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473 Matching Results
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L'Hospital's Rule
The purpose of this paper is to present proofs for six cases of L'Hospital's Rule for the evaluation of indeterminate forms. It is also a purpose to reduce to one of these six cases some other indeterminate forms to which L'Hospital's Rule is applicable. In the course of presenting these proofs several theorems and definitions will be used without proof.
Date:
1950
Creator:
Spidell, William H.
System:
The UNT Digital Library
Planar Lebesgue Measure
This thesis attempts to prove the Lebesgue measure is a concrete realization of measure.
Date:
1950
Creator:
Martin, Nat G.
System:
The UNT Digital Library
Convergence Tests for Infinite Series
The field of infinite series is so large that any investigation into that field must necessarily be limited to a particular phase. An attempt has been made to develop a number of tests having a wide range of applications. Particular emphasis has been placed on tests for series of positive terms.
Date:
1950
Creator:
Latimer, Philip W.
System:
The UNT Digital Library
Continuation of Real Functions Defined by Power Series
This thesis looks at power series, particularly in the areas of: radius of convergence, properties of functions represented by power series, algebra of power series, and Taylor's Theorem and continuation by means of power series.
Date:
1948
Creator:
Strickland, Warren, G.
System:
The UNT Digital Library
Conditions under which Certain Inequalities Become Equalities
The object of this paper is to consider necessary and sufficient conditions in order for certain important inequalities, which are frequently used in analysis, to reduce to equalities.
Date:
1948
Creator:
Vaughan, Nick H.
System:
The UNT Digital Library
Uniformly σ-Finite Disintegrations of Measures
A disintegration of measure is a common tool used in ergodic theory, probability, and descriptive set theory. The primary interest in this paper is in disintegrating σ-finite measures on standard Borel spaces into families of σ-finite measures. In 1984, Dorothy Maharam asked whether every such disintegration is uniformly σ-finite meaning that there exists a countable collection of Borel sets which simultaneously witnesses that every measure in the disintegration is σ-finite. Assuming Gödel’s axiom of constructability I provide answer Maharam's question by constructing a specific disintegration which is not uniformly σ-finite.
Date:
August 2011
Creator:
Backs, Karl
System:
The UNT Digital Library
Mycielski-Regular Measures
Let μ be a Radon probability measure on M, the d-dimensional Real Euclidean space (where d is a positive integer), and f a measurable function. Let P be the space of sequences whose coordinates are elements in M. Then, for any point x in M, define a function ƒn on M and P that looks at the first n terms of an element of P and evaluates f at the first of those n terms that minimizes the distance to x in M. The measures for which such sequences converge in measure to f for almost every sequence are called Mycielski-regular. We show that the self-similar measure generated by a finite family of contracting similitudes and which up to a constant is the Hausdorff measure in its dimension on an invariant set C is Mycielski-regular.
Date:
August 2011
Creator:
Bass, Jeremiah Joseph
System:
The UNT Digital Library
Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces
In the study of Banach spaces, the development of some key properties require studying topologies on the collection of closed convex subsets of the space. The subcollection of closed linear subspaces is studied under the relative slice topology, as well as a class of topologies similar thereto. It is shown that the collection of closed linear subspaces under the slice topology is homeomorphic to the collection of their respective intersections with the closed unit ball, under the natural mapping. It is further shown that this collection under any topology in the aforementioned class of similar topologies is a strong Choquet space. Finally, a collection of category results are developed since strong Choquet spaces are also Baire spaces.
Date:
August 2011
Creator:
Farmer, Matthew Ray
System:
The UNT Digital Library
The Stability of the Solutions of Ordinary Differential Equations
This thesis is a study of stability of the solutions of differential equations.
Date:
1949
Creator:
Richmond, Donald Everett, 1898-
System:
The UNT Digital Library
Some Properties of a Lebesgue-Stieltjes Integral
It is the purpose of this paper to define a Lebesgue integral over a measurable set, the integration being performed with respect to a monotone non-decreasing function as in the Stieltjes integral, and to develop a few of the fundamental properties of such an integral.
Date:
1951
Creator:
Dean, Lura C.
System:
The UNT Digital Library
The Analytical Development of the Trigonometric Functions
This thesis is a study of the analytical development of the trigonometric functions.
Date:
1951
Creator:
Mackey, Pearl Cherrington
System:
The UNT Digital Library
Some Properties of Derivatives
This paper is concerned with certain properties of derivatives and some characterizations of linear point sets with derivatives. In 1946, Zygmunt Zahorski published a letter on this topic listing a number of theorems without proof, and no proof of these assertions has been published. Some of the theorems presented here are paraphrases of Zahorski's statements, developed in a slightly different order.
Date:
1951
Creator:
Dibben, Philip W.
System:
The UNT Digital Library
On Uniform Convergence
In this paper, we will be concerned primarily with series of functions and a particular type of convergence which will be described. The purpose of this paper is to familiarize the reader with the concept of uniform convergence. In the main it is a compilation of material found in various references and revised to conform to standard notation.
Date:
1951
Creator:
Drew, Dan Dale
System:
The UNT Digital Library
The Development of the Natural Numbers by Means of the Peano Postulates
This thesis covers the development of the natural numbers by means of the peano postulates.
Date:
1951
Creator:
Baugh, Orvil Lee
System:
The UNT Digital Library
Means and Mean Value Theorems
This study covers means, mean value theorems of the differential calculus, and mean value theorems of integral calculus.
Date:
1951
Creator:
Blummer, Raymond O.
System:
The UNT Digital Library
The Solution of Equations in Integers
This paper is devoted to finding integral solutions of algebraic equations. Only algebraic equations with integral coefficients are considered. The elementary properties of integers are assumed.
Date:
January 1964
Creator:
Read, Billy D.
System:
The UNT Digital Library
Comparison of Some Mappings in Topology
The main purpose of this paper is the study of transformations in topological space and relationships between special types of transformations.
Date:
January 1964
Creator:
Aslan, Farhad
System:
The UNT Digital Library
A Relation for Point Sets in a Topological Space
The purpose of this thesis is to investigate the relation Z for point sets in a topological space. There were two original goals which caused the study.
Date:
August 1962
Creator:
Warndof, Joseph C.
System:
The UNT Digital Library
Linear Transformations in Linear Spaces
This thesis is a study of linear spaces and linear transformations in normed linear spaces. The notion of a field, in particular the complex number field, is assumed in this paper.
Date:
August 1962
Creator:
Westley, Kent N.
System:
The UNT Digital Library
Plane Curves
The purpose of this thesis is to present a definition and some properties of a curved arc in a plane and to present a definition and some properties of the Jordan curve.
Date:
January 1963
Creator:
Heflin, Billy M.
System:
The UNT Digital Library
Additive Functions
The purpose of this paper is the analysis of functions of real numbers which have a special additive property, namely, f(x+y) = f(x)+f(y).
Date:
June 1963
Creator:
McNeir, Ridge W.
System:
The UNT Digital Library
A Development of the Peano Postulates
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 postulates are assumed. The word class is never used in the thesis, though the variables can be interpreted as classes.
Date:
May 1963
Creator:
Peek, Darwin Eugene
System:
The UNT Digital Library
Euclidean N-space
This study of the Euclidean N-space looks at some definitions and their characteristics, some comparisons, boundedness and compactness, and transformations and mappings.
Date:
August 1962
Creator:
Horner, Donald R.
System:
The UNT Digital Library
Ordered Triples
The purpose of this paper is the investigation of various properties of ordered triples whose components are elements of certain sets.
Date:
August 1962
Creator:
Monozingo, Montie Gene
System:
The UNT Digital Library