J. Pyne

Bachelors’ Theses

The purpose of this work is the verification of the above relationship between saturated emission current and temperature, and especially, the evaluation of the current-temperature relating constants, A and theta.

Additional Equations For The Wigner_Seitz Model Of Solids, Alex Sharley Keene

Bachelors’ Theses

This report consists of an extension of the Wigner-Seitz equations to particular cases and boundary conditions. These equations are tools whereby energy bands and wave functions for a face centered lattice can be determined.

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 Analytic Study Of Eight-Grade Pupil Performance As Revealed Through The Stanford Achievement Test In Arithmetic, Dominic J. Brungardt

Master's Theses or Doctor of Nursing Practice

The immediate purpose of the study were: (a) to determine how closely the grade equivalents of two-hundred and sixty pupils follow the normal curve ; (b) to plot the results of the one-step problems on a graph with an analytic explanation of the graph ; (c) to place the results of the two-step problems on a graph with an analytic explanation of the graph; to determine what types of error were most prevalent; to discover apparent causes of error ; (d) to make suggestions helpful to teachers for improving pupil achievement.

Certain Loci Associated With A One Parameter Family Of Conics In Three Dimensions, Raymond Francis Lausmann

Bachelors’ Theses

The conic sections and also the types of traces that might be obtained by the intersection of a plane with the ten real quadric surfaces have always been a source of great interest to me.

Lack of time has always been an obstacle to satisfying this curiosity. However, the opportunity for taking time was presented when the Department granted permission to write this thesis.

On Matrices With Elements In A Principal Ideal Ring, William Leavitt, George Whaples

Department of Mathematics: Faculty Publications

We prove the following theorem.
THEOREM 1. Let D be any commutative principal ideal ring without divisors of zero, and A any matrix with elements in D whose characteristic equation factors into linear factors in D. Then there exists a unimodular matrix T, with elements in D, such that T^-1 AT has zeros below the main diagonal.

The Application Of The Law Of Virtual Work In The Solution Of Civil Engineering Structures, Martin Trester Dyke

University of the Pacific Theses and Dissertations

The purpose of this thesis is to explore the civil engineering application of the law of virtual work to the determination of defelections, shears, bending stresses in truss structures, beams, structures subjected to both direct stress and bending, and indeterminate structures, and further to give examples of their mathematical solutions.

Arithmetical Vocabulary : A Factor In Verbal Problem Solving In Sixth Grade Arithmetic, Ernest A. Hoopes

Master's Theses or Doctor of Nursing Practice

During the writer's experience of teaching in elementary and junior high schools in Kansas he had excellent opportunity through supervision and classroom teaching to note a more-than-ordinary difficulty experienced by most children in the subject of arithmetic. Not only was the dull student baffled by the subject but many times the average and good students were "lost" when certain problems were presented. The exceptional. troublesomeness of this subject led the writer to ponder on the possible cause or causes of incorrect problem solving. One thing was apparent from observation and this was that many children seemed to lack a readiness …

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.

A Study Of Retention Of Percentage, Fred Dellett

Master's Theses or Doctor of Nursing Practice

The problem of this thesis was to determine by means of a test the retention of the fundamentals of percentage as shown by beginning eighth grade pupils, who were taught percentage the previous year in the seventh grade. The fundamentals of percentage are here considered as the changing of percents to decimal fractions or common fractions, the reverse procedures, and the three types of problems arising from the relation, base times rate equals part. These quantities, base, rate, and part, are represented in the example, 300 X 12% = 36, respectively. Because of the inherent relationship of decimal fractions and …

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.

Torsional Deflection Of Miter-Type Lock Gates And Design Of The Diagonals, Edwin Gustav Hoffmann

Retrospective Theses and Dissertations

No abstract provided.

On Certain Arithmetical Functions Due To G. Humbert, M. A. Basoco

Department of Mathematics: Faculty Publications

G. Humbert has discussed, in a series of brief notes, a certain class of entire functions with interesting arithmetical properties. These functions are defined, in an essentially unique manner, by certain functional equations. The Fourier series representations of the solutions of these equations are similar in form to those for the elliptic functions snu, cnu, dnu, and so on. They differ from these, however, in that their domain of validity extends throughout the entire complex plane (Z_∞ excluded) and moreover, in that their arithmetized forms involve incomplete numerical functions of the divisors of an integer.
In the …

A Theorem On The Unit Groups Of Simple Algebras, Ralph Hull

Department of Mathematics: Faculty Publications

Let k be an algebraic number field of finite degree m and let A be a normal simple algebra of degree n, order n², over k. Our object is to prove the following theorem.
THEOREM. If A is an R-algebra, that is, if n>2 or at least one infinite prime place of k is unramified in A when n=2, then any two distinct maximal orders of A have distinct groups of units.

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 …