### Borel Sets and Baire Functions

**Date:**January 1970

**Creator:**Wemple, Fred W.

**Description:**This paper examines the relationship between Borel sets and Baire functions.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc163964/

### The Buckling of a Uniformly Compressed Plate with Intermediate Supports

**Date:**1949

**Creator:**Dean, Thomas S.

**Description:**This problem has been selected from the mathematical theory of elasticity. We consider a rectangular plate of thickness h, length a, and width b. The plate is subjected to compressive forces. These forces act in the neutral plane and give the plate a tendency to buckle. However, this problem differs from other plate problems in that it is assumed that there are two intermediate supports located on the edges of the plate parallel to the compressive forces.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc83479/

### The Cantor Ternary Set and Certain of its Generalizations and Applications

**Date:**1942

**Creator:**Hembree, Gwendolyn

**Description:**This thesis covers the Cantor Ternary Set and generalizations of the Cantor Set, and gives a complete existential theory for three set properties: denumerability, exhaustibility, and zero measure.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc70344/

### Centers of Invariant Differential Operator Algebras for Jacobi Groups of Higher Rank

**Date:**August 2013

**Creator:**Dahal, Rabin

**Description:**Let G be a Lie group acting on a homogeneous space G/K. The center of the universal enveloping algebra of the Lie algebra of G maps homomorphically into the center of the algebra of differential operators on G/K invariant under the action of G. In the case that G is a Jacobi Lie group of rank 2, we prove that this homomorphism is surjective and hence that the center of the invariant differential operator algebra is the image of the center of the universal enveloping algebra. This is an extension of work of Bringmann, Conley, and Richter in the rank 1case.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc283833/

### Certain Properties of Functions Related to Exhaustibility

**Date:**1952

**Creator:**Bradford, James C.

**Description:**In this thesis, we shall attempt to present a study of certain properties of real functions related to the set property exhaustible.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc107821/

### A characterization of homeomorphic Bernoulli trial measures.

**Date:**August 2006

**Creator:**Yingst, Andrew Q.

**Description:**We give conditions which, given two Bernoulli trial measures, determine whether there exists a homeomorphism of Cantor space which sends one measure to the other, answering a question of Oxtoby. We then provide examples, relating these results to the notions of good and refinable measures on Cantor space.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc5331/

### Characterizations of Continua of Finite Degree

**Date:**August 2006

**Creator:**Irwin, Shana

**Description:**In this thesis, some characterizations of continua of finite degree are given. It turns out that being of finite degree (by formal definition) can be described by saying there exists an equivalent metric in which Hausdorff linear measure of the continuum is finite. I discuss this result in detail.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc5367/

### Characterizations of Some Combinatorial Geometries

**Date:**August 1992

**Creator:**Yoon, Young-jin

**Description:**We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic geometries : If a non-splitting supersolvable ternary geometry does not contain the Reid geometry as a subgeometry, then it is signed—graphic.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc277894/

### A Classification of Regular Planar Graphs

**Date:**December 1972

**Creator:**McCalla, Linda F.

**Description:**The purpose of this paper is the investigation and classification of regular planar graphs. The motive behind this investigation was a desire to better understand those properties which allow a graph to be represented in the plane in such a manner that no two edges cross except perhaps at vertices.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc164029/

### A Collapsing Result Using the Axiom of Determinancy and the Theory of Possible Cofinalities

**Date:**May 2001

**Creator:**May, Russell J.

**Description:**Assuming the axiom of determinacy, we give a new proof of the strong partition relation on ω1. Further, we present a streamlined proof that J<λ+(a) (the ideal of sets which force cof Π α < λ) is generated from J<λ+(a) by adding a singleton. Combining these results with a polarized partition relation on ω1

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc2789/