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 Degree Discipline: Mathematics
Differentiation in Banach Spaces

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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Dimension spectrum and graph directed Markov systems.

Dimension spectrum and graph directed Markov systems.

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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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Dimensions in Random Constructions.

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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Direct Sums of Rings

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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Divisibility in Abelian Groups

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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Dually Semimodular Consistent Lattices

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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The Dyadic Operator Approach to a Study in Conics, with some Extensions to Higher Dimensions

The Dyadic Operator Approach to a Study in Conics, with some Extensions to Higher Dimensions

Date: 1940
Creator: Shawn, James Loyd
Description: The discovery of a new truth in the older fields of mathematics is a rare event. Here an investigator may hope at best to secure greater elegance in method or notation, or to extend known results by some process of generalization. It is our purpose to make a study of conic sections in the spirit of the above remark, using the symbolism developed by Josiah Williard Gibbs.
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Dynamics of One-Dimensional Maps: Symbols, Uniqueness, and Dimension

Dynamics of One-Dimensional Maps: Symbols, Uniqueness, and Dimension

Date: May 1988
Creator: Brucks, Karen M. (Karen Marie), 1957-
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 formula is given that counts the number of MSS sequences of length n. Next, the number of distinct primitive colorings of n beads with two colors, as counted by Gilbert and Riordan, is shown to equal the number of MSS sequences of length n. An algorithm is given that produces a bisection between these two quantities for each n. Lastly, the number of negative orbits of size n for the function f(z)=z^2-2, as counted by P.J. Myrberg, is shown to equal the number of MSS sequences of length n. For an MSS sequence P, let H_ϖ(P) be the unique common extension of the harmonics of P. In Chapter three it is proved that there is exactly one J(P)Σ[0,1] such that the ...
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Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type

Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type

Date: May 2005
Creator: Coiculescu, Ion
Description: In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff dimension of the set of returning points, is the unique zero of the pressure function. We shall also study conjugacies in the family H, perturbation of functions in the family and related dynamical properties. We define Perron-Frobenius operators for some functions naturally associated with functions in the family H and then, using fundamental properties of these operators, we shall prove the important result that the Hausdorff dimension of the subset of returning points depends analytically on the parameter taken from a small open subset of the n-dimensional parameter space.
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Electronic Analog Computer Study of Effects of Motor Velocity and Driving Voltage Limits upon Servomechanism Performance

Electronic Analog Computer Study of Effects of Motor Velocity and Driving Voltage Limits upon Servomechanism Performance

Date: 1956
Creator: Haynes, Joe Preston
Description: The object of this thesis is (1) to demonstrate the value of an electronic analog computer for the solution of non-linear ordinary differential equations particularly when a large family of solutions is required; and (2) to obtain as a by-product results of practical applicability to servomechanism selection and analysis.
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