Thesis (Dr. rer. nat.)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2001. / Pt. 1. with Gero Kleineidam. Includes bibliographical references.

Honors Project--Smith College, Northampton, Mass., 2010. / Includes bibliographical references (p. 64-65).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1973. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Orientador: Ariane Luzia dos Santos / Banca: Alice Kimie Miwa Libardi / Banca: Érica Regina Filletti Nascimento / Resumo: Este trabalho aborda em especial a análise dos pontos críticos de uma função diferenciável. Fazemos inicialmente uma abordagem sobre funções diferenciáveis com duas variáveis e outros temas necessários para a compreensão de algumas demonstrações e conceitos que serão abordados neste trabalho e em seguida apresentamos uma abordagem sobre curvas e superfícies. Depois, apresentamos um estudo sobre pontos críticos e as funções de Morse, que estão relacionadas ao estudo dos pontos críticos não degenerados de uma função diferenciável f: X → IR em uma superfície, e mostramos ainda que toda função diferenciável em torno de um ponto crítico não degenerado pode ser escrita como um polinômio quadrático. Para finalizar o trabalho, fazemos uma proposta de abordagem dos pontos críticos de uma função diferenciável destinada à 3ª série do ensino médio usando o conceito de derivada com uma variável / Abstract: This work deals in particular with the analysis of the critical points of a differentiable function. We make an initial approach on differentiable functions with two variables and other topics necessary for the understanding of the sampled concepts and concepts that will be approached in this work and next we present an approach on curves and surfaces.Then, we present a study on critical points and Morse functions, which are related to the study of the nondegenerate critical points of a differentiable f: X → IR function on a surface, and we show that any differentiable function around a nondegenerated critical point can be written as a quadratic polynomial.To finalize the work, we make a proposal to approach the critical points of a differentiable function destined for the 3rd grade of high school using the concept of derivative with one variable / Mestre

Over the past quarter of a century a vast amount of research investigating the synthesis and properties of mechanically interlocked molecules has been reported. This can be largely attributed to the emergence of non-statistical, supramolecular strategies for their synthesis, starting with Jean-Pierre Sauvage’s metal template capture of a catenane – a single molecule comprising two macrocycles which could not be unlinked without breaking a covalent bond. Other molecules possessing interlocked architectures, namely rotaxanes and knots, have also been synthesised and studied. While a variety of other template strategies have been developed over the years, the use of metal ions remains popular and widespread amongst supramolecular chemists due to their diversity as both templates and catalysts. The research presented in this thesis explores that remarkable diversity, demonstrating the rapid progress that has been achieved towards the synthesis of increasingly complex molecules by the continued usage of metal template strategies. Chapter 1 reviews the current state of the art regarding metal template synthesis of mechanically interlocked molecules. Chapter 2 reports the synthesis of doubly-interlocked [2]catenanes (otherwise known as Solomon links) from supramolecular interwoven 2×2 grids. Chapter 3 details progress towards the synthesis of an “endless” knot with seven crossings from an unprecedented interwoven 3×3 grid. Chapter 4 illustrates the use of a circular iron(II) double helicate to construct a highly compact and complex molecular knot with eight crossings. Chapter 5 describes an active metal template strategy for the synthesis of the first [4]rotaxanes containing one ring and three threads.

No description available.

No description available.

A non-trivial example of an L-topological space, the fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.