Digital Commons Network^™

Patricia-Ii Two Level Overlayed Indexes For Large Libraries., James Leon Clark

Mathematics & Statistics ETDs

PATRICIA is a Practical Algorithm To Retrieve Informa­tion Coded In Alphanumeric. The library index built by PATRICIA is entirely core resident. PATRICIA-II extends PATRICIA by building both a lower index and an upper index. This allows for the indexing of a much larger library. The lower index is core resident and the upper index is divided into upper pages which are stored on disk. At any given time only the lower index and one upper page are in core. Upper pages reference only themselves, not each other. In addition to these innovations, PATRICIA-II retains all of the features of its …

Application Of Fast Poisson Solvers To The Numerical Approzimation Of Parabolic Problems., Billy Lewis Buzbee

Mathematics & Statistics ETDs

Let T be a positive constant, let D^n be the interior of the unit hypercube in R^n with boundary ∂D^n, let a(t;x1,x2,…,xn) be a strictly positive funtion, and consider the parabolic problem ut= ∇*a ∇u + s(t;x1,x2,…,xn) in D^nx[0,T]

Where

U(t)=0 on ∂D^nx[0,T]

And

U(0)=f

This report compares three A-stable marching procedures for approximating this problem by finite differences. The procedures considered are the pure explicit procedure (APX) with 6t sufficiently restricted to insure A-stability, the pure implicit procedure (PM) or backwards difference equation, and a recently developed pure implicit procedure (SOC) which is second order correct in time and …

Professor Leo Moser -- Reflections Of A Visit, Walter E. Mientka

Department of Mathematics: Faculty Publications

Professor Leo Moser' was known throughout the Mathematical Community as a significant researcher and excellent lecturer. I first met Leo during the Summer Research Institute in the Theory of Numbers held at the University of Colorado in 1959. After talking with him and hearing his lectures during the Institute, I felt that arrangements would have to be made in the near future for a visit to Nebraska. During the academic year 1962-63 while Professor Moser was on a lecture tour for the MAA, I invited him to present two research lectures to the Nebraska Section on May 3 and 4, …

Branches And Completions For Real Algebraic Curves, Arthur E. Bukowski

Mathematics & Statistics ETDs

Let Q be a real ideal in a commutative ring A over an ordered field k. Do the classical results of cummutative rings hold for the ideal Q, the realradical of Q, and the real primes of A? We deal with these questions in Section 1. We prove that the minimal realprimes of Q are the minimal primes of Hence the minimal real primes of A are the minimal primes of some a_iϵ A}. A finitely generated realsimple ring isin fact a field and so any maximal realideal in a finitely generated ring A|k is a maximal ideal. …

Some Problems In Combinatorial Number Theory., Frank Ernest Higgins

Mathematics & Statistics ETDs

In this paper we consider three unrelated problems in combinational number theory. The first of these pertains to minimal residual polynomials, the second to certain group factorizations and the third to the addition of positive integers in their Zeckendorf representations.

In section II We show that for any given positive integer m there exists a unique integer monic polynomial P of least degree and whose coefficients satisfy certain inequalities with the property that m divides P(x) for every integer x. This polynomial is called the minimal residual polynomial modulo m. We then show that this polynomial assumes various forms which …

Isopathic Graphs And Airport Graphs, Kim T. Rawlinson

Mathematics & Statistics ETDs

This paper explores two kinds of graphs, isopathic graphs and air­ port graphs. A distance property of graphs in general is also examined.

Isopathic graphs are graphs in which every maximal path has the same length. The major theorem of this section characterizes isopathic graphs as extended stars, bipartite or hamiltonian. There is then a discussion of the latter two classes of isopathic graphs.

At the end of Section I, there is an introduction to isopathic di­graphs, a natural concern after an exposure to isopathic graphs.

Airport graphs, more appropriately snob graphs, can be thought of in the following way. …

A Maximum Principle For Time-Lag Control Problems With Bounded States, Gary R. Bunce

Mathematics & Statistics ETDs

A maximum principle is obtained for control problems involving system equations with a constant time lag in the control and state variables. The arcs under consideration are subject to constraints of the form

The results are obtained using the method of M. R. Hestenes.

Operators As Elements In A Partially Ordered Linear Algebra., Edward Wayne Davenport

Mathematics & Statistics ETDs

R. DeMarr {unpublished) has begun a study of linear operators as elements in a Dedekind O-complete partially ordered linear algebra {dsc-pola). The order structure necessary to produce elements in a dsc-pola which behave as specific operators on a specific space of functions is studied.

Discrete Approximations To Continuous Optimal Control Problems, Maurice L. Eggen

Dissertations

No abstract provided.

Convergence Of Bounds In Optimization, Pascal D. Mubenga

Dissertations

No abstract provided.

Contributions To Measure Theory., Merepalli Bhaskara Rao Dr.

Doctoral Theses

This thesis 1s devoted to a study of measures vith emplas sis on nonatonie nea sures. Me briefrly desoribe here the work carried out in various chapters. In Chapter 1, we study various aspects of nonatomic nea sures based on some characterisations obtained early in the Chapter. In Chapter 2, the problem - when a mixture of nonatoftic mea sures is nonatomic - is exanined. An example and rive sufficient conditions are given. In Chapter 3, we examine when a mixture of 1nvariant non-ergorlie mesures is non-ergodic. An example and three sufficient eonditions are given. In Chapter 4, we study …

Some Contribution To The Theory Applications And Computations Of Generalized Inverses Of Matrices., Pochiraju Bhimasankaram Dr.

Doctoral Theses

The origin of the concept of a generalized inverse dates back to as early as 1920 when Moore defined the generalized inverse of matrix which is equivalent toDefinition 1 (Moore) : Let A be a m >< n matrix over the field of complex numbers. Then a is the generalized Inverse of A if AG is the orthogonal projection operator projecting arbitrary vectors onto the column space of A and GA is the orthogonal projection operator projecting arbitrary sectors onto, the column space of G.Mod re (1935) discussed this concept and its properties in some detail. Tsong (1949a, 1949b, 1956) discussed about generalized 1nverses of operators in more general spaces and Bjerhammer (1951) discussed the generalized inverse of a matrix in connection with an application to geodetic calculations. Unaware of the work of Hoore and others, Penrose (1955) defined a generalized inverse of a matrix as follows :Definition 2 (Penrosel) : Let A be a m *n -matrix over the field of complex numbers. Then G is a generalized inverse of a if (i) AFA= A; (ii) GAG=G; (iii) (AG)*=AG and (iv) (GA)*-GA.Penrose (1955,1956) showed that for every matrix there exists a unique generalized inverse, discussed several of its important properties, gave applications to solution of matrix equations and suggested a practical method of computation of the generalised inverse.As was pointed out by Rado (1956) Moo res definition of generalized inverse is equivalent to that of Penrose, Such generalized inverse is called the Moore-Penrose inverse and A is used to denote the Moore-Penrose inverse of A.Rao (1955), unaware of the earlier or contemporary Work, constructed a pseudo-inverse of a matrix which he used in some least squares computations, In a paper in 1962, he defined a generalized inverse (g-inverse) as follows, proved some interesting properties and gave applications of g-inverses to Mathomatical Statistics.Definition 3 (Rao) : Lot A be am x n matrix, Then a n >< m matrix. Then a n >< m matrix G is a g-inverse of A if x = Gy is a solution of the linear system Ax = y whenever it is consistent.A g-inverse if u matrix (in the sense of Rao) is in general not unique, As 1s easily observed (from definitions 2 and 4) the class of all g-inverses of a matrix A contains A*. Rạo (1965, 1967) developed a calculus of g-inverses, classified the g-inverses according to their use and according to the proporties they possess similar to those of the inverse of a nonsingular matrix and suggested further applications to Mathematical Statistics. Mitra (1968a, 1968b) gave an equivalem definition of a g-inverse, developed further calculus of z-inverses, used g-invorses to solve some matrix equations of interest and explored the possibilities of some new classes of g-inverses with applications. In a series of papers, and a monograph Mitra and Rao (1968, 1970) pursued the research on generalized inverses of matrix's and their applications to various scientific disciplines.

Some Quasi-Uniform Space Examples, Troy L. Hicks, J. W. Carlson

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Radicals And Torsion Theories In Locally Compact Groups, Robert R. Bruner

Mathematics Faculty Research Publications

In this paper we will study the properties of locally compact Abelian Hausdorff topological groups (hereafter known as LCA groups) by means of their mapping properties. The results contained herein are an outgrowth of work done by Professor Armacost [Al] on "sufficiency classes" of LCA groups. The sufficiency class S\textunderscore(H) of an LCA group H is the class of all LCA groups G such that there are sufficiently many continuous homomorphisms from G to H to separate the points of G. This condition is easily seen to be equivalent to the requirement that ∩ker(f)=0, where f ranges over all elements …

An Acceleration Technique For A Conjugate Direction Algorithm For Nonlinear Regression, Larry Wilmer Cornwell

Doctoral Dissertations

"A linear acceleration technique, LAT, is developed which is applied to three conjugate direction algorithms: (1) Fletcher-Reeves algorithm, (2) Davidon-Fletcher-Powell algorithm and (3) Grey's Orthonormal Optimization Procedure (GOOP). Eight problems are solved by the three algorithms mentioned above and the Levenberg-Marquardt algorithm. The addition of the LAT algorithm improves the rate of convergence for the GOOP algorithm in all problems attempted and for some problems using the Fletcher-Reeves algorithm and the Davidon-Fletcher-Powell algorithm. Using the number of operations to perform function and derivative evaluations, the algorithms mentioned above are compared. Although the GOOP algorithm is relatively unknown outside of the …

Generalized Inverse Matrices And Applications In Statistics, James Manville King Iv

All Master's Theses

In the theory of linear statistical models, one frequently encounters consistent systems of linear equations Ax= y. If A is nonsingular then a unique solution is given by x - 1 A y. If A is singular or rectangular however, then there are an infinite number of solutions; and the theory of generalized matrix inverses can be used to generate and characterize the solution set.

This thesis examines properties of generalized matrix inverses, and their use in solving linear equations, and in particular the role they play in treating the concept of estimability.

D-Structures And Their Semantics, Rohit J. Parikh

Publications and Research

"Many logicians are familiar with the game theoretic approach to semantics, due to Jaakko Hintikka. This paper by me contains class notes of a logic course at Boston University in fall 1972. It has similar game theoretic ideas, developed quite independently, but influenced by the work of A. Ehrenfeucht. It applies to a larger class of logics, including classical logic, intuitionistic logic and the *-semantics of Ehrenfeucht. The treatment is via D-structures which are finite approximations of infinite structures. For various reasons I did not publish this paper then, but some abstracts, both by myself as well as joint abstracts …

Transient Solutions For Field Propagated By An Electric Source In A Perfectly Conducting Cone, Jon A. Sholberg

All Master's Theses

This paper makes use of the results of the doctoral thesis written by Professor K. Gamon entitled "The propagation of waves and pulses in the presence of conical structures." The use of such results is made by considering the expression for the field of a cone due to a ring source excitation and then obtaining the solution of a new field propagated by a given pulse.

Also, the electric and magnetic components for these new fields are derived along with the expression for the radiated energy.

Quasi-Pseudometrics Over Tikhonov Semifields And Fixed Point Theorems, Ronald Evans Satterwhite

Doctoral Dissertations

"It has been shown that topological spaces are characterized as quasi-pseudometric spaces over some Tikhonov semifield.

Sufficient conditions are given for a T₁ space to be metrizable over some Tikhonov semifield.

Completely regular (uniform) spaces are characterized as pseudornetric spaces over some Tikhonov semifield.

Certain metric, pseudornetric, quasi-metric, quasipseudometric spaces over a Tikhonov semifield are shown to be respectively metric, pseudometric, quasi-metric, quasipseudometric spaces in the usual sense.

Several results from fixed point theory in the metric space setting are generalized to the setting of completely regular (uniform) Hausdorff spaces."--Abstract, page ii.

The Jordan Canonical Form, Richard A. Freeman

College of Graduate Studies: Theses & Dissertations (1964–2006)

No abstract provided.

Statistical Studies Of Various Time-To-Fail Distributions, James Addison Eastman

Doctoral Dissertations

"Three models are considered that have U-shaped hazard functions, and a fourth model is considered that has a linear hazard function. Several methods for estimating the parameters are given for each of these models. Also, various tests of hypotheses are considered in the case of the model with the linear hazard function. One of the models with a U-shaped hazard function has a location and a scale parameter, and it is proved in general that any other parameters in a distribution of this type are distributed independently of the location and scale parameters.

A new method used to estimate the …

Elementary Length Topologies Constructed Using Pseudo-Norms With Values In Tikhohov Semi-Fields, Jackie Ray Hamm

Doctoral Dissertations

"Elementary length topologies defined on normed and pseudo-normed linear spaces are studied. It is shown that elementary length topologies constructed with different pseudo-norms are never equivalent. Elementary length topologies are constructed on certain topological spaces and some of their properties are investigated. It is shown that certain "measuring devices" (i.e., norms, pseudo-norms, semi-norms, and pseudo-metrics) which take their values in Tikhonov semifields may be used to construct elementary length topologies on any topological linear space. Relationships between two elementary length topologies generated with different measuring devices are considered.

Let (X,t) be a topological linear space such that t is determined …

Nonrandom Characteristics Of Common Stock Prices, Donald Leroy Gaitros

Doctoral Dissertations

"This study presents an application of operations research techniques to the development of stock price generation and simulation models to aid in the understanding of price movement. Relationships between stock price and volume and stock price and market averages which follow descernible trends and patterns are discovered. Technical trading rules are developed based on these relationships which empirically have shed doubt on the random walk hypothesis of price movement. This in turn gives evidences that technical analysis can be an aid to price forecasting"--Abstract, page ii.

Structure Of Zero Divisors, And Other Algebraic Structures, In Higher Dimensional Real Cayley-Dickson Algebras, Harmon Caril Brown

Doctoral Dissertations

"Real Cayley-Dickson algebras are a class of 2ⁿ-dimensional real algebras containing the real numbers, complex numbers, quaternions, and the octonions (Cayley numbers) as special cases. Each real Cayley-Dickson algebra of dimension greater than eight (a higher dimensional real Cayley-Dickson algebra) is a real normed algebra containing a multiplicative identity and an inverse for each nonzero element. In addition, each element a in the algebra has defined for it a conjugate element ā analogous to the conjugate in the complex numbers. These algebras are not alternative, but are flexible and satisfy the noncommutative Jordan identity. Each element in these algebras can …

Mathematical Modeling Of River Water Temperatures, Leland Lovell Long

Doctoral Dissertations

"The applicability of power spectral density techniques, Fourier series analysis, and linear regression to the mathematical modeling of river water temperature is demonstrated. Consideration is also given to the problem of estimating thermal inputs to rivers from man-made sources such as electrical power plants. First, power spectral density techniques are used in the time-series analysis of water temperature records which were taken from the Missouri River. Two spectral ranges are then studied from the standpoint of their applicability to (1) mathematical model building and (2) detection and identification of cyclic thermal inputs. Next, a Fourier regression fit to the time-series …

A Comparison Of The Effectiveness Of Worksheets And Manipulative Games Used In Seventh-Grade Mathematics As Methods Of Drill On The Four Basic Operations With Whole Numbers And Fractions, Richard Lee Capps

Dissertations and Theses @ UNI

This study was conducted in the fall of 1971 at Nell McGowen Junior High School, Knoxville, Iowa. The subjects of the study were 146 seventh-grade mathematics students. The students were ability grouped by the principal. No attempt was made to keep a constant sex ratio. The problem of this study was the comparison of two methods of drill on the four basic operations with whole numbers and fractions. The methods were games and worksheets. An analysis of covariance design was used to analyze the data. Achievement and attitude pre-test scores were covariates. Achievement and attitude post-test scores were dependent variables. …

Classifications Of Plane Continua, Steven Ray Matthews

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

In the course of studying continua in the plane it has been asked if a given continuum has uncountably many disjoint duplications in the plane, and if so, what are the consequences of the existence of such a collection. The object of this paper is to study these problems and to develop some machinery useful in their resolution. In Section I, we review the definition of convergence and homeomorphic convergence of point sets in a metric space S. We then consider the space, π of all continuous functions from a compact metric space P to a separable metric space Q …

The Constructive Theory Of Distributions, Elsie M. Gustafson

Masters Theses

No abstract provided.

A New Test For Normality, Richard Leroy Roller

All Master's Theses

This paper presents a new test for normality which is based on a complete characterization of the normal distribution. Motivation for the test is given in terms of a proof of this characterization. The test is derived and evaluated by computer-simulated sampling from alternative distributions. The empirical powers of the test generated from such samplings are tabled and compared to nine commonly used tests. Evaluation of the proposed test is discussed and further avenues of investigation are suggested.

Imbedding Graphs In Pseudosurfaces, Wayne S. Petroelje

Masters Theses

No abstract provided.