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**Degree Discipline:**Mathematics

**Collection:**UNT Theses and Dissertations

### Uniqueness Results for the Infinite Unitary, Orthogonal and Associated Groups

**Date:**May 2008

**Creator:**Atim, Alexandru Gabriel

**Description:**Let H be a separable infinite dimensional complex Hilbert space, let U(H) be the Polish topological group of unitary operators on H, let G be a Polish topological group and φ:G→U(H) an algebraic isomorphism. Then φ is a topological isomorphism. The same theorem holds for the projective unitary group, for the group of *-automorphisms of L(H) and for the complex isometry group. If H is a separable real Hilbert space with dim(H)≥3, the theorem is also true for the orthogonal group O(H), for the projective orthogonal group and for the real isometry group. The theorem fails for U(H) if H is finite dimensional complex Hilbert space.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc6136/

### Infinite Planar Graphs

**Date:**May 2000

**Creator:**Aurand, Eric William

**Description:**How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs. Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the identity automorphism.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc2545/

### A Method for Approximating the Distributed Loads of an Airplane by Sets of Point Loads

**Date:**1957

**Creator:**Austin, Charles Wayne

**Description:**This paper gives the derivation of a method for determining the forces to be applied to these points which will simulate the load distributed over all the airplane.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc107936/

### Uniformly σ-Finite Disintegrations of Measures

**Date:**August 2011

**Creator:**Backs, Karl

**Description:**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.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc84165/

### π-regular Rings

**Date:**May 1993

**Creator:**Badawi, Ayman R.

**Description:**The dissertation focuses on the structure of π-regular (regular) rings.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc279388/

### Complemented Subspaces of Bounded Linear Operators

**Date:**August 2003

**Creator:**Bahreini Esfahani, Manijeh

**Description:**For many years mathematicians have been interested in the problem of whether an operator ideal is complemented in the space of all bounded linear operators. In this dissertation the complementation of various classes of operators in the space of all bounded linear operators is considered. This paper begins with a preliminary discussion of linear bounded operators as well as operator ideals. Let L(X, Y ) be a Banach space of all bounded linear operator between Banach spaces X and Y , K(X, Y ) be the space of all compact operators, and W(X, Y ) be the space of all weakly compact operators. We denote space all operator ideals by O.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc4349/

### Level Curves of the Angle Function of a Positive Definite Symmetric Matrix

**Access:**Use of this item is restricted to the UNT Community.

**Date:**December 2009

**Creator:**Bajracharya, Neeraj

**Description:**Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following question: if A and B are commuting positive definite symmetric matrices such that p(A) + p(B) is obtuse, what is the minimal p(S) such that {A, SBS^(-1)} indefinite? In this dissertation we will describe the level curves of the angle function mapping a unit vector x to the angle between x and Ax for a 3 by 3 PDS matrix A, and discuss their interaction with those of a second such matrix.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc28376/

### Near-Rings

**Date:**May 1972

**Creator:**Baker, Edmond L.

**Description:**The primary objective of this work is to discuss some of the elementary properties of near-rings as they are related to rings. This study is divided into three subdivisions: (1) Basic Properties and Concepts of Near-Rings; (2) The Ideal Structure of Near-Rings; and (3) Homomorphism and Isomorphism of Near-Rings.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131500/

### Completely Simple Semigroups

**Date:**August 1968

**Creator:**Barker, Bruce W.

**Description:**The purpose of this thesis is to explore some of the characteristics of 0-simple semigroups and completely 0-simple semigroups.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130974/

### T-Functions

**Date:**June 1960

**Creator:**Barlow, John Rice

**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.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc108077/