Physical Sciences and Mathematics Commons^™

The History And Nature Of Pi, Karen A. Rand

Honors Theses

No abstract provided.

Some Statistical Inferences For The Bivariate Exponential Distribution, Bruce Mohr Bemis

Doctoral Dissertations

"The bivariate exponential distribution is neither absolutely continuous nor discrete due to the property that there is a positive probability that the two random variables may be equal. Basic properties of the distribution are presented as well as methods of parameter estimation including maximum likelihood. The distribution is shown to satisfy the usual regularity conditions in spite of its possession of a singularity. The maximum likelihood estimates are asymptotically efficient. Two other methods of estimation are compared with the maximum likelihood method in terms of efficiency. Tests of the hypothesis that two random variables each have independent exponential distributions versus …

Integrability Of The Sums Of The Trigonometric Series 1/2 Aₒ + ∞ [Over] Σ [Over] N=1 AN Cos Nθ And ∞ [Over] Σ [Over] N=1 AN Sin Nθ, John William Garrett

Masters Theses

"The trigonometric series C = 1/2 aₒ + ∞ [over] Σ [over] [n=1] a[subscript n] cos nΘ and S = ∞ [over] Σ [over] n=1 a[subscript n] sin nΘ, where {a[subscript n]} monotonically decreases to zero both converge almost everywhere to functions f and g respectively. f (or g) is L iff C (or S) is the Fourier series of f (or g) iff term-by-term integration of C (or S) is valid. There are three equivalent conditions, each of which implies that C is the Fourier series of f...."--Abstract, page ii.

The Influence On A Finite Group Of The Cofactors And Subcofactors Of Its Subgroups, Larry R. Nyhoff

University Faculty Publications and Creative Works

The effect on a finite group G of imposing a condition 6 on its proper subgroups has been studied by Schmidt, Iwasawa, ltd, Huppert, and others. In this paper, the effect on G of imposing 6 on only the cofactor H/corGHor more generally, the subcofactor ///scorGH) of certain subgroups H of G is investigated, where corGH (scorGH) is the largest G-normal (07-subnormal) subgroup of H. It is shown, for example, that if (a) ///scorGH is p-nilpotent for all self-normalizing H> G, or if (b) ///scorGH is />-nilpotent for all abnormal H> G and p is odd or the p-Sylows …

On The Measurement Of Fund Performance, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.

I. Existence Of Eigenvalues For Integral Equations; Ii. A Collocation Method For Boundary Value Problems, Robert Dodd Russell

Mathematics & Statistics ETDs

I. The existence of eigenvalues is shown for certain classes of integral equations with continuous kernels. A number of interesting and useful results are thereby treated in a unified and relatively elementary way. The simplicity of these new proofs make the results accessible to introductory courses on the theory of integral equations.

II. Collocation with piecewise polynomial functions is developed as a method for solving two-point bour:rlary value problems. Convergence is shown for a general class of linear problems and a rather broad class of nonlinear problems. Some computational examples are presented to illustrate the wide applicability and efficiency of …

Studies In Borel Structures., Bhamidi Visweswara Rao Dr.

Doctoral Theses

It ts the nurposo of this chapter to collect together the problons that were acattored throughout the provious two chapters. This chaptor has sovon scctions. The first threo soc tions doal with the probloms that arc raised in or have c onnec tion witl: the topic of chaptor 1. The last tihree sectiona dcal with thc ne of chapter 2. Soction 4 stands mid- vay betweon bo tli, We ahall nunber the problomsi sorially and the nunber appears in bracko to. Wherover posaible wo shall includo somo dincuscion abcut the problcn involvod. There are no now rocults in thin chapter …

Goursat Problems For The Abstract Equation Urs = Lu, Walter J. Roth

Mathematics & Statistics ETDs

A Comparative Study Of Business Arithmetic Students: The Use Of Calculators Vs. Manual Computation, Marietta Crawford

Morehead State Theses and Dissertations

A thesis presented to the Business Education Graduate Committee at Morehead State University in partial fulfillment of the requirements for the Degree of Master of Business Education by Marietta Crawford on May 25, 1970.

Distribution Of The Sum Of Independent Unity-Truncated Logarithmic Series Variables, Russell James Wayland

Dissertations and Theses

Let X₁, X₂, ..., X_n be n independent and identically distributed random variables having the unity-truncated logarithmic series distribution with probability function given by f(x;θ) = αθ^X/x x ε T where α = [-log(1-θ) - θ]^-1, 0 < θ < 1, and T = {2,3,...,∞}. Define their sum as Z = X₁ + X₂ + ... + X_n.

We derive here the distribution of Z, denoted by p(z;n,θ), using the inversion formula for characteristic functions, in an explicit form in terms of a linear combination of Stirling numbers of the first kind. A recurrence relation for the probability function p(z;n,θ) is obtained …

A Survey In Mean Value Theorems, David A. Neuser

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A variety of new mean value theorems are presented along with interesting proofs and generalizations of the standard theorems.

Three proofs are given for the ordinary Mean Value Theorem for derivatives, the third of which is interesting in that it is independent of of Rolle's Theorem. The Second Mean Value Theorem for derivatives is generalized, with the use of determinants, to three functions and also generalized in terms of n-th order derivatives.

Observing that under certain conditions the tangent line to the curve of a differentiable function passes through the initial point, we find a new type of mean value …

A Fortran List Processor (Flip), Karl A. Fugal

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A series of Basic Assembler Language subroutines were developed and made available to the FORTRAN IV language processor which makes list processing possible in a flexible and easily understood way.

The subroutine will create and maintain list structures in the computer's core storage. The subroutines are sufficiently general to permit FORTRAN programmers to tailor list processing routines to their own individual requirements. List structure sizes are limited only by the amount of core storage available.

Bayesian Estimate Of System Reliability, Naresh Shah

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

A Bayesian estimate of reliability for each component in the system of n-components, each exponentially distributed, is developed which utilizes the basic notion of loss in estimation theory. Here we assume that each component is independently dis­tributed. In reliability estimation, the loss associated with over­estimation is usually greater than the loss associated with under­estimation; and hence loss function can be a very useful tool. The prior distribution and loss function of reliability considered in this paper are flexible to be compatible with other situations in which reliability estimates are required. When the loss function is symmetric and no prior information …

An Introduction To And Discussion Of Automata And Sequential Machines, Joseph Philip Seab

Honors Theses

No abstract provided.

On Extremal Partitions Of Graphs, John A. Mitchem

Dissertations

No abstract provided.

Some External Problems And Charecterization In The Theory Of Graphs., Ramachandra Rao Dr.

Doctoral Theses

Graph theory has become such a well known and widely applied subject that it is not nocessary to give a general Introduetion to it. Instead ve eive helov a summary of the results of the thesis chapterwise.The study of extremal problems in Graph theory was started by Turan who deternined the minimum independence number of a graph on n vertices vith m edges. More recently Harary determined the maxinum conneetivity of a graph on n vortices vith m edges.In a paper concerning the degrees of the vertices of a graphy laktnd posed the following two problems : dotermin the maximum …

Some Contributions To The Analysis Of Circular Data., J. S. Rao Dr.

Doctoral Theses

In many diverae scientifie fields, one cones serose experimente where the basie variable unter obaervation ia a direction. We ahall be conoerned, throughout this theais, only with diraations in two-dimensions and wo refer to such a collection of directione an 'circular data or dimenstionl data. In order to make a statintical analyaie of circular data, the first prerequisite is to put thom in a quantitative form. One way of doing thie is to represent the directiona anglea no aaured d thre apeet to eone mui tably choscn sero direation. Al ternately, einee a direetion han no nagni- tude, it can …

Theory Of Equitable Quality Level And Errors- Areas Under The Operating Characteristic Curves Of Lot Acceptance Sampling Plans., M. T. Subramanya Dr.

Doctoral Theses

This monograph deals with the theory of Equitable Quality Level and error-areas under the operating characte- ristic curves of lot acceptance sampling plans. A brief sumnary of the contents is given in Sections 1.2b (pages 15-16) and 2.9 (pages 107-111). A fairly good idea of the topics considored in this monograph can be obtained from the detailod list of contents given in pagos iv- xi.Most of the results given in the monograph are new and have not been published anywhe re. They are based on author's own research work and are contained in his doctoral dissertation.Most of the work connected …

Calculus And The Computer: A Conservative Approach, Melvin Henriksen

All HMC Faculty Publications and Research

This paper describes a program for making the use of numerical methods an integral part of the freshman college course in single variable calculus.

A Brief Study Of Topology, Mary Beth Mangrum

Honors Theses

Topology is the study of topological properties of figures -- those properties which do not change under "elastic" motion. It is generally divided into two branches: set topology and algebraic topology. Set topology discusses the nature of a topological space, the properties of sets of points, the definitions of limits and continuity, the special properties of metric spaces, and questions concerning separation and connectedness. Algebraic topology deals with groups which are defined on a space, their structure and invariants.

Federal Careers And Opportunities For Mathematicians, Gail Ray

Honors Theses

The purpose of this paper is to research the opportunities for a math major in the Federal Civil Service, and the requirements for positions. Those occupations which require courses only in math are few. However, there are several more which requires a combination of math with some other subject matter.

Those positions requiring only math are: Agricultural marketing specialist, cartographer, equipment specialist, geodesist, and mathematician.

Simple Algebraic Extensions And Characteristics Polynomials, Don Stokes

Journal of the Arkansas Academy of Science

No abstract provided.

Extension Of Some Theorems Of Complex Functional Analysis To Linear Spaces Over The Quaternions And Cayley Numbers, James E. Jamison

Doctoral Dissertations

"In this work certain aspects of Functional Analysis are considered in the setting of linear spaces over the division rings of the real Quaternions and the real Cayley algebra. The basic structure of Banach spaces over these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite dimensional spaces over these division rings are given. Questions concerning linear functionals, the Hahn-Banach Theorem and Reflexivity are considered. The Stone-Weierstrass Theorem is proven for functions with values in a real Cayley Dickson algebra of dimension n. The concepts of inner product spaces and Hilbert …

Mathematics On An International Basis, Sandra Lee Sawyer

Honors Theses

Is the math of the United States inferior? In 1967 there was an international study of mathematics comparing twelve different countries: United States, Japan, Australia, Belgium, England, Finland, France, Germany, Israel, The Netherlands, Scotland, and Sweden. Funded in part by the United States Office of Education and five years in the making, the report was based on a test given to 133,000 students in different countries at the age of thirteen and at the end of high school.

The Evolution And Application Of Pi, Carolyn Rhodes

Honors Theses

There is no part of the arithmetic that deals with approximations that is more interesting than that which seeks to find the ratio of the circumference of a circle to its diameter. This ratio has been studied from both a practical and a theoretical standpoint. Under the name "quadrature of the circle" it occupied mathematicians for many thousands of years, beginning with the Bible and extending to the twentieth century.

An Elementary Mathematics Curriculum Study To Determine If Achievement And Attitude Can Be Influenced By A Textbook Adoption, Elsie M. Railey

All Master's Theses

There is on the market a wide range of contemporary mathematics textbooks available. Textbooks approach mathematics differently and there is a variation in terms of the amount of time allocated to a topic, the development of elementary concepts and laws of arithmetic, and the amount of drill and repetition. The sequential development of the texts follows closely, but the scope and content differ significantly. Specifically, it is the purpose of this study to determine if there is a significant difference between series, as opposed to those in another mathematics series, in the variables of attitude and achievement. The two textbooks …

A Heuristic Algorithm For Determining A Constructive Suboptimal Solution To The Combinatorial Problem Of Facility Allocation, Harry Kerry Edwards

Doctoral Dissertations

"The major problem in plant layout is to determine the most economical relative location of facilities. There are two distinct types of suboptimal solutions to this combinatorial problem: construction and improvement. The writer has developed Modular Allocation Technique (MAT) which is the first useful construction suboptimal technique. The MAT general algorithm, a theorem relating the MAT solution to the optimal solution and an example problem are given. A computer program has been written that will apply MAT to the allocation problem for a maximum of 40 facilities. Results are given to demonstrate how MAT solutions may be used as initial …

A Coordinate Oriented Algorithm For The Traveling Salesman Problem, Joseph Sidney Greene

Doctoral Dissertations

"The traveling salesman problem may be stated as follows: "A salesman is required to visit each of n given cities once and only once, starting from any city and returning to the original place of departure. What route should be chosen in order to minimize the total distance traveled?" A new algorithm is developed which gives a good approximation to the solution for a large number of cities using reasonable computer time and which will converge to the exact solution if allowed to continue. This algorithm is a branch and bound technique which utilizes the distance between cities in its …

Heuristic Algorithms For The Generalized Vehicle Dispatch Problem, Leland Ray Miller

Doctoral Dissertations

"A heuristic algorithm, called the sweep algorithm, is developed for the vehicle dispatch problem with distance and load constraints for each vehicle. A mathematical development and a step procedure for the sweep algorithm is given. Also given are eight problems and their solutions derived by the sweep algorithm. The solutions for this algorithm are compared with solutions from other vehicle dispatch algorithms, and the sweep algorithm is found to give better results for almost every problem. Various modifications are also presented for the sweep algorithm. A mathematical formulation is given for the vehicle dispatch problem with arbitrary cost functions at …

The General Linear Group Related Groups, J. William Beck

Masters Theses

No abstract provided.