### The Dyadic Operator Approach to a Study in Conics, with some Extensions to Higher Dimensions

**Date:**1940

**Creator:**Shawn, James Loyd

**Description:**The discovery of a new truth in the older fields of mathematics is a rare event. Here an investigator may hope at best to secure greater elegance in method or notation, or to extend known results by some process of generalization. It is our purpose to make a study of conic sections in the spirit of the above remark, using the symbolism developed by Josiah Williard Gibbs.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc75602/

### Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type

**Date:**May 2005

**Creator:**Coiculescu, Ion

**Description:**In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff dimension of the set of returning points, is the unique zero of the pressure function. We shall also study conjugacies in the family H, perturbation of functions in the family and related dynamical properties. We define Perron-Frobenius operators for some functions naturally associated with functions in the family H and then, using fundamental properties of these operators, we shall prove the important result that the Hausdorff dimension of the subset of returning points depends analytically on the parameter taken from a small open subset of the n-dimensional parameter space.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc4783/

### Electronic Analog Computer Study of Effects of Motor Velocity and Driving Voltage Limits upon Servomechanism Performance

**Date:**1956

**Creator:**Haynes, Joe Preston

**Description:**The object of this thesis is (1) to demonstrate the value of an electronic analog computer for the solution of non-linear ordinary differential equations particularly when a large family of solutions is required; and (2) to obtain as a by-product results of practical applicability to servomechanism selection and analysis.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc107908/

### The Elementary Transcendental Functions of a Complex Variable as Defined by Integration

**Date:**1940

**Creator:**Wilson, Carroll K.

**Description:**The object of this paper is to define the elementary transcendental functions of a complex variable by means of integrals, and to discuss their properties.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc70281/

### Elements of Boolean Algebra Theory

**Date:**1957

**Creator:**Harvill, John Bowman

**Description:**The primary purpose of this paper is to state a set of postulates for Boolean algebra and show the characteristic theorems derivable from them, and to unify in one paper the more important methods of representing Boolean algebra and show their equivalence.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc107933/

### Elliptic Geometry

**Date:**January 1966

**Creator:**Robertson, Barbara McKinzie

**Description:**This thesis discusses elliptic geometry including the order and incidence properties, projective properties and congruence properties.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc163883/

### Equivalence Classes of Cauchy Sequences of Rational Numbers

**Date:**January 1965

**Creator:**Darnell, Linda Jane

**Description:**The purpose of this thesis is to define equivalence classes of Cauchy sequences of rational numbers and the operations of taking a sum and a product and then to show that this system is an uncountable, ordered, complete field. In so doing, a mathematical system is obtained which is isomorphic to the real number system.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130561/

### Equivalence Classes of Subquotients of Pseudodifferential Operator Modules on the Line

**Date:**August 2012

**Creator:**Larsen, Jeannette M.

**Description:**Certain subquotients of Vec(R)-modules of pseudodifferential operators from one tensor density module to another are categorized, giving necessary and sufficient conditions under which two such subquotients are equivalent as Vec(R)-representations. These subquotients split under the projective subalgebra, a copy of ????2, when the members of their composition series have distinct Casimir eigenvalues. Results were obtained using the explicit description of the action of Vec(R) with respect to this splitting. In the length five case, the equivalence classes of the subquotients are determined by two invariants. In an appropriate coordinate system, the level curves of one of these invariants are a pencil of conics, and those of the other are a pencil of cubics.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc149627/

### Euclidean N-space

**Date:**August 1962

**Creator:**Horner, Donald R.

**Description:**This study of the Euclidean N-space looks at some definitions and their characteristics, some comparisons, boundedness and compactness, and transformations and mappings.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc108157/

### Examples and Applications of Infinite Iterated Function Systems

**Date:**August 2000

**Creator:**Hanus, Pawel Grzegorz

**Description:**The aim of this work is the study of infinite conformal iterated function systems. More specifically, we investigate some properties of a limit set J associated to such system, its Hausdorff and packing measure and Hausdorff dimension. We provide necessary and sufficient conditions for such systems to be bi-Lipschitz equivalent. We use the concept of scaling functions to obtain some result about 1-dimensional systems. We discuss particular examples of infinite iterated function systems derived from complex continued fraction expansions with restricted entries. Each system is obtained from an infinite number of contractions. We show that under certain conditions the limit sets of such systems possess zero Hausdorff measure and positive finite packing measure. We include an algorithm for an approximation of the Hausdorff dimension of limit sets. One numerical result is presented. In this thesis we also explore the concept of positively recurrent function. We use iterated function systems to construct a natural, wide class of such functions that have strong ergodic properties.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc2642/