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Connectedness and Some Concepts Related to Connectedness of a Topological Space
The purpose of this thesis is to investigate the idea of topological "connectedness" by presenting some of the basic ideas concerning connectedness along with several related concepts.
Date:
August 1969
Creator:
Wallace, Michael A.
System:
The UNT Digital Library
Atmospheric Gusts and Their Effect on Aircraft
This thesis investigates atmospheric gusts and their effect on aircraft.
Date:
August 1958
Creator:
Walling, Waunnetta Keene
System:
The UNT Digital Library
Iterative Solution of Linear Boundary Value Problems
The investigation is initially a continuation of Neuberger's work on linear boundary value problems. A very general iterative procedure for solution of these problems is described. The alternating-projection theorem of von Neumann is the mathematical starting point for this study. Later theorems demonstrate the validity of numerical approximation for Neuberger's method under certain conditions. A sampling of differential equations within the scope of our iterative method is given. The numerical evidence is that the procedure works well on neutral-state equations, for which no software is written now.
Date:
August 1983
Creator:
Walsh, John Breslin
System:
The UNT Digital Library
Topics in Fractal Geometry
In this dissertation, we study fractal sets and their properties, especially the open set condition, Hausdorff dimensions and Hausdorff measures for certain fractal constructions.
Date:
August 1994
Creator:
Wang, JingLing
System:
The UNT Digital Library
Some Properties of the Cantor Set
The purpose of this paper is to explore some of the properties of the Cantor set and to extend the idea of this set to metric spaces, in general, and to other sets of real numbers and sets in N-dimensional Euclidean space, in particular.
Date:
August 1965
Creator:
Ward, Jo Alice
System:
The UNT Digital Library
A Relation for Point Sets in a Topological Space
The purpose of this thesis is to investigate the relation Z for point sets in a topological space. There were two original goals which caused the study.
Date:
August 1962
Creator:
Warndof, Joseph C.
System:
The UNT Digital Library
Linear Transformations in Linear Spaces
This thesis is a study of linear spaces and linear transformations in normed linear spaces. The notion of a field, in particular the complex number field, is assumed in this paper.
Date:
August 1962
Creator:
Westley, Kent N.
System:
The UNT Digital Library
Lyapunov Exponents, Entropy and Dimension
We consider diffeomorphisms of a compact Riemann Surface. A development of Oseledec's Multiplicative Ergodic Theorem is given, along with a development of measure theoretic entropy and dimension. The main result, due to L.S. Young, is that for certain diffeomorphisms of a surface, there is a beautiful relationship between these three concepts; namely that the entropy equals dimension times expansion.
Date:
August 2004
Creator:
Williams, Jeremy M.
System:
The UNT Digital Library
The Riesz Representation Theorem
In 1909, F. Riesz succeeded in giving an integral represntation for continuous linear functionals on C[0,1]. Although other authors, notably Hadamard and Frechet, had given representations for continuous linear functionals on C[0,1], their results lacked the clarity, elegance, and some of the substance (uniqueness) of Riesz's theorem. Subsequently, the integral representation of continuous linear functionals has been known as the Riesz Representation Theorem. In this paper, three different proofs of the Riesz Representation Theorem are presented. The first approach uses the denseness of the Bernstein polynomials in C[0,1] along with results of Helly to write the continuous linear functionals as Stieltjes integrals. The second approach makes use of the Hahn-Banach Theorem in order to write the functional as an integral. The paper concludes with a detailed presentation of a Daniell integral development of the Riesz Representation Theorem.
Date:
August 1980
Creator:
Williams, Stanley C. (Stanley Carl)
System:
The UNT Digital Library
Universally Measurable Sets And Nonisomorphic Subalgebras
This dissertation is divided into two parts. The first part addresses the following problem: Suppose 𝑣 is a finitely additive probability measure defined on the power set 𝒜 of the integer Z so that each singleton set gets measure zero. Let X be a product space Π/β∈B * Zᵦ where each Zₐ is a copy of the integers. Let 𝒜ᴮ be the algebra of subsets of X generated by the subproducts Π/β∈B * Cᵦ where for all but finitely many β, Cᵦ = Zᵦ. Let 𝑣_B denote the product measure on 𝒜ᴮ which has each factor measure a copy of 𝑣. A subset E of X is said to be 𝑣_B -measurable iff [sic] there is only one finitely additive probability on the algebra generated by 𝒜ᴮ ∪ [E] which extends 𝑣_B. The set E ⊆ X is said to be universally product measurable (u.p.m.) iff [sic] for each finitely additive probability measure μ on 𝒜 which gives each singleton measure zero,E is μ_B -measurable. Two theorems are proved along with generalizations. The second part of this dissertation gives a proof of the following theorem and some generalizations: There are 2ᶜ nonisomorphic subalgebras of the power set algebra of the …
Date:
August 1983
Creator:
Williams, Stanley C. (Stanley Carl)
System:
The UNT Digital Library
Stieljes Integral and Related Topics
The principal purpose of this paper is to develop the properties of Riemann-Stieljes Integrals. Consequently, a knowledge of the terminology and theory of point sets and functions of real variables shall be assumed.
Date:
August 1958
Creator:
Willis, Charles L.
System:
The UNT Digital Library
Continuity of Hausdorff Dimension of Julia Sets of Expansive Polynomials
This dissertation is in the area of complex dynamics, more specifically focused on the iteration of rational functions. Given a well-chosen family of rational functions, parameterized by a complex parameter, we are especially interested in regularity properties of the Hausdorff dimension of Julia sets of these polynomials considered as a function of the parameters. In this dissertation I deal with a family of polynomials of degree at least 3 depending in a holomorphic way on a parameter, focusing on the point where the dynamics and topology of the polynomials drastically change. In such a context proving continuity is quite challenging while real analyticity will most likely break. Our approach will, on the one hand, build on the existing methods of proving continuity of Hausdorff dimension, primarily based on proving continuity, in the weak* topology of measures on the Riemann sphere, of canonical conformal measures, but will also require methods which, up to my best knowledge, have not been implemented anywhere yet. Our main result gives a surprising example where the Hausdorff dimension of the Julia set is continuous in the parameter, but where the Julia set itself is not.
Date:
August 2022
Creator:
Wilson, Timothy Charles
System:
The UNT Digital Library
On Continuity of Functions Defined on Unrestricted Point Sets
This thesis is concerned with an investigation of the generalizations of continuous real functions of a real variable. In particular, the relationship between uniform continuity and ordinary continuity is concerned. The concept of uniform continuity was first introduced by Heine about 1900.
Date:
August 1958
Creator:
Wilson, Ural
System:
The UNT Digital Library
A Global Spatial Model for Loop Pattern Fingerprints and Its Spectral Analysis
Access:
Use of this item is restricted to the UNT Community
The use of fingerprints for personal identification has been around for thousands of years (first established in ancient China and India). Fingerprint identification is based on two basic premises that the fingerprint is unique to an individual and the basic characteristics such as ridge pattern do not change over time. Despite extensive research, there are still mathematical challenges in characterization of fingerprints, matching and compression. We develop a new mathematical model in the spatial domain for globally modeling loop pattern fingerprints. Although it is based on the well-known AM-FM (amplitude modulation and frequency modulation) image representation, the model is constructed by a global mathematical function for the continuous phase and it provides a flexible parametric model for loop pattern fingerprints. In sharp contrast to the existing methods, we estimate spatial parameters from the spectral domain by combining the exact values of frequencies with their orientations perpendicular to the fingerprint ridge flow. In addition, to compress fingerprint images and test background Gaussian white noise, we propose a new method based on periodogram spacings. We obtain the joint pdf of these m-dependent random variables at Fourier frequencies and derive the asymptotic distribution of the test statistic.
Date:
August 2019
Creator:
Wu, Di
System:
The UNT Digital Library
On Steinhaus Sets, Orbit Trees and Universal Properties of Various Subgroups in the Permutation Group of Natural Numbers
In the first chapter, we define Steinhaus set as a set that meets every isometric copy of another set at exactly one point. We show that there is no Steinhaus set for any four-point subset in a plane.In the second chapter, we define the orbit tree of a permutation group of natural numbers, and further introduce compressed orbit trees. We show that any rooted finite tree can be realized as a compressed orbit tree of some permutation group. In the third chapter, we investigate certain classes of closed permutation groups of natural numbers with respect to their universal and surjectively universal groups. We characterize two-sided invariant groups, and prove that there is no universal group for countable groups, nor universal group for two-sided invariant groups in permutation groups of natural numbers.
Date:
August 2012
Creator:
Xuan, Mingzhi
System:
The UNT Digital Library
A General Approach to Buhlmann Credibility Theory
Credibility theory is widely used in insurance. It is included in the examination of the Society of Actuaries and in the construction and evaluation of actuarial models. In particular, the Buhlmann credibility model has played a fundamental role in both actuarial theory and practice. It provides a mathematical rigorous procedure for deciding how much credibility should be given to the actual experience rating of an individual risk relative to the manual rating common to a particular class of risks. However, for any selected risk, the Buhlmann model assumes that the outcome random variables in both experience periods and future periods are independent and identically distributed. In addition, the Buhlmann method uses sample mean-based estimators to insure the selected risk, which may be a poor estimator of future costs if only a few observations of past events (costs) are available. We present an extension of the Buhlmann model and propose a general method based on a linear combination of both robust and efficient estimators in a dependence framework. The performance of the proposed procedure is demonstrated by Monte Carlo simulations.
Date:
August 2017
Creator:
Yan, Yujie yy
System:
The UNT Digital Library
A Characterization of Homeomorphic Bernoulli Trial Measures.
We give conditions which, given two Bernoulli trial measures, determine whether there exists a homeomorphism of Cantor space which sends one measure to the other, answering a question of Oxtoby. We then provide examples, relating these results to the notions of good and refinable measures on Cantor space.
Date:
August 2006
Creator:
Yingst, Andrew Q.
System:
The UNT Digital Library
Characterizations of Some Combinatorial Geometries
We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic geometries : If a non-splitting supersolvable ternary geometry does not contain the Reid geometry as a subgeometry, then it is signed—graphic.
Date:
August 1992
Creator:
Yoon, Young-jin
System:
The UNT Digital Library
Schwarz Differentiability
The primary purpose of this paper is to develop a rigorous study of the Schwarz derivative. This study will be based primarily on the comparison of the ordinary derivative to the Schwarz derivative.
Date:
August 1968
Creator:
Young, William G.
System:
The UNT Digital Library
Topological Conjugacy Relation on the Space of Toeplitz Subshifts
We proved that the topological conjugacy relation on $T_1$, a subclass of Toeplitz subshifts, is hyperfinite, extending Kaya's result that the topological conjugate relation of Toeplitz subshifts with growing blocks is hyperfinite. A close concept about the topological conjugacy is the flip conjugacy, which has been broadly studied in terms of the topological full groups. Particularly, we provided an equivalent characterization on Toeplitz subshifts with single hole structure to be flip invariant.
Date:
August 2022
Creator:
Yu, Ping
System:
The UNT Digital Library
Steepest Sescent on a Uniformly Convex Space
This paper contains four main ideas. First, it shows global existence for the steepest descent in the uniformly convex setting. Secondly, it shows existence of critical points for convex functions defined on uniformly convex spaces. Thirdly, it shows an isomorphism between the dual space of H^{1,p}[0,1] and the space H^{1,q}[0,1] where p > 2 and {1/p} + {1/q} = 1. Fourthly, it shows how the Beurling-Denny theorem can be extended to find a useful function from H^{1,p}[0,1] to L_{p}[1,0] where p > 2 and addresses the problem of using that function to establish a relationship between the ordinary and the Sobolev gradients. The paper contains some numerical experiments and two computer codes.
Date:
August 1995
Creator:
Zahran, Mohamad M.
System:
The UNT Digital Library