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**Partner:**UNT Libraries

**Department:**Department of Mathematics

**Collection:**UNT Theses and Dissertations

### 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/

### The Fundamental Group of Certain Toplogical Spaces

**Date:**December 1971

**Creator:**Hopkins, Billy L.

**Description:**The problem confronted in this thesis is that of determining direct calculations of the fundamental group of certain topological spaces.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131469/

### Fundamental Issues in Support Vector Machines

**Date:**May 2014

**Creator:**McWhorter, Samuel P.

**Description:**This dissertation considers certain issues in support vector machines (SVMs), including a description of their construction, aspects of certain exponential kernels used in some SVMs, and a presentation of an algorithm that computes the necessary elements of their operation with proof of convergence. In its first section, this dissertation provides a reasonably complete description of SVMs and their theoretical basis, along with a few motivating examples and counterexamples. This section may be used as an accessible, stand-alone introduction to the subject of SVMs for the advanced undergraduate. Its second section provides a proof of the positive-definiteness of a certain useful function here called E and dened as follows: Let V be a complex inner product space. Let N be a function that maps a vector from V to its norm. Let p be a real number between 0 and 2 inclusive and for any in V , let ( be N() raised to the p-th power. Finally, let a be a positive real number. Then E() is exp(()). Although the result is not new (other proofs are known but involve deep properties of stochastic processes) this proof is accessible to advanced undergraduates with a decent grasp of linear algebra. Its ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc500155/

### Fundamental Properties of Fourier Series

**Date:**August 1954

**Creator:**Hubbard, Geogre U.

**Description:**This thesis is intended as an introduction to the study of one type of trigonometric series, the Fourier series.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130383/

### Fundamental Properties of the Contingent

**Date:**August 1960

**Creator:**Haggard, Paul W.

**Description:**This thesis explores the fundamental properties of the contingent.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc108099/

### A Fundamental Study of Cardinal and Ordinal Numbers

**Date:**August 1966

**Creator:**Thornton, Robert Leslie

**Description:**The purpose of this paper is to present a discussion on the basic fundamentals of the theory of sets. Primarily, the discussion will be confined to the study of cardinal and ordinal numbers. The concepts of sets, classes of sets, and families of sets will be undefined quantities, and the concept of the class of all sets will be avoided.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130761/

### Fundamentals of Partially Ordered Sets

**Date:**August 1968

**Creator:**Compton, Lewis W.

**Description:**Gives the basic definitions and theorems of similar partially ordered sets; studies finite partially ordered sets, including the problem of combinatorial analysis; and includes the ideas of complete, dense, and continuous partially ordered sets, including proofs.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130984/

### G-domains, G-ideals, and Hilbert Rings

**Date:**August 1972

**Creator:**Draper, Ruben P.

**Description:**The problem with which this investigation is concerned is that of determining the properties of the following: a particular type of integral domain, the G-domain; a type of prime ideal, the G-ideal; and a special type of ring, the Hilbert ring.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131539/

### A Generalization of Newton's Method

**Date:**1948

**Creator:**LeBouf, Billy Ruth

**Description:**It is our purpose here to investigate the method of solving equations for real roots by Newton's Method and to indicate a generalization arising from this method.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc75705/

### A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence

**Date:**August 1998

**Creator:**Risley, Rebecca N.

**Description:**We investigate a class of minimal sequences on a finite alphabet Ak = {1,2,...,k} having (k - 1)n + 1 distinct subwords of length n. These sequences, originally defined by P. Arnoux and G. Rauzy, are a natural generalization of binary Sturmian sequences. We describe two simple combinatorial algorithms for constructing characteristic Arnoux-Rauzy sequences (one of which is new even in the Sturmian case). Arnoux-Rauzy sequences arising from fixed points of primitive morphisms are characterized by an underlying periodic structure. We show that every Arnoux-Rauzy sequence contains arbitrarily large subwords of the form V^2+ε and, in the Sturmian case, arbitrarily large subwords of the form V^3+ε. Finally, we prove that an irrational number whose base b-digit expansion is an Arnoux-Rauzy sequence is transcendental.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc278440/