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  Partner: UNT Libraries
 Department: Department of Mathematics
 Collection: UNT Theses and Dissertations
Some Effects of the War Upon the Mathematics Curriculum and the Motivating Forces at Work as Reflected in the Dallas City Schools

Some Effects of the War Upon the Mathematics Curriculum and the Motivating Forces at Work as Reflected in the Dallas City Schools

Date: August 1945
Creator: Smith, R. N.
Description: "To discuss the effect all this war activity has had upon the Dallas Schools and to voice a protest against those who seek to discredit mathematics and at the same time to contribute a readable thesis upon the subject is largely the purpose of this study." --leaf 2
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Duals and Weak Completeness in Certain Sequence Spaces

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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Subdirectly Irreducible Semigroups

Subdirectly Irreducible Semigroups

Date: December 1978
Creator: Winton, Richard Alan
Description: Definition 1.1. The ordered pair (S,*) is a semi-group iff S is a set and * is an associative binary operation (multiplication) on S. Notation. A semigroup (S,*) will ordinarily be referred to by the set S, with the multiplication understood. In other words, if (a,b)e SX , then *[(a,b)] = a*b = ab. The proof of the following proposition is found on p. 4 of Introduction to Semigroups, by Mario Petrich. Proposition 1.2. Every semigroup S satisfies the general associative law.
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Interpolation and Approximation

Interpolation and Approximation

Date: May 1977
Creator: Lal, Ram
Description: In this paper, there are three chapters. The first chapter discusses interpolation. Here a theorem about the uniqueness of the solution to the general interpolation problem is proven. Then the problem of how to represent this unique solution is discussed. Finally, the error involved in the interpolation and the convergence of the interpolation process is developed. In the second chapter a theorem about the uniform approximation to continuous functions is proven. Then the best approximation and the least squares approximation (a special case of best approximation) is discussed. In the third chapter orthogonal polynomials as discussed as well as bounded linear functionals in Hilbert spaces, interpolation and approximation and approximation in Hilbert space.
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Complete Ordered Fields

Complete Ordered Fields

Date: August 1977
Creator: Arnold, Thompson Sharon
Description: The purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a least upper bound) and the set of real numbers are also stated. Chapter III presents eight conditions which are equivalent to completeness in an ordered field. These conditions include the concepts of nested intervals, Dedekind cuts, bounded monotonic sequences, convergent subsequences, open coverings, cluster points, Cauchy sequences, and continuous functions.
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The Wallman Spaces and Compactifications

The Wallman Spaces and Compactifications

Date: December 1976
Creator: Liu, Wei-kong
Description: If X is a topological space and Y is a ring of closed sets, then a necessary and sufficient condition for the Wallman space W(X,F) to be a compactification of X is that X be T1 andYF separating. A necessary and sufficient condition for a Wallman compactification to be Hausdoff is that F be a normal base. As a result, not all T, compactifications can be of Wallman type. One point and finite Hausdorff compactifications are of Wallman type.
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Integrability, Measurability, and Summability of Certain Set Functions

Integrability, Measurability, and Summability of Certain Set Functions

Date: December 1977
Creator: Dawson, Dan Paul
Description: The purpose of this paper is to investigate the integrability, measurability, and summability of certain set functions. The paper is divided into four chapters. The first chapter contains basic definitions and preliminary remarks about set functions and absolute continuity. In Chapter i, the integrability of bounded set functions is investigated. The chapter culminates with a theorem that characterizes the transmission of the integrability of a real function of n bounded set functions. In Chapter III, measurability is defined and a characterization of the transmission of measurability by a function of n variables is provided, In Chapter IV, summability is defined and the summability of set functions is investigated, Included is a characterization of the transmission of summability by a function of n variables.
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Hyperspaces

Hyperspaces

Date: December 1976
Creator: Voas, Charles H.
Description: This paper is an exposition of the theory of the hyperspaces 2^X and C(X) of a topological space X. These spaces are obtained from X by collecting the nonempty closed and nonempty closed connected subsets respectively, and are topologized by the Vietoris topology. The paper is organized in terms of increasing specialization of spaces, beginning with T1 spaces and proceeding through compact spaces, compact metric spaces and metric continua. Several basic techniques in hyperspace theory are discussed, and these techniques are applied to elucidate the topological structure of hyperspaces.
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Valuations on Fields

Valuations on Fields

Date: May 1977
Creator: Walker, Catherine A.
Description: This thesis investigates some properties of valuations on fields. Basic definitions and theorems assumed are stated in Capter I. Chapter II introduces the concept of a valuation on a field. Real valuations and non-Archimedean valuations are presented. Chapter III generalizes non-Archimedean valuations. Examples are described in Chapters I and II. A result is the theorem stating that a real valuation of a field K is non-Archimedean if and only if $(a+b) < max4# (a), (b) for all a and b in K. Chapter III generally defines a non-Archimedean valuation as an ordered abelian group. Real non-Archimedean valuations are either discrete or nondiscrete. Chapter III shows that every valuation ring identifies a non-Archimedean valuation and every non-Archimedean valuation identifies a valuation ring.
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Fundamental Issues in Support Vector Machines

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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