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A Development of the Peano Postulates

Description: The purpose of this paper is to develop the Peano postulates from a weaker axiom system than the system used by John L. Kelley in General Topology. The axiom of regularity which states "If X is a non-empty set, then there is a member Y of X such that the intersection of X and Y is empty." is not assumed in this thesis. The axiom of amalgamation which states "If X is a set, then the union of the elements of X is a set." is also not assumed. All other axioms used by Kelley relevant to the Peano p… more
Date: May 1963
Creator: Peek, Darwin Eugene
Item Type: Refine your search to only Thesis or Dissertation
open access

The Runge-Kutta Method

Description: This paper investigates the Runge-Kutta method of numerically integrating ordinary differential equations. An existence theorem is given insuring a solution to the differential equation, then the theorem is modified to yield an analytic solution. The derivation of the method itself is followed by an analysis of the inherent error.
Date: June 1961
Creator: Powell, Don Ross
Item Type: Refine your search to only Thesis or Dissertation
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A Set of Axioms for a Topological Space

Description: Axioms for a topological space are generally based on neighborhoods where "neighborhood" is an undefined term. Then, limit points are defined in terms of neighborhoods. However, limit points seem to be the basic concept of a topological space, rather than neighborhoods. For this reason, it will be attempted to state a set of axioms for a topological space, using limit point as the undefined concept, and to delete the idea of neighborhoods from the theory.
Date: August 1960
Creator: Batcha, Joseph Patrick
Item Type: Refine your search to only Thesis or Dissertation
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Finite Dimensional Vector Space

Description: The object of this thesis is to examine properties of an abstract vector space of finite dimension n. The properties of the set of complex numbers are assumed, and the definition of a field and of an abelian group are not stated, although reference to these systems is made.
Date: August 1960
Creator: Power, Billy Joe
Item Type: Refine your search to only Thesis or Dissertation
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Some Diophantine Equations

Description: This paper will be devoted to an examination of several general and specific equations and systems of equations of the diophantine type. Only algebraic equations with integral coefficients, not all zero, will considered. The elementary properties of the integers will be assumed.
Date: January 1960
Creator: Pressly, Kirby Smith
Item Type: Refine your search to only Thesis or Dissertation
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T-Functions

Description: The main purpose of this paper is to make a detailed study of a certain class T of complex functions. The functions of the class T have a special mapping property and are meromorphic in every region. As an application of this study, certain elementary functions are defined and studied in terms of a special T-function.
Date: June 1960
Creator: Barlow, John Rice
Item Type: Refine your search to only Thesis or Dissertation
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Topological Groups

Description: The notion of a topological group follows naturally from a combination of the properties of a group and a topological space. Since a group consists of a set G of elements which may be either finite or infinite and since this is also common to a topological space, a question is opened as to whether or not it is possible to assign a topology to a set of elements which form a group under a certain operation. Now it is possible to assign a topology to any set of elements if no restriction is placed… more
Date: May 1960
Creator: Carry, Laroy Ray
Item Type: Refine your search to only Thesis or Dissertation
open access

Partially Ordered Groups and Rings

Description: This report presents both the most essential known results and new results in the theory of partially ordered groups and rings. This report deals with partially ordered groups and rings in an algebraic aspect because it is more important than partially ordered, fully ordered and lattice-ordered semigroup theory.
Date: August 1968
Creator: Lott, Kenneth L.
Item Type: Refine your search to only Thesis or Dissertation
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