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Spaces of H-Integrable Functions

Description: In this thesis we consider integrals of a certain class of interval functions. Specifically we consider a nondegenerate number interval [a,b], a real valued function m, defined and nondecreasing on [a,b], and the set Hm, of real valued functions f, defined on [a,b] such that: 1) f(a)=0; 2) for each subinterval [p,q] of [a,b], if m(q)-m(p)=0, then f(q)-f(p)=0; and 3) the set of all sums of the form Σ(Δf)2/Δm for subdivisions D of [a,b] is bounded above.
Date: May 1968
Creator: Wittenmyer, Eugene L.
Item Type: Refine your search to only Thesis or Dissertation
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Polynomial Curve and Surface Fitting

Description: The main problems of numerical analysis involve performing analytical operations, such as integration, differentiation, finding zeroes, interpolation, and so forth, of a function when all the data available are some samples of the function. Therefore, the purpose of this paper is to investigate the following problem: given a set of data points (x[sub i], y[sub i]) which are samples of some function, determine an approximating function. Further, extend the problem to that of determining an appro… more
Date: January 1968
Creator: Capps, Ann Dowdy
Item Type: Refine your search to only Thesis or Dissertation
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A Study of Functions on Metric Spaces

Description: This thesis describes various forms of metric spaces and establishes some of the properties of functions defined on metric spaces. No attempt is made in this paper to examine a particular type of function in detail. Instead, some of properties of several kinds of functions will be observed as the functions are defined on various forms of metric spaces such as connected spaces, compact spaces, complete spaces, etc.
Date: January 1968
Creator: Brice, Richard S.
Item Type: Refine your search to only Thesis or Dissertation
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Compactness and Equivalent Notions

Description: One of the classic theorems concerning the real numbers states that every open cover of a closed and bounded subset of the real line contains a finite subcover. Compactness is an abstraction of that notion, and there are several ideas concerning it which are equivalent and many which are similar. The purpose of this paper is to synthesize the more important of these ideas. This synthesis is accomplished by demonstrating either situations in which two ordinarily different conditions are equivale… more
Date: August 1967
Creator: Bell, Wayne Charles
Item Type: Refine your search to only Thesis or Dissertation
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Field Extensions and Galois Theory

Description: This paper will be devoted to an exposition of some of the relationships existing between a field and certain of its extension fields. In particular, it will be shown that many fields may be characterized rather simply in terms of their subfields which, in turn, may be directly correlated with the subgroups of a finite group of automorphisms of the given field.
Date: August 1967
Creator: Votaw, Charles I.
Item Type: Refine your search to only Thesis or Dissertation
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A Generalized Study of the Conjugate and Inner-Product Functions

Description: The usual practice in any discussion of an inner-product space is to restrict the field over which the inner-product space is defined to the field of complex numbers. In defining the inner-product function, (x,y), a second function is needed; namely the conjugate function (x,y)* so that (x,y) ± (y,x)*. We will attempt to generalize this concept by investigating the existence of a conjugate function defined on fields other than the field of complex numbers and relate this function to an inner-pr… more
Date: June 1967
Creator: Wright, Dorothy P.
Item Type: Refine your search to only Thesis or Dissertation
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Some Properties of the Fibonacci Numbers

Description: This thesis is presented as an introduction to the Fibonacci sequence of integers. It is hoped that this thesis will create in the reader more interest in this type of sequence and especially the Fibonacci sequence. It seems that this particular area of mathematics is often ignored in the classroom or touched upon far too briefly to stimulate curiosity and develop further interest in this field.
Date: June 1967
Creator: Willey, Wm. Riley
Item Type: Refine your search to only Thesis or Dissertation
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Direct Sums of Rings

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.
Date: August 1966
Creator: Hughes, Dolin F.
Item Type: Refine your search to only Thesis or Dissertation
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A Fundamental Study of Cardinal and Ordinal Numbers

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.
Date: August 1966
Creator: Thornton, Robert Leslie
Item Type: Refine your search to only Thesis or Dissertation
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Lattices

Description: Because lattice theory is so vast, the primary purpose of this paper will be to present some of the general properties of lattices, exhibit examples of lattices, and discuss the properties of distributive and modular lattices.
Date: August 1966
Creator: Rintala, Richard Arne
Item Type: Refine your search to only Thesis or Dissertation
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On Bounded Variation

Description: This paper is primarily concerned with developing the theory of real-valued functions of bounded variation and those ideas which are closely related to this main topic. In addition to this, some emphasis has been placed on the relationship of the theory of functions of bounded variation to specific areas of analysis. In particular, integration theory has been chosen as the vehicle to demonstrate this connection.
Date: August 1966
Creator: Lewis, Paul Weldon
Item Type: Refine your search to only Thesis or Dissertation
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The Role of the Quasigroup in the Development of Binary Systems

Description: The objective here is to give a logical development of some mathematical systems beginning with those having relatively little algebraic structure, and progressing to systems rich in structure. The discussion will commence with a mathematical system called the groupoid, a nonempty set with a binary operation.
Date: August 1966
Creator: Stingel, Charles Willard
Item Type: Refine your search to only Thesis or Dissertation
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Semigroups

Description: The purpose of this paper is to present some fundamental properties of algebraic semigroups. The development of the theory of semigroups has appeared for the most part in the past few years of this century. A semigroup is the result of a weakening of the axioms for a group. Thus all groups are semigroups. That the study of semigroups is very closely related to the abstract study of general transformations is, perhaps, one of the reasons for the rapid development of semigroup theory.
Date: August 1966
Creator: Jeter, Melvyn W.
Item Type: Refine your search to only Thesis or Dissertation
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Some Properties of Partially Ordered Sets

Description: It may be said of certain pairs of elements of a set that one element precedes the other. If the collection of all such pairs of elements in a given set exhibits certain properties, the set and the collection of pairs is said to constitute a partially ordered set. The purpose of this paper is to explore some of the properties of partially ordered sets.
Date: August 1966
Creator: Hudson, Philip Wayne
Item Type: Refine your search to only Thesis or Dissertation
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