Repositório RCAAP

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

The main purpose of this dissertation is to study the theory of holomorphy types between Banach spaces, mainly the differentiation of holomorphy types and the interplay between holomorphy types and ideals of homogeneous polynomials. To do so we first study continuous multilinear mappings and homogeneous polynomials between Banach spaces. Then we define and give examples of holomorphy types. Next we study the differentiation of holomorphy types as a method to generate new holomorphy types from a given one and we brie y study holomorphic functions associated to a given holomorphy type. Finally we show that every Banach ideal of homogeneous polynomials with property (B) is a holomorphy type and that, in the complex case, a closed ideal of polynomials is a holomorphy type if and only if it has property (B). We finish the work proving that, surprisingly, in the real case no closed ideal of polynomials has property (B).

We study how we can relate codes to different mathematical structures and how we can use such tools to obtain different systematic coding and relations between its parameters.

Through quantitative and qualitative descriptive research, we intended to study experimental activities in teaching Biology for the purpose of determining if simple experimental activities can affect student motivation in Biology classes. Furthermore, we intended to examine the possibilities and difficulties in developing such activities in Biology classes in the public school, and create an educational product that assists teachers in their teaching practice and then place it on the site of the Graduate Studies Program in the Teaching of Math and Sciences of the Universidade Federal de Uberlândia, Uberlandia, MG, Brazil. This study was developed with students in the three years of High School of the Escola Estadual Arlindo Porto (Arlindo Porto State School), Chumbo district, in the city of Patos de Minas, MG, Brazil. Data were collected through application of initial and final individual questionnaires, through writing up reports, and through filming and taking pictures of some Biology classes. The themes of the practical and experimental classes were chosen in accordance with theory, based on the Common Basic Curriculum (CBC) of Biology of the State of Minas Gerais, Brazil. All the experimental activities were carried out in the classroom, schoolyard, or area just outside the classrooms since the school does not have a Science Laboratory. To develop the activities, guides were prepared in which the students analyzed the results and answered some questions about the concepts dealt with, so as to analyze the spontaneous concepts of the students. The result of the study indicated that there is greater motivation of the students with the experimental activities. It also indicated that such activities, if used within a well-based teaching practice based on the Dynamics of Three Pedagogical moments and cultural-historical perspective is a pedagogical tool linked to theory, can improve student learning.

Fundação de Amparo a Pesquisa do Estado de Minas Gerais

In this work we study the geometric aspects of Lie groups from the view point of the Riemannian geometry, by means of invariant geometric structures associated. We present some properties on curvatures of metrics left invariants and bi-invariant one on Lie groups. We also present a treatment of the Lie algebras unimodular, including the tridimensional case. Most of the results studied are from the article of John Milnor: Curvatures of Left Invariant Metrics on Lie Groups.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

The main purpose of this dissertation is to formulate and prove the Averaging Theorem for ordinary differential equations and apply it in the investigation of periodic orbits. Two systems are studied: a Rössler s system and a hamiltonian system related to the study of Dynamic of Galaxies.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Several of our daily occurring phenomena may be modeled by means of differential equations. In general, there are some difficulties in modeling such phenomena through those equations since they depend on the precision of the estimates of the parameters. The objective of this research is to study the numerical approximation to the solution for some types of differential equations through the use of the finite elements method, such as: a uni-dimensional, a stationary bi-dimensional and a non stationary bi-dimensional equation. We also present the estimates for the numerical errors committed when the approximations of the solutions are determined. More specifically, by means of an advective-diffusive partial differential equation with evolution in time, we model a pollution source that we consider as the chimney of a plant with constant parameters and with a homogeneous Dirichlet boundary condition in the city of Uberlândia. Finally, we were able to perform this modeling by merging the advective-diffusive partial differential equation with evolution in time with the fuzzy set theory, on the grounds that three parameters of this equation are determined by Fuzzy Rule-Based Systems. The diffusion parameter depends on temperature and concentration of the pollutants and the velocity towards x and y depends on the friction force presented in the city. This friction force is due to buildings, vegetation, terrain profile and other factors. We utilized satellite images in order to determine the temperatures in the city and the intervals of variation for diffusion whereas velocities were obtained through literature. The merge of those two types of theory provided the means to determine which is the best localization of an industrial district amongst the five points studied within different regional sectors of the city of Uberlândia.

Fundação de Amparo a Pesquisa do Estado de Minas Gerais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Fundação de Amparo a Pesquisa do Estado de Minas Gerais

Fundação de Amparo a Pesquisa do Estado de Minas Gerais

Fundação de Amparo a Pesquisa do Estado de Minas Gerais

Fundação de Amparo a Pesquisa do Estado de Minas Gerais