This dissertation is a uniïfication of an analysis-based approach and the traditional topological-based approach to Poincaré duality. We examine the role of the discrete Hodge star operator in proving and in realizing the Poincaré duality isomorphism (between cohomology and homology in complementary degrees) in a cellular setting without reference to a dual cell complex. More specifically, we provide a proof of this version of Poincaré duality over R via the simplicial discrete Hodge star defined by Scott Wilson in [19] without referencing a dual cell complex. We also express the Poincaré duality isomorphism over both R and Z in terms of this discrete operator. Much of this work is dedicated to extending these results to a cubical setting, via the introduction of a cubical version of Whitney forms. A cubical setting provides a place for Robin Forman's complex of nontraditional differential forms, defined in [7], in the uniïfication of analytic and topological perspectives discussed in this dissertation. In particular, we establish a ring isomorphism (on the cohomology level) between Forman's complex of differential forms with his exterior derivative and product and a complex of cubical cochains with the discrete coboundary operator and the standard cubical cup product. / Ph. D.

Neste trabalho, estudamos famílias de curvas genericamente reduzidas. Estendemos para o caso genericamente reduzido alguns resultados conhecidos para famílias de curvas reduzidas como a equivalência entre a Whitney equisingularidade e a resolução simultânea forte da família e a equivalência entre a Whitney equisingularidade e a constância do número de Milnor e da multiplicidade de cada curva Xt da família. Estudamos também a equisingularidade topológica e a Whitney equisingularidade de famílias de superfícies em C3 parametrizadas por germes de aplicações A-finitamente determinados. Em ([51]), Ruas apresentou uma conjectura cujo enunciado diz que se f : (C2, 0) r→ (C3, 0) é um germe de aplicação finitamente determinado, então um desdobramento F a 1-parâmetro de f é topologicamente trivial se, e somente se F é Whitney equisingular se, e somente se o número de Milnor μ(D(ft)) de D(ft) é constante, onde D(ft) é a curva de pontos duplos de ft. Apresentamos contra-exemplos que mostram como esta conjectura pode falhar. Mostramos também uma classe de famílias de germes aplicações ft : (C2, 0) → (C3, 0) em que a conjectura é verdadeira. No caso em que f é homogênea e de coposto 1, mostramos também algumas fórmulas para a multiplicidade da imagem da curva de pontos duplos f(D(f)), o número de Milnor da seção transversal μ1(f(C2)) e o invariante J(f) em termos dos graus de f. Em [44], Nuño-Ballesteros e Jorge Pérez apresentam alguns resultados sobre germes de aplicações f : (Cn, 0) → (C2n-1, 0) com n ≥ 3. Quando f é finitamente determinado, a curva dos pontos duplos D(f) de f tem uma estrutura de curva genericamente reduzida. Apresentamos uma outra forma de abordar alguns problemas descritos em [44] usando resultados sobre curvas genericamente reduzidas. / In this work, we study families of generically reduced curves. We extend to the generically reduced case some results known for families of reduced curves as the equivalence between Whitney equisingularity and strong simultaneous resolution of the family and the equivalence between Whitney equisingularity and the constancy of the Milnor number and the multiplicity of each curve Xt of the family. We also study the topological triviality and the Whitney equisingularity of families of surfaces in C3 parametrized by A-finitely determined map germs. In [51], Ruas presented a conjecture whose statement says that if f : (C2, 0) → (C3, 0) is a finitely determined map germ, then an 1-parameter unfolding F = (ft, t) of f is topological trivial if and only if it is Whitney equisingular if and only if the Milnor number μ(D(ft)) is constant, where D(ft) is the double point curve of ft. We present counter-examples that show how the conjecture can fail. We also show a class of families of map germs ft : (C2, 0) → (C3, 0) in which the conjecture is true. We also give formulas for the multiplicity of the image of the double point curve f(D(f)), the Milnor number of the transversal generic section μ 1f(C2)) and the invariant J(f) in terms of degrees of f in the case in which f is homogeneous and has corank 1. In [44], Nuño-Ballesteros and Jorge Pérez give some results in the case of families of map germs f : (Cn, 0) → (C2n-1, 0) with n ≥ 3. When f is finitely determined, the double point. curve D(f) of f is a generically reduced curve. We present another way of approaching some problems in [44] using results on generically reduced curves.

Neste trabalho, estudamos famílias de curvas genericamente reduzidas. Estendemos para o caso genericamente reduzido alguns resultados conhecidos para famílias de curvas reduzidas como a equivalência entre a Whitney equisingularidade e a resolução simultânea forte da família e a equivalência entre a Whitney equisingularidade e a constância do número de Milnor e da multiplicidade de cada curva Xt da família. Estudamos também a equisingularidade topológica e a Whitney equisingularidade de famílias de superfícies em C3 parametrizadas por germes de aplicações A-finitamente determinados. Em ([51]), Ruas apresentou uma conjectura cujo enunciado diz que se f : (C2, 0) r→ (C3, 0) é um germe de aplicação finitamente determinado, então um desdobramento F a 1-parâmetro de f é topologicamente trivial se, e somente se F é Whitney equisingular se, e somente se o número de Milnor μ(D(ft)) de D(ft) é constante, onde D(ft) é a curva de pontos duplos de ft. Apresentamos contra-exemplos que mostram como esta conjectura pode falhar. Mostramos também uma classe de famílias de germes aplicações ft : (C2, 0) → (C3, 0) em que a conjectura é verdadeira. No caso em que f é homogênea e de coposto 1, mostramos também algumas fórmulas para a multiplicidade da imagem da curva de pontos duplos f(D(f)), o número de Milnor da seção transversal μ1(f(C2)) e o invariante J(f) em termos dos graus de f. Em [44], Nuño-Ballesteros e Jorge Pérez apresentam alguns resultados sobre germes de aplicações f : (Cn, 0) → (C2n-1, 0) com n ≥ 3. Quando f é finitamente determinado, a curva dos pontos duplos D(f) de f tem uma estrutura de curva genericamente reduzida. Apresentamos uma outra forma de abordar alguns problemas descritos em [44] usando resultados sobre curvas genericamente reduzidas. / In this work, we study families of generically reduced curves. We extend to the generically reduced case some results known for families of reduced curves as the equivalence between Whitney equisingularity and strong simultaneous resolution of the family and the equivalence between Whitney equisingularity and the constancy of the Milnor number and the multiplicity of each curve Xt of the family. We also study the topological triviality and the Whitney equisingularity of families of surfaces in C3 parametrized by A-finitely determined map germs. In [51], Ruas presented a conjecture whose statement says that if f : (C2, 0) → (C3, 0) is a finitely determined map germ, then an 1-parameter unfolding F = (ft, t) of f is topological trivial if and only if it is Whitney equisingular if and only if the Milnor number μ(D(ft)) is constant, where D(ft) is the double point curve of ft. We present counter-examples that show how the conjecture can fail. We also show a class of families of map germs ft : (C2, 0) → (C3, 0) in which the conjecture is true. We also give formulas for the multiplicity of the image of the double point curve f(D(f)), the Milnor number of the transversal generic section μ 1f(C2)) and the invariant J(f) in terms of degrees of f in the case in which f is homogeneous and has corank 1. In [44], Nuño-Ballesteros and Jorge Pérez give some results in the case of families of map germs f : (Cn, 0) → (C2n-1, 0) with n ≥ 3. When f is finitely determined, the double point. curve D(f) of f is a generically reduced curve. We present another way of approaching some problems in [44] using results on generically reduced curves.

En 1979, Trotman a démontré que les stratifications réelles lisses qui satisfont la condition de (a)-régularité sont précisément celles pour lesquelles la transversalité aux strates des applications est une condition stable dans la topologie forte. C'était un résultat surprenant puisque la (t)-régularité semblait être plus appropriée pour la stabilité de la transversalité, une erreur qui a été faite dans plusieurs articles avant que ce résultat soit montré par Trotman. Notre premier résultat est un analogue au résultat de Trotman pour la topologie faible.Il y a une dizaine d'années Trotman a demandé si le même résultat est valable pour les stratifications analytiques complexes. Dans ce travail on démontre un analogue du résultat de Trotman dans le cas complexe, en utilisant la notion de variété de Oka introduite par Forstneric et on montre que la conjecture n'est pas vraie en général en donnant des contre-exemples.Dans sa thèse, Trotman a formulé une conjecture pour généraliser son résultat pour les stratifications (a_f)-régulières de Thom. Dans une tentative de résolution de cette conjecture on a observé que la transversalité par rapport à un feuilletage est une condition stable, cependant ce n'est pas une condition générique. Donc, en voulant imiter la preuve de Trotman on ne pourra pas obtenir cette généralisation. Néanmoins, on donne ici une preuve de cette conjecture. Ce résultat peut être résumé en disant que les (a_f)-défauts dans une stratification peuvent être détectés en perturbant les applications transverses au feuilletage induit par f. Certaines techniques pour détecter (a_f)-défauts sont aussi données vers la fin. / Trotman in 1979 proved that real smooth stratifications which satisfy the condition of $(a)$-regularity are precisely those stratifications for which transversality to the strata of smooth mappings is a stable condition in the strong topology. This was a surprising result since $(t)$-regularity seemed to be more appropriate for stability of transversality, a mistake that was made in several articles before this result of Trotman. Our first result is an analogue of this result of Trotman for the weak topology.Trotman asked more than ten years ago whether a similar result holds for complex analytic stratifications. We will give an analogue of Trotman's result in the complex setting using Forstneriv c's notion of Oka manifolds and show that the result is not true in general by giving counterexamples.In his Ph.D. thesis Trotman conjectured a generalization of his result for Thom $(a_f)$-regular stratifications. In an attempt to prove this conjecture we noticed that while transversality to a foliation is a stable condition, it is not generic in general. Thus, mimicking the proof of the result of Trotman would not suffice to obtain this generalization. Nevertheless, we will present a proof of this conjecture in this work. This result can be summarized by saying that Thom $(a_f)$-faults in a stratification can be detected by perturbation of maps transverse to the foliation induced by $f$. Some other techniques of detecting $(a_f)$-faults are also given towards the end.

Nosso objetivo neste trabalho é estudar a obstrução de Euler de uma função, este conceito foi definido por J.-P. Brasselet, D. Massey, A. J. Parameswaran e J. Seade, e generaliza dois conceitos importantes, a obstrução de Euler definida por R. D. MacPherson assim como o número de Milnor de uma função. O resultado principal deste trabalho mostra a relação existente entre a obstrução de Euler e a obstrução de Euler de uma função / Our goal in this work is to study the Euler obstruction of a function, this concept was defined by J.-P. Brasselet, D. Massey, A. J. Parameswaran and J. Seade, and it generalizes two important concepts, the Euler obstruction defined by R. D. MacPherson and the Milnor number of a function. The main result of this study shows the relation between the Euler obstruction and the Euler obstruction of a function

Submitted by Alex Melges Barbosa (alex.melgesb@gmail.com) on 2017-03-02T15:41:01Z No. of bitstreams: 1 PDF_final_cd - Alex.pdf: 1031527 bytes, checksum: d71a279fd3f7c761ebeb48e598e07b22 (MD5) / Approved for entry into archive by LUIZA DE MENEZES ROMANETTO (luizamenezes@reitoria.unesp.br) on 2017-03-08T13:52:00Z (GMT) No. of bitstreams: 1 barbosa_am_me_sjrp.pdf: 1031527 bytes, checksum: d71a279fd3f7c761ebeb48e598e07b22 (MD5) / Made available in DSpace on 2017-03-08T13:52:00Z (GMT). No. of bitstreams: 1 barbosa_am_me_sjrp.pdf: 1031527 bytes, checksum: d71a279fd3f7c761ebeb48e598e07b22 (MD5) Previous issue date: 2017-02-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho, apresentaremos uma descrição axiomática das classes de Stiefel-Whitney e, assumindo válidos estes axiomas, mostraremos algumas de suas aplicações. Posteriormente, definiremos as classes de Stiefel-Whitney e mostraremos que esta definição satisfaz os axiomas, além de garantir a unicidade das classes de Stiefel-Whitney. Por fim, definiremos a classe de Euler e mostraremos algumas de suas aplicações, bem como sua relação com as classes de Stiefel-Whitney. / In this work, we will present an axiomatic description of the Stiefel-Whitney classes and, taking these axioms true, we will show some of their applications. After that, we will define the Stiefel-Whitney classes and we will show this definition meets the axioms, besides it ensures the unity of the Stiefel-Whitney classes. Lastly, we will define the Euler class and we will show some of its applications as well as its relationship with the Stiefel-Whitney classes.

Nosso objetivo neste trabalho é estudar a obstrução de Euler de uma função, este conceito foi definido por J.-P. Brasselet, D. Massey, A. J. Parameswaran e J. Seade, e generaliza dois conceitos importantes, a obstrução de Euler definida por R. D. MacPherson assim como o número de Milnor de uma função. O resultado principal deste trabalho mostra a relação existente entre a obstrução de Euler e a obstrução de Euler de uma função / Our goal in this work is to study the Euler obstruction of a function, this concept was defined by J.-P. Brasselet, D. Massey, A. J. Parameswaran and J. Seade, and it generalizes two important concepts, the Euler obstruction defined by R. D. MacPherson and the Milnor number of a function. The main result of this study shows the relation between the Euler obstruction and the Euler obstruction of a function

The aim of this dissertation is to understand and analyze the museum location decision, defined as where museum founders choose to establish or relocate their institution. The empirical case is the museum population of New York City from 1910-2010. In three substantive chapters, I explore this complex decision process from the organizational-level, the population-level, and the audience-level. In the first chapter, I argue that the museum location decision has evolved over the past century, and has experienced three major paradigm shifts. Out of each era, a new model of the museum location decision has taken hold, resulting in the current organizational landscape. I demonstrate how these eras emerged through historical, comparative case studies of two New York museums, the Museum of Modern Art and the Whitney Museum of American Art. In second chapter, I show that the location decisions illustrated through the histories of the Whitney Museum of American Art and the Museum of Modern Art are representative of New York's museum population overall. Using a dataset of all museums that have existed in New York City (and all of those museums' relocations), I chronicle the aggregated movements of the museum population between 1910 and 2010. I argue that the three eras of the museum location decision interacted with key demographic changes to create the unique distribution we observe today. The insights from these findings indicate that the spatial diffusion of museums in New York is systematically patterned in relation to demographic changes. The final substantive chapter is devoted to exploring the possibility that institutional location impacts audience composition. I argue that proximity to museums and other kinds of arts institutions is a significant, yet understudied determinant of attendance. The introduced concept of institutional exposure suggests that local access to arts institutions has cognitive, behavioral, and interactional consequences. Although directly testing the effect of institutional exposure is beyond the parameters of this dissertation, I show that there is a strong correlation between exposure and attendance. I illustrate the increasingly unequal access to arts between white and African American New Yorkers, which correlates highly with still-unexplained low attendance rates of African Americans. The observed evolution of the museum location decision explains when and how New York institutions adopted and then abandoned each institutionalized practice of museum location. In the Conclusion, I highlight several implications of this work, both of sociological theory and on current cultural policy.

The purpose of this writing is to present a biography of Newel Kimball Whitney with emphasis on his personal life and his contributions to the Church of Jesus Chirst of Latter-day Saints.

It is a well documented fact that primary teachers as a group are quite lacking in their enthusiasm for science, a subject of constant concern for those committed to its role as a component of the primary school curriculum. In order to test the effects of various treatments on groups of teachers and pre-service trainees, a 21 item questionnaire was developed to measure attitudes towards science in the primary school curriculum, towards improving expertise in the area, and in the traditional &quotescientific attitudes and values&quote. A new group of pre-service students provided one group and the pilot population, students in their final semester of a Diploma in Teaching programme another group, and teachers attending residential schools for UG2 conversion and PGl teacher education courses provided several other groups based on teaching location. Items were selected from the pilot instrument on their ability to discriminate between high scoring and low scoring groups measured with the Mann-Whitney U test. Analyses in the main survey between groups, were carried out using Mann-Whitney U test and Kruskal-Wallis one way analysis of variance, and between items, using Wilcoxon matched-pairs signed-ranks test. All manipulation and analysis of data was carried out with the assistance of two computer programs, written in PASCAL by the author specifically for this study � one for item analysis, the other, a statistical package for analysing the main survey data. Findings include 'support for prediction in the literature that change in education is a slow process, demanding ongoing support by the system and teacher education institutions, for teachers committed to the change. Also, the value of computer support, and advantages of tailoring a statistical package to the study, rather than the study to analyses readily accessible, are clearly demonstrated.