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Full-Text Articles in Physical Sciences and Mathematics

Characterizing Topologies By Continuous Selfmaps, Derald David Rothmann Jan 1969

Characterizing Topologies By Continuous Selfmaps, Derald David Rothmann

Doctoral Dissertations

"Various topological spaces are examined in an effort to describe topological spaces from a knowledge of their class of continuous selfmaps or their class of autohomeomorphisms. Relationships between topologies and their continuous selfmaps are considered. Several examples of topological spaces are given and their corresponding classes of continuous selfmaps are described completely. The problem, given a set X and a topology U when does there exist a topology V either weaker or stronger than U such that the class of continuous selfmaps of (X,V) contains the class of continuous selfmaps of (X,U), is considered. M* and S** spaces are defined …


Statistical Inferences For Location And Scale Parameter Distributions, Robert Henry Dumonceaux Jan 1969

Statistical Inferences For Location And Scale Parameter Distributions, Robert Henry Dumonceaux

Doctoral Dissertations

"The problem of discriminating between two location and scale parameter distributions is investigated. A general test based on a ratio of likelihoods is presented. A test based on a Pearson Goodness of Fit statistic is also considered. Tables are given for discriminating between the normal and exponential, the normal and double exponential, the normal and extreme value, and also between the normal and logistic. For location and scale parameter distributions, two-sided tolerance limits are shown to always be obtainable by Monte Carlo simulation. A method for obtaining confidence intervals on the reliability at a fixed time t is also given. …


Statistical Inferences For The Cauchy Distribution Based On Maximum Likelihood Estimators, Gerald Nicholas Haas Jan 1969

Statistical Inferences For The Cauchy Distribution Based On Maximum Likelihood Estimators, Gerald Nicholas Haas

Doctoral Dissertations

"Various estimators of the location and scale parameters in the Cauchy distribution are investigated, and the superiority of the maximum likelihood estimators is established. Tables based on maximum likelihood estimators are presented for use in making statistical inferences for the Cauchy distribution. Those areas considered include confidence intervals, tests of hypothesis, power of the tests, and tolerance intervals. Both one- and two-sample problems are considered. Tables for testing the hypothesis of whether a sample came from a normal distribution or a Cauchy distribution are presented. The problems encountered in finding maximum likelihood estimators for the Cauchy parameters are discussed, and …


Inferences On The Parameters Of The Weibull Distribution, Darrel Ray Thoman Jan 1968

Inferences On The Parameters Of The Weibull Distribution, Darrel Ray Thoman

Doctoral Dissertations

"For the most part, solutions to the problems of making inferences about the parameters in the Weibull distribution have been limited to providing simple estimators of the parameters. Little has been known about the properties of the estimators. In this paper the small and moderate sample size properties of the maximum likelihood estimators are studied and their superiority is established. The problem of making further inferences which are based on the maximum likelihood estimates of the parameters is then considered. The inferences that are presented can be divided into those based on a single sample and those based on two …


Minimal Weinstein Discs In A Subspace, William Lewis Morris Aug 1967

Minimal Weinstein Discs In A Subspace, William Lewis Morris

Doctoral Dissertations

The basic features of Clanton's algorithm are reviewed and it is shown that the analysis of ρ(A; Sx) leads to a refinement of the algorithm. A new algorithm to solve Ay = λy is the concluding item in this investigation


Green's Relations And Dimension In Abstract Semi-Groups, George F. Hampton Aug 1964

Green's Relations And Dimension In Abstract Semi-Groups, George F. Hampton

Doctoral Dissertations

This thesis originated in an effort to find an efficient algorithm for the construction of finite inverse semigroups of small order. At one stage in trying to devise such a scheme, an attempt was made to construct an inverse semigroup by adjoining two non-idempotent elements to a semi-lattice in such a way that each of them would be D-equivalent to a pair of distinct D-equivalent idempotents. It was noticed taht such adjunction yielded an inverse semigroup only when the elements of the pari were incomparable in the partial ordering of the semilattice, and only when, for each positive integar n, …


Concentric Tori In The Three-Spere, Charles Henry Edwards Jr. Dec 1960

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.


Groups And Algebraicity In Complete Rank Rings, Robert James Smith Dec 1959

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 …


Topological Groupoids, Ronson J. Warne Jun 1959

Topological Groupoids, Ronson J. Warne

Doctoral Dissertations

A groupoid is a set G in which a single valued product ab is defined for every pair of elements a, b ε G. If G is a groupoid and at the same time a Hausdorff topological space, and, moreover, the multiplication in the groupoid G is continuous in the topological space G, then G is called a topological groupoid. Our aim in this dissertation is two-fold: (1) to study topological groupoids for their own sake; (2) to investigate the relation of certain topological properties to associativity. We note, in relation to the first motif, that many authors have dealt …


Spectral Theory Of Self-Adjoint Ordinary Differential Operators, Charles C. Oehring Dec 1958

Spectral Theory Of Self-Adjoint Ordinary Differential Operators, Charles C. Oehring

Doctoral Dissertations

Introduction: Many of the properties of the ordinary Fourier series expansion of a given function are shared by the orthogonal expansion in terms of eigenfunctions of a second order ordinary differential operator. Let p = p(x) and q = q(x) be real-valued functions such that p, p', and q are continuous, and p(x) > 0, on a finite interval a ≤ x ≤ b. Let λ be a complex parameter. The classical Strum-Liouville theory [9, section 27; 4, Chapter 7; 21, Chapter 1]1 is concerned with solutions of the differential equation -(py') + qy = λ, which satisfy certain real …


Tame, Finite Complexes In Three-Space, P. H. Doyle Iii Aug 1957

Tame, Finite Complexes In Three-Space, P. H. Doyle Iii

Doctoral Dissertations

Introduction: A fundamental problem in topology of Euclidean n-space is to determine under what conditions two homeomorphic subsets of an n-space are strongly homeomorphic; that is, to determine when one can be carried onto the other by homeomorphism of space onto itself. This problem is of particular importance when one of the two subsets is a polyhedron.


Approximately Finite Geometries And Their Coordinate Rings, James Howard Alexander Jun 1957

Approximately Finite Geometries And Their Coordinate Rings, James Howard Alexander

Doctoral Dissertations

Introduction: Von Newmann [8]1 has discovered a class of geometries in which the undefined elements are subspaces and the undefined operations are meets and joins of subspaces. His axioms require that the system consisting of the set ℒ of subspaces together with the two operations form an irreducible, complete, complemented, modular lattice satisfying an additional dual pair of continuity of conditions.