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A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence

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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Infinite Matrices

Infinite Matrices

Date: August 1957
Creator: Smallwood, James D.
Description: This paper will be mostly concerned with matrices of infinite order with elements which lie in Hilbert Space. All the properties of real and complex numbers and all the properties of infinite series and infinite sequences that are not listed will be assumed.
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Some Generalizations in the Theory of Summable Series

Some Generalizations in the Theory of Summable Series

Date: August 1950
Creator: Penner, Jimmie G.
Description: It will be our purpose to study a generalized definition of sum of a series and the restrictions which must be placed upon it in order that it shall satisfy the generally accepted requirements of any generalized definition of sum of a series. We shall then proceed to investigate the possibilities of further generalizing this process.
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Some Properties of Dini Derivatives

Some Properties of Dini Derivatives

Date: August 1953
Creator: Pinkerton, Jane W.
Description: The purpose of this paper is to derive certain of the fundamental properties of the Dini derivatives of an arbitrary real function. To this end it will be necessary to investigate the properties of the limits superior and inferior of real functions and to prove the Vitali Covering Theorem as well as a fundamental theorem on the metric density of arbitrary point sets.
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Quaternion Representation of Crystal Point Groups

Quaternion Representation of Crystal Point Groups

Date: August 1959
Creator: West, Richard Harrison
Description: The physical behavior of crystalline solids is very closely related to the internal symmetry of the crystal structure. For this reason it is desirable to represent mathematically this symmetry in such a way that the actual physical problems can be handled as they arise. In the case of this thesis the research has been guided by a list of desired properties for such a representation. No claim is made that the list is complete.
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Quadratic Forms

Quadratic Forms

Date: June 1959
Creator: Cadenhead, Clarence Tandy
Description: This paper shall be mostly concerned with the development and the properties of three quadratic polynomials. The primary interest will by with n-ary quadratic polynomials, called forms.
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Some Diophantine Equations

Some Diophantine Equations

Date: January 1960
Creator: Pressly, Kirby Smith
Description: This paper will be devoted to an examination of several general and specific equations and systems of equations of the diophantine type. Only algebraic equations with integral coefficients, not all zero, will considered. The elementary properties of the integers will be assumed.
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Properties of Order Relations and Certain Partly Ordered Systems

Properties of Order Relations and Certain Partly Ordered Systems

Date: June 1961
Creator: Barros, David Nicholas
Description: The purpose of this paper is to present a study of partly ordered sets. It includes a rigorous development of relations based on the notion of a relation as a set, lattices, and theorems concerning the lattice of subgroups of a group.
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Theory of Congruences

Theory of Congruences

Date: June 1961
Creator: Green, Harold Rugby
Description: This thesis presents a series of theorems along with proofs to establish a theory of congruences.
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Convergence Preserving Matrices

Convergence Preserving Matrices

Date: August 1961
Creator: Line, Harrell Harvey
Description: This paper is the result of a study of triangular matrices with particular emphasis on those which are convergence preserving transformations.
Contributing Partner: UNT Libraries
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