Physical Sciences and Mathematics Commons^™

Some Decomposition Theorems For The Vector Space Of Matrix Summability Operators, Ed Kelly Jr., Tetsundo Sekiguchi

Journal of the Graduate Research Center

Consider the set T = {(aij) I aij are real } of matrix summability operators on the set B of bounded sequences of real numbers.

A Proof Of A Theorem On Giffin's Paradox, Don E. Edmondson

Journal of the Graduate Research Center

For the uninitiated, Giflin's paradox is the name of a condition from economic analysis. One considers a consumer with a certain income faced with the decision of how much of two goods to purchase. Intuitively, one anticipates that this will depend upon the prices to be paid for the goods, and anticipates that if a price is increased the amount purchased by the consumer will decrease ( the other price being constant). If it happens that with an increase in price of a good, the demand for that good increases, then this paradoxical situation is called Giflin's Paradox. The theorem …

Some Results Concerning Asymptotic Distributions And Their Applications., J. Sethuraman Dr.

Doctoral Theses

This thesis is being submitted to the Indian statistical Institute in support of the author's application for the degree of doctor of philosophy. The thesis embodies research carried out by the author during the period 1958-1961 under the supervision of dr.R.R. Bahadur, Professor of statistics are the Indian Statistical Institute Calcutta.This thesis is concerned with development of a new method of establishing asymptotic distributions and the elaboration of some of its applications in several fields of statistics.The thesis consists of five chapters. Chapter I describes, in general terms, the various problems considered in the thesis. Chapter II Deals with the …

Mathematics And The Managerial Imagination, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.

Extremal Problems For Functions Starlike In The Exterior Of The Unit Circle, Wimberly C. Royster

Mathematics Faculty Publications

No abstract provided.

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 …

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.

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.

Separation Of The N-Sphere By An (N - 1)-Sphere, James C. Cantrell

Masters Theses

In this thesis we consider certain (n-1)-spheres embedded in S^n (we will frequently use the fact that S^n is topologically equivalent to the one point compactification of E^n). The problem is then to establish the existence or non-existence of certain topological properties of the two domains into which S^n is separated by the given (n-1)-spheres.

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 …

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 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. …

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

Mathematics Faculty Publications

No abstract provided.

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.

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.

Concentric Tori In The Three-Spere, Charles Henry Edwards Jr.

Doctoral Dissertations

A torus is the topological product of two circles, while a solid torus is the topological product of a circle and a disk. Two solid tori B1 and B2 in the three-sphere S^3, with B2 interior to B1, are said to be concentric if and only if the closure of B1-B2 (the set of points in B1 but not in B2) is homeomorphic to the topological product of a torus and a closed interval. Two tori in S^3 are concentric if and only if they are respectively the boundaries of two concentric solid tori.

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.

Econometric Analysis Of The United States Manganese Problem, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.

On Periodicities Of Certain Sequences Of Residues, William F. Trench

William F. Trench

No abstract provided.

Smoothing In Inventory Processes - Notes, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.

A Study In Promotional Competition, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.

Groups And Algebraicity In Complete Rank Rings, Robert James Smith

Doctoral Dissertations

Introduction: It is well known that many of the results in classical linear algebra have an unequivocal extension to the more general situation when the scalars are drawn from an arbitrary division ring K. There are, however, three distinct theories of determinants for matrices over a division ring. One of these, originated by Study, "apples only to very particular non-communicative fields and to matrices of special type" (Dieudonne) and will not concern us here. The remaining two, one due to Ore and the other due to Dieudonne, reflect together, if not separately, the basic properties of the classical determinant. The …

Smoothing In Discrete Servo-Stochastic Processes, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.

Equilibrium Points In Finite Games, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.

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

Mathematics Faculty Publications

No abstract provided.

Navy Supply System Research - Objectives And Plans, Harlan D. Mills

The Harlan D. Mills Collection

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.