Orientador: Nelson Antonio Pirola / Banca: Maria Elizabete Rambo Kochhann / Banca: José Luciano Santinho Lima / Resumo: A presente pesquisa teve por objetivo investigar de que forma as atitudes em relação à Geometria, de alunos e professores do ciclo de alfabetização, se correlacionam com o desempenho dos alunos na resolução de problemas geométricos. Participaram deste estudo, 70 alunos do 3º ano do Ensino Fundamental de uma escola da rede municipal de Bauru/SP. Optou-se pelo método misto de pesquisa (quantitativa e qualitativa). Para a coleta de dados foram utilizados dois questionários informativos para professores e alunos, uma prova de Geometria para os alunos, uma escala de atitudes para intervenção com os alunos, escala de atitudes em relação à Geometria (para professores e alunos), entrevista ("pensar em voz alta"), com quatro alunos selecionados de acordo com as notas obtidas na prova de Geometria e na escala de atitudes em relação à Geometria. Os dados da prova de Geometria mostraram que os alunos estão no nível de desenvolvimento do pensamento geométrico esperado para 3º ano, ou seja, já atingiram o nível 0 e estão iniciando o nível 1 do modelo Van Hiele. Os alunos e professores demonstraram possuir atitudes positivas em relação à Geometria e a análise estatística mostrou que não houve correlação significativa entre as atitudes em relação à Geometria e o desempenho dos alunos na prova, assim como não houve correlação significativa entre as atitudes dos professores e as atitudes dos alunos do ciclo de alfabetização. / Abstract: The present research had the goal to investigate how attitudes towards Geometry, from students and teachers of the literacy cycle, correlate with the performance of students in resolving geometric problems. Participated, in this study, 70 students of the 3rd grade from the Elementary Education Level of a city school located in Bauru/SP. We chose to use the mixed method of research (quantitative and qualitative). For the data collection, two informative questionnaires were used for teachers and students; A Geometry test for the students; a range of attitudes for intervention with the students; a scale of attitudes towards Geometry, for teachers and students; Interview ("think aloud") with four students selected accordingly to the grades obtained in the Geometry test and the attitudes scale in relation to Geometry. The Geometry test data showed that the students are at the level of development of the geometric thinking expected for the 3rd grade, meaning that they have already reached the level 0 and are starting the level 1 of the Van Hiele model. The students and teachers showed positive attitudes towards Geometry and the statistical analysis showed that there was no significant correlation between the attitudes towards Geometry and the students' performance in the test, as well as there was no significant correlation between the teachers' attitudes and the students' attitudes from the Literacy cycle. / Mestre

The aim of this thesis is to explain some basic facts, examples, ideas and results in Tate’s theory and its applications. / In the first chapter, we will introduce some preliminaries of Banach algebras over k. The Tate algebra (resp. affinoid algebra) is analogous to the power series defined on the unit disc (resp. analytic set of unit disc). There are some properties of its algebraic structure. / In the second chapter we will construct the rigid analytic variety X, the topology on it, and the structure sheaf Oₓ. Tate found an interesting property, now called Tate’ Acyclicity Theorem, which makes analytic continuation stand. Moreover, by using G-topology, we define rigid analytic spaces, and we are able to paste them. The Tate curve is a good example. / In the last chapter, we introduce Schottky group and Mumford curve. A Mumford curve is obtained from P¹ discarding a compact set quotient by a group action, and it can be characterized as an algebraic curve with totally split reduction. The converse is also true. / 這篇文章的目的是闡釋Tate理論中的一些基本事實、例子、想法和結果，以及一些應用。 / 在第一章中，我們會介紹一些關於k上的Banach代數的初等事實。Tate代數（affinoid代數）類似於定義在單位圓（單位圓的解析集）上的冪級數。關於它的代數結構有一些結論。 / 在第二章中，我們會構造剛性解析簇，它的拓撲，以及它的層結構。Tate發現了一個它的有趣的性質，現在被稱為Tate Acyclicity Theorem；這個性質使得我們可以做解析延拓。此外，通過使用G-拓撲，我們構造剛性解析空間，並且我們可以將幾塊剛性解析空間“粘”起來。Tate曲線是它的一個很好的應用。 / 在第三章中，我們將介紹Schottky群和Mumford曲線。一條Mumford曲線是P¹挖掉一個緊集后除掉一個群作用而得到的，並且可以被表徵為擁有totally split reduction的代數曲線。反之亦然。 / Yuan, Zhiri. / Thesis M.Phil. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaf 65 ). / Abstracts also in Chinese. / Title from PDF title page (viewed on 13, September, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.

by Chan Chun-hing. / Bibliography: leaves 66-68 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1984

by Ng Kwok Choi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1980. / Bibliography: leaves 39-43.

Xiao, Chang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 37-[38]). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography: leaves 132-137. / Ph.D.

Given a Liouville manifold, symplectic cohomology is defined as the Hamiltonian Floer homology for the symplectic action functional on the free loop space. In this thesis, we propose two versions of periodic S^1-equivariant homology or S^1-equivariant Tate homology for the natural S^1-action on the free loop space. The first version is called periodic symplectic cohomology. We prove that there is a localization theorem or a fix point property for periodic symplectic cohomology. The second version is called the completed periodic symplectic cohomology which satisfies Goodwillie's excision isomorphism. Inspired by the work of Seidel and Solomon on the existence of dilations on symplectic cohomology, we formulate the notion of Liouville manifolds admitting higher dilations using Goodwillie's excision isomorphism on the completed periodic symplectic cohomology. As an application, we derive obstructions to existence of certain exact Lagrangian immersions in Liouville manifolds admitting higher dilations.

Algebraic geometry in positive characteristic has a quite different flavour than in characteristic zero. Many of the pathologies disappear when a variety admits a lift to characteristic zero. It is known since the sixties that such a lift does not always exist. However, for applications it is sometimes enough to lift a variety dominating the given variety, and it is natural to ask when this is possible. The main result of this dissertation is the construction of a smooth projective variety over any algebraically closed field of positive characteristic that cannot be dominated by another smooth projective variety admitting a lift to characteristic zero. We also discuss some cases in which a dominating liftable variety does exist.

In this work, we study the Hull-Strominger system. New solutions are found on hyperkahler fibrations over a Riemann surface. This class of solutions is the first which admits infinitely many topological types. Next, we study the Fu-Yau solutions of the Hull-Strominger system and their generalizations to higher dimensions. We solve the Fu-Yau equation in higher dimensions, and in fact, solve a new class of fully nonlinear elliptic PDE which contains the Fu-Yau equation as a special case. Lastly, we introduce a geometric flow to study the Hull-Strominger system and non-Kahler Calabi-Yau threefolds. Basic properties are established, and we study this flow in the geometric settings of fibrations over a Riemann surface and fibrations over a K3 surface. In both cases, the flow descends to a nonlinear evolution equation for a scalar function on the base, and we study the dynamical behavior of these evolution equations.

In this thesis, we explore the restrictions imposed on the genus of a smooth curve $X$ which possesses at least three independent gonal morphisms to $\Pp^1$. We will prove a sharp lower bound on the dimension of global sections given by the sum of the divisors for the gonal morphisms. This inequality will provide an upper bound on the genus of a curve with the described properties. By considering the birational image of $X$ in $\Pp^1 \times \Pp^1 \times \Pp^1$ under the product of three pairwise independent morphisms, we observe that the boundary case for the previously mentioned inequality is closely related to the case where the image of $X$ is contained in a type 1-1-1 surface. Motivated by this phenomenon, we examine the constraints on the arithmetic genus of an irreducible curve in $\Pp^1 \times \Pp^1 \times \Pp^1$ whose natural projections are pairwise independent and all have degree 7.