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Banach Spaces and Weak and Weak* Topologies

Description: This paper examines several questions regarding Banach spaces, completeness and compactness of Banach spaces, dual spaces and weak and weak* topologies. Examples of completeness and isometries are given using the c₀ and 𝓁ᴰ spaces. The Hahn-Banach extension theorem is presented, along with some applications. General theory about finite and infinite dimensional normed linear spaces is the bulk of the second chapter. A proof of the uniform boundedness principle is also given. Chapter three talks i… more
Date: August 1989
Creator: Kirk, Andrew F. (Andrew Fitzgerald)
Item Type: Refine your search to only Thesis or Dissertation
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Hausdorff, Packing and Capacity Dimensions

Description: In this thesis, Hausdorff, packing and capacity dimensions are studied by evaluating sets in the Euclidean space R^. Also the lower entropy dimension is calculated for some Cantor sets. By incorporating technics of Munroe and of Saint Raymond and Tricot, outer measures are created. A Vitali covering theorem for packings is proved. Methods (by Taylor and Tricot, Kahane and Salem, and Schweiger) for determining the Hausdorff and capacity dimensions of sets using probability measures are discussed… more
Date: August 1989
Creator: Spear, Donald W.
Item Type: Refine your search to only Thesis or Dissertation
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The Maximum Size of Combinatorial Geometries Excluding Wheels and Whirls as Minors

Description: We show that the maximum size of a geometry of rank n excluding the (q + 2)-point line, the 3-wheel W_3, and the 3-whirl W^3 as minor is (n - 1)q + 1, and geometries of maximum size are parallel connections of (q + 1)-point lines. We show that the maximum size of a geometry of rank n excluding the 5-point line, the 4-wheel W_4, and the 4-whirl W^4 as minors is 6n - 5, for n ≥ 3. Examples of geometries having rank n and size 6n - 5 include parallel connections of the geometries V_19 and PG(2,3).
Date: August 1989
Creator: Hipp, James W. (James William), 1956-
Item Type: Refine your search to only Thesis or Dissertation
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Properties of R-Modules

Description: This thesis investigates some of the properties of R-modules. The material is presented in three chapters. Definitions and theorems which are assumed are stated in Chapter I. Proofs of these theorems may be found in Zariski and Samuel, Commutative Algebra, Vol. I, 1958. It is assumed that the reader is familiar with the basic properties of commutative rings and ideals in rings. Properties of R-modules are developed in Chapter II. The most important results presented in this chapter include exis… more
Date: August 1989
Creator: Granger, Ginger Thibodeaux
Item Type: Refine your search to only Thesis or Dissertation
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Applications of Graph Theory and Topology to Combinatorial Designs

Description: This dissertation is concerned with the existence and the isomorphism of designs. The first part studies the existence of designs. Chapter I shows how to obtain a design from a difference family. Chapters II to IV study the existence of an affine 3-(p^m,4,λ) design where the v-set is the Galois field GF(p^m). Associated to each prime p, this paper constructs a graph. If the graph has a 1-factor, then a difference family and hence an affine design exists. The question arises of how to determine … more
Date: December 1988
Creator: Somporn Sutinuntopas
Item Type: Refine your search to only Thesis or Dissertation
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On the Development of Descriptive Set Theory

Description: In the thesis, the author traces the historical development of descriptive set theory from the work of H. Lebesgue to the introduction of projective descriptive set theory. Proofs of most of the major results are given. Topics covered include Corel lattices, universal sets, the operation A, analytic sets, coanalytic sets, and the continuum hypothesis The appendix contains a translation of the famous letters exchanged between R. Baire, E. Borel, J. Hadamard and H. Lebesgue concerning Zermelo's a… more
Date: August 1988
Creator: Schlee, Glen A. (Glen Alan)
Item Type: Refine your search to only Thesis or Dissertation
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Operators on Continuous Function Spaces and Weak Precompactness

Description: If T:C(H,X)-->Y is a bounded linear operator then there exists a unique weakly regular finitely additive set function m:-->L(X,Y**) so that T(f) = ∫Hfdm. In this paper, bounded linear operators on C(H,X) are studied in terms the measure given by this representation theorem. The first chapter provides a brief history of representation theorems of these classes of operators. In the second chapter the represenation theorem used in the remainder of the paper is presented. If T is a weakly compact o… more
Date: August 1988
Creator: Abbott, Catherine Ann
Item Type: Refine your search to only Thesis or Dissertation
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Dually Semimodular Consistent Lattices

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… more
Date: May 1988
Creator: Gragg, Karen E. (Karen Elizabeth)
Item Type: Refine your search to only Thesis or Dissertation
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Dynamics of One-Dimensional Maps: Symbols, Uniqueness, and Dimension

Description: This dissertation is a study of the dynamics of one-dimensional unimodal maps and is mainly concerned with those maps which are trapezoidal. The trapezoidal function, f_e, is defined for eΣ(0,1/2) by f_e(x)=x/e for xΣ[0,e], f_e(x)=1 for xΣ(e,1-e), and f_e(x)=(1-x)/e for xΣ[1-e,1]. We study the symbolic dynamics of the kneading sequences and relate them to the analytic dynamics of these maps. Chapter one is an overview of the present theory of Metropolis, Stein, and Stein (MSS). In Chapter two a… more
Date: May 1988
Creator: Brucks, Karen M. (Karen Marie), 1957-
Item Type: Refine your search to only Thesis or Dissertation
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Containment Relations Between Classes of Regular Ideals in a Ring with Few Zero Divisors

Description: This dissertation focuses on the significance of containment relations between the above mentioned classes of ideals. The main problem considered in Chapter II is determining conditions which lead a ring to be a P-ring, D-ring, or AM-ring when every regular ideal is a P-ideal, D-ideal, or AM-ideal, respectively. We also consider containment relations between classes of regular ideals which guarantee that the ring is a quasi-valuation ring. We continue this study into the third chapter; in parti… more
Date: May 1987
Creator: Race, Denise T. (Denise Tatsch)
Item Type: Refine your search to only Thesis or Dissertation
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Invertible Ideals and the Strong Two-Generator Property in Some Polynomial Subrings

Description: Let K be any field and Q be the rationals. Define K^1[X] = {f(X) e K[X]| the coefficient of X in f(X) is zero} and Q^1β[X] = {f(X) e Q[X]| the coefficent of β1(X) in the binomial expansion of f(X) is zero}, where {β1(X)}^∞ i=0 are the well-known binomial polynomials. In this work, I establish the following results: K^1[X] and Q^1β[X] are one-dimensional, Noetherian, non-Prüfer domains with the two-generator property on ideals. Using the unique factorization structure of the overrings K[X] and Q… more
Date: May 1987
Creator: Chapman, Scott T. (Scott Thomas)
Item Type: Refine your search to only Thesis or Dissertation
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Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial

Description: The problem under consideration is that of determining a simple and effective invariant of knots. To this end, the Conway polynomial is defined as a generalization of Alexander's original knot polynomial. It is noted, however, that the Conway polynomial is not a complete invariant. If two knots are equivalent, as defined in this investigation, then they receive identical polynomials. Yet, if two knots have identical polynomials, no information about their equivalence may be obtained. To define … more
Date: December 1986
Creator: Woodard, Mary Kay
Item Type: Refine your search to only Thesis or Dissertation
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Automorphism Groups of Strong Bruhat Orders of Coxeter Groups

Description: In this dissertation, we describe the automorphism groups for the strong Bruhat orders A_n-1, B_n, and D_n. In particular, the automorphism group of A_n-1 for n ≥ 3 is isomorphic to the dihedral group of order eight, D_4; the automorphism group of B_n for n ≥ 3 is isomorphic to C_2 x C_2 where C_2 is the cyclic group of order two; the automorphism group of D_n for n > 5 and n even is isomorphic to C_2 x C_2 x C_2; and the automorphism group of D_n for n ≥ 5 and n odd is isomorphic to the dihedr… more
Date: August 1986
Creator: Sutherland, David C. (David Craig)
Item Type: Refine your search to only Thesis or Dissertation
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Dimension Theory

Description: This paper contains a discussion of topological dimension theory. Original proofs of theorems, as well as a presentation of theorems and proofs selected from Ryszard Engelking's Dimension Theory are contained within the body of this endeavor. Preliminary notation is introduced in Chapter I. Chapter II consists of the definition of and theorems relating to the small inductive dimension function Ind. Large inductive dimension is investigated in Chapter III. Chapter IV comprises the definition of … more
Date: August 1986
Creator: Frere, Scot M. (Scot Martin)
Item Type: Refine your search to only Thesis or Dissertation
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Consistency in Lattices

Description: Let L be a lattice. For x ∈ L, we say x is a consistent join-irreducible if x V y is a join-irreducible of the lattice [y,1] for all y in L. We say L is consistent if every join-irreducible of L is consistent. In this dissertation, we study the notion of consistent elements in semimodular lattices.
Date: May 1986
Creator: Race, David M. (David Michael)
Item Type: Refine your search to only Thesis or Dissertation
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Some Properties of Noetherian Rings

Description: This paper is an investigation of several basic properties of noetherian rings. Chapter I gives a brief introduction, statements of definitions, and statements of theorems without proof. Some of the main results in the study of noetherian rings are proved in Chapter II. These results include proofs of the equivalence of the maximal condition, the ascending chain condition, and that every ideal is finitely generated. Some other results are that if a ring R is noetherian, then R[x] is noetherian… more
Date: May 1986
Creator: Vaughan, Stephen N. (Stephen Nick)
Item Type: Refine your search to only Thesis or Dissertation
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The Mean Integral

Description: The purpose of this paper is to examine properties of the mean integral. The mean integral is compared with the regular integral. If [a;b] is an interval, f is quasicontinuous on [a;b] and g has bounded variation on [a;b], then the man integral of f with respect to g exists on [a;b]. The following theorem is proved. If [a*;b*] and [a;b] each is an interval and h is a function from [a*;b*] into R, then the following two statements are equivalent: 1) If f is a function from [a;b] into [a*;b*], gi… more
Date: December 1985
Creator: Spear, Donald W.
Item Type: Refine your search to only Thesis or Dissertation
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An Existence Theorem for an Integral Equation

Description: The principal theorem of this thesis is a theorem by Peano on the existence of a solution to a certain integral equation. The two primary notions underlying this theorem are uniform convergence and equi-continuity. Theorems related to these two topics are proved in Chapter II. In Chapter III we state and prove a classical existence and uniqueness theorem for an integral equation. In Chapter IV we consider the approximation on certain functions by means of elementary expressions involving "bent … more
Date: May 1985
Creator: Hunt, Cynthia Young
Item Type: Refine your search to only Thesis or Dissertation
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Nonlinear Boundary Conditions in Sobolev Spaces

Description: The method of dual steepest descent is used to solve ordinary differential equations with nonlinear boundary conditions. A general boundary condition is B(u) = 0 where where B is a continuous functional on the nth order Sobolev space Hn[0.1J. If F:HnCO,l] —• L2[0,1] represents a 2 differential equation, define *(u) = 1/2 IIF < u) li and £(u) = 1/2 l!B(u)ll2. Steepest descent is applied to the functional 2 £ a * + £. Two special cases are considered. If f:lR —• R is C^(2), a Type I boundary con… more
Date: December 1984
Creator: Richardson, Walter Brown
Item Type: Refine your search to only Thesis or Dissertation
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The Reciprocal Dunford-Pettis and Radon-Nikodym Properties in Banach Spaces

Description: In this paper we give a characterization theorem for the reciprocal Dunford-Pettis property as defined by Grothendieck. The relationship of this property to Pelczynski's property V is examined. In particular it is shown that every Banach space with property V has the reciprocal Dunford-Pettis property and an example is given to show that the converse fails to hold. Moreover the characterizations of property V and the reciprocal Dunford-Pettis property lead to the definitions of property V* and … more
Date: August 1984
Creator: Leavelle, Tommy L. (Tommy Lee)
Item Type: Refine your search to only Thesis or Dissertation
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