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**Partner:**UNT Libraries

**Department:**Department of Mathematics

**Collection:**UNT Theses and Dissertations

### A Development of the Real Number System

**Date:**August 1961

**Creator:**Matthews, Ronald Louis

**Description:**The purpose of this paper is to construct the real number system. The foundation upon which the real number system will be constructed will be the system of counting numbers.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130475/

### A Development of the Real Number System by Means of Nests of Rational Intervals

**Date:**1949

**Creator:**Williams, Mack Lester

**Description:**The system of rational numbers can be extended to the real number system by several methods. In this paper, we shall extend the rational number system by means of rational nests of intervals, and develop the elementary properties of the real numbers obtained by this extension.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc83636/

### Differentiable Functions

**Date:**June 1966

**Creator:**McCool, Kenneth B.

**Description:**The primary purpose of this thesis is to carefully develop and prove some of the fundamental, classical theorems of the differential calculus for functions of two real variables.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130691/

### Differentiation in Banach Spaces

**Date:**December 1972

**Creator:**Heath, James Darrell

**Description:**This thesis investigates the properties and applications of derivatives of functions whose domain and range are Banach spaces.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131585/

### Dimension spectrum and graph directed Markov systems.

**Access:**Use of this item is restricted to the UNT Community.

**Date:**May 2006

**Creator:**Ghenciu, Eugen Andrei

**Description:**In this dissertation we study graph directed Markov systems (GDMS) and limit sets associated with these systems. Given a GDMS S, by the Hausdorff dimension spectrum of S we mean the set of all positive real numbers which are the Hausdorff dimension of the limit set generated by a subsystem of S. We say that S has full Hausdorff dimension spectrum (full HD spectrum), if the dimension spectrum is the interval [0, h], where h is the Hausdorff dimension of the limit set of S. We give necessary conditions for a finitely primitive conformal GDMS to have full HD spectrum. A GDMS is said to be regular if the Hausdorff dimension of its limit set is also the zero of the topological pressure function. We show that every number in the Hausdorff dimension spectrum is the Hausdorff dimension of a regular subsystem. In the particular case of a conformal iterated function system we show that the Hausdorff dimension spectrum is compact. We introduce several new systems: the nearest integer GDMS, the Gauss-like continued fraction system, and the Renyi-like continued fraction system. We prove that these systems have full HD spectrum. A special attention is given to the backward continued fraction ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc5226/

### Dimensions in Random Constructions.

**Date:**May 2002

**Creator:**Berlinkov, Artemi

**Description:**We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc3160/

### Direct Sums of Rings

**Date:**August 1966

**Creator:**Hughes, Dolin F.

**Description:**This paper consists of a study of the direct sum U of two rings S and T. Such a direct sum is defined as the set of all ordered pairs (s1, t1), where s1 is an arbitrary element in S and t1 is an arbitrary element in T.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130723/

### Divisibility in Abelian Groups

**Date:**August 1966

**Creator:**Huie, Douglas Lee

**Description:**This thesis describes properties of Abelian groups, and develops a study of the properties of divisibility in Abelian groups.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130724/

### Dually Semimodular Consistent Lattices

**Date:**May 1988

**Creator:**Gragg, Karen E. (Karen Elizabeth)

**Description:**A lattice L is said to be dually semimodular if for all elements a and b in L, a ∨ b covers b implies that a covers a ∧ b. L is consistent if for every join-irreducible j and every element x in L, the element x ∨ j is a join-irreducible in the upper interval [x,l]. In this paper, finite dually semimodular consistent lattices are investigated. Examples of these lattices are the lattices of subnormal subgroups of a finite group. In 1954, R. P. Dilworth proved that in a finite modular lattice, the number of elements covering exactly k elements is equal to the number of elements covered by exactly k elements. Here, it is established that if a finite dually semimodular consistent lattice has the same number of join-irreducibles as meet-irreducibles, then it is modular. Hence, a converse of Dilworth's theorem, in the case when k equals 1, is obtained for finite dually semimodular consistent lattices. Several combinatorial results are shown for finite consistent lattices similar to those already established for finite geometric lattices. The reach of an element x in a lattice L is the difference between the rank of x*, the join of x and all ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc330641/

### Duals and Weak Completeness in Certain Sequence Spaces

**Date:**August 1980

**Creator:**Leavelle, Tommy L. (Tommy Lee)

**Description:**In this paper the weak completeness of certain sequence spaces is examined. In particular, we show that each of the sequence spaces c0 and 9, 1 < p < c, is a Banach space. A Riesz representation for the dual space of each of these sequence spaces is given. A Riesz representation theorem for Hilbert space is also proven. In the third chapter we conclude that any reflexive space is weakly (sequentially) complete. We give 01 as an example of a non-reflexive space that is weakly complete. Two examples, c0 and YJ, are given of spaces that fail to be weakly complete.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc504338/