Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 106-107). Available also in a digital version from Dissertation Abstracts.

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Thesis (Ph. D.)--University of North Texas, May, 2008. / Title from title page display. Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 1999. / Includes bibliographical references. Also available on the Internet.

Orientador: Jorge Tulio Mujica Ascui / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-08T22:02:35Z (GMT). No. of bitstreams: 1 Kuo_PoLing_D.pdf: 378648 bytes, checksum: 3724407371cc36985fd2257b4bc5fe8c (MD5) Previous issue date: 2007 / Resumo: Este trabalho está dedicado ao estudo dos operadores de Nicodemi, introduzidos em [7] a partir de uma idéia em [12]. Os operadores de Nicodemi levam aplicações multilineares (resp. polinômios homogêneos) de um espaço de Banach E em aplicações multilineares (resp. polinômios homogêneos) em um espaço de Banach F. O nosso primeiro objetivo é encontrar condições para que os operadores de Nicodemi preservem certos tipos de aplicações multilineares (resp. polinômios homogêneos). Em particular estudamos a preservação de aplicações multilineares simétricas, de tipo finito, nucleares, compactas ou fracamente compactas. O segundo objetivo é encontrar condições para que, se os espaços duais E¿ e F¿ são isomorfos, os espaços de aplicações multilineares (resp. polinômios homogêneos) em E e F sejam isomorfos também. Estudamos também o problema correspondente para os espaços de aplicações multilineares (resp. polinômios homogêneos) de um determinado tipo, como por exemplo, de tipo finito, nuclear, compacto ou fracamente compacto / Abstract: This work is devoted to studying the Nicodemi operators, introduced in [7], following an idea in [12]. The Nicodemi operators map multilinear mappings (resp. homogeneous polynomials) on a Banach spaces E into multilinear mappings (resp. homogeneous polynomials) on a Banach spaces F. Our first objective is to find conditions under which the Nicodemi operators preserve certain types of multilinear mappings (resp. homogeneous polynomials). In particular we examine the preservation of the multilinear mappings that are symmetric, of finite type, nuclear, compact or weakly compact. Our second objective is tofind conditions under which, whenever the dual spaces E¿ and F¿ are isomorphic, the spaces of multilinear mappings (resp. homogeneous polynomials) on E and F are isomorphic as well. We also examine the corresponding problem for the spaces of multilinear mappings (resp. homogeneous polynomials) of a certain type, for instance of finite, nuclear, compact or weakly compact type / Doutorado / Analise Funcional / Doutor em Matemática

We compute the partial isomorphism rank, in the sense Scott and Karp, of a pair of ordinal structures using an Ehrenfeucht-Fraisse game. A complete formula is proven by induction given any two arbitrary ordinals written in Cantor normal form.

Let G be a group. A weak Cayley table isomorphism $\phi$: G $\rightarrow$ G is a bijection satisfying two conditions: (i) $phi$ sends conjugacy classes to conjugacy classes; and (ii) $\phi$(g1)$\phi$(g2) is conjugate to $\phi$(g1g2) for all g1, g2 in G. The set of all such mappings forms a group W(G) under composition. We study W(G) for fifty-six of the two hundred nineteen three-dimensional crystallographic groups G as well as some other groups. These fifty-six groups are related to our previous work on wallpaper groups.

Two applications of a binary tree data type based on a simple pairing function (a bijection between natural numbers and pairs of natural numbers) are explored. First, the tree is used to encode natural numbers, and algorithms that perform basic arithmetic computations are presented along with formal proofs of their correctness. Second, using this "canonical" representation as a base type, algorithms for encoding and decoding additional isomorphic data types of other mathematical constructs (sets, sequences, etc.) are also developed. An experimental application to a memory management system is constructed and explored using these isomorphic types. A practical analysis of this system's runtime complexity and space savings are provided, along with a proof of concept framework for both applications of the binary tree type, in the Java programming language.

The purpose of this thesis was to present the technique of double coset enumeration and apply it to construct finite homomorphic images of infinite semidirect products. Several important homomorphic images include the classical groups, the Projective Special Linear group and the Derived Chevalley group were constructed.

In this thesis we revisit some classical results about the MacWilliams equivalence theorems for codes over fields and rings. These theorems deal with the question whether, for a given weight function, weight-preserving isomorphisms between codes can be described explicitly. We will show that a condition, which was already known to be sufficient for the MacWilliams equivalence theorem, is also necessary. Furthermore we will study a local-global property that naturally generalizes the MacWilliams equivalence theorems. Making use of F-partitions, we will prove that for various subgroups of the group of invertible matrices the local-global extension principle is valid.