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UNT Theses and Dissertations
The Moore-Smith Limit
Date: 1952
Creator: Alexander, Donnie B.
Description: It is the purpose of this thesis to indicate in more detail how various limits defined in analysis, as well as other concepts not ordinarily defined as limits, may be obtained as special cases of the Moore-Smith limit.
Contributing Partner: UNT Libraries
Permallink:digital.library.unt.edu/ark:/67531/metadc107833/
Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups
Access: Use of this item is restricted to the UNT Community.
Date: May 2006
Creator: Alhaddad, Shemsi I.
Description: The Iwahori-Hecke algebras of Coxeter groups play a central role in the study of representations of semisimple Lie-type groups. An important tool is the combinatorial approach to representations of Iwahori-Hecke algebras introduced by Kazhdan and Lusztig in 1979. In this dissertation, I discuss a generalization of the Iwahori-Hecke algebra of the symmetric group that is instead based on the complex reflection group G(r,1,n). Using the analogues of Kazhdan and Lusztig's R-polynomials, I show that this algebra determines a partial order on G(r,1,n) that generalizes the Chevalley-Bruhat order on the symmetric group. I also consider possible analogues of Kazhdan-Lusztig polynomials.
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Permallink:digital.library.unt.edu/ark:/67531/metadc5235/
A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions
Date: August 1954
Creator: Allen, Alfred I.
Description: The purpose of this paper is to define and develop a set of functions of an area in such a manner as to be analogous to the trigonometric and the hyperbolic functions.
Contributing Partner: UNT Libraries
Permallink:digital.library.unt.edu/ark:/67531/metadc130370/
Understanding Ancient Math Through Kepler: A Few Geometric Ideas from The Harmony of the World
Date: August 2002
Creator: Arthur, Christopher
Description: Euclid's geometry is well-known for its theorems concerning triangles and circles. Less popular are the contents of the tenth book, in which geometry is a means to study quantity in general. Commensurability and rational quantities are first principles, and from them are derived at least eight species of irrationals. A recently republished work by Johannes Kepler contains examples using polygons to illustrate these species. In addition, figures having these quantities in their construction form solid shapes (polyhedra) having origins though Platonic philosophy and Archimedean works. Kepler gives two additional polyhedra, and a simple means for constructing the “divine” proportion is given.
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Permallink:digital.library.unt.edu/ark:/67531/metadc3269/
The History of the Calculus
Date: 1945
Creator: Ashburn, Andrew
Description: The purpose of this essay is to trace the development of the concepts of the calculus from their first known appearance, through the formal invention of the method of the calculus in the second half of the seventeenth century, to our own day.
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Permallink:digital.library.unt.edu/ark:/67531/metadc75389/
Comparison of Some Mappings in Topology
Date: January 1964
Creator: Aslan, Farhad
Description: The main purpose of this paper is the study of transformations in topological space and relationships between special types of transformations.
Contributing Partner: UNT Libraries
Permallink:digital.library.unt.edu/ark:/67531/metadc108253/
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/