Análise de superfícies seletivas em frequência com geometria multifractal

Frequency Selective surfaces are increasingly common structures in telecommunication systems due to their geometric and electromagnetic advantages. As a matter of fact, the frequency selective surfaces with fractal geometry type would allow an even bigger reduction of the electrical length which provided greater flexibility in the design of these structures. In this work, we investigated the use of multifractal geometry in frequency selective surfaces. Three structures with different multifractal geometries have been proposed and analyzed. The first structure allowed the design of multiband structures with greater flexibility in controlling the resonant frequencies and bandwidth. The second structure provided a bandwidth increase even with the rising of the fractal level. The third structure showed response with angle stability, dual polarization and provided room for a bandwidth increase with the rising of the structural multifractality. Furthermore, the proposed structures increased the degree of freedom in the multiband designs because they have multiple resonant frequencies ratios between adjacent bands and are easy to deploy. The validation of the proposed structures was initially verified through simulations in Ansoft Designer software and then the structures were constructed and the experimental results obtained

A geometria do compasso (1797) de Mascheroni (1750 – 1800) em atividades com o GeoGebra

The present work aims to show a possible relationship between the use of the History of Mathematics and Information and Communication Technologies (TIC) in teaching Mathematics through activities that use geometric constructions of the “Geometry of the Compass” (1797) by Lorenzo Mascheroni (1750-1800). For this, it was performed a qualitative research characterized by an historical exploration of bibliographical character followed by an empirical intervention based on use of the History of Mathematics combined with TIC through Mathematical Investigation. Thus, studies were performed in papers dealing with the topic, as well as a survey to highlight problems and /or episodes of the history of mathematics that can be solved with the help of TIC, allowing the production of a notebook of activities addressing the resolution of historical problems in a computer environment. In this search, we came across the problems of geometry that are presented by Mascheroni stated previously in the work that we propose solutions and investigations using GeoGebra software. The research resulted in the elaboration of an educational product, a notebook of activities, which was structure to allow during its implementation, students can conduct historical and/or Mathematics research, therefore, we present the procedures for realization of each construction, followed at some moments by original solution of the work. At the same time, we encourage students to investigate/reflect its construction (GeoGebra), in addition to making comparisons with the solution Mascheroni. This notebook was applied to two classes of the course of Didactics of Mathematics I (MAT0367) Course in Mathematics UFRN in 2014. Knowing the existence of some unfavorable arguments regarding the use of history of mathematics, such as loss of time, it was found that this factor can be mitigated with the aid of computational resource, because we can make checks using only the dynamism of and software without repeating the construction. It is noteworthy that the minimized time does not mean loss of reflection or maturation of ideas, when we adopted the process of historical and/or Mathematics Investigation

Aprendizagem significativa: uma proposta de ensino e aprendizagem da geometria euclidiana espacial no ensino médio

This dissertation is a research based on the Meaningful Learning Theory, with students from the second year of High School, in the city named Capinzal do Norte, state of Maranhão. The pedagogic approach of this research focuses on what to do and how to do so students can better grasp knowledge inherent to the Euclidean Special Geometry in a more meaningful and changing way, also that information may be kept longer in their brain, so it can last longer in the present and future. The methodological strategy adopted was the research-action, followed by the constant observance of a researcher on the matter with the purpose to ensure consistent results, which come from the use of a variety of data collector instruments, such as: Concept Maps, manipulatives, educational softwares and application of evaluative tests, besides the observations made throughout the process of investigation and the diagnosis itself. It is all due to the fact that we rely on the premise that knowledge is assimilated in particular and idiosyncratic ways, which means each and every student learns in different ways and in different periods of time. That is why it is so important to develop diversified methodologies to the same subject. This research adds to the other ones related to the theoretical frameworks of the Meaningful Learning Theory, of Concept Maps, of the use of technology on the educational process and of manipulatives, which purpose is to connect their common dots. This pedagogical intervention also focuses on the construction of the educational orientations with applicability directly on class, directed specially by the Mathematics teacher of the basic education, who might use them during your teaching practice. Such guidelines established here as an educational product aim to follow the Theory's assumptions that serves as basis to this research, thus becoming an educational element with a relevant significance. The results, with which we are faced, proved overwhelming to the proposed objectives in terms of learning, which were evident in the construction of Conceptual Maps, as well as in the use of Concrete Materials, in addition to serving as a motivational element to participating students of research. The results obtained are indeed reliable in terms of learning, considered the expected goals, and made us certain that the way we have approached the subject is consistent with a holistic education and that at the same time values the tiniest details, which are fundamental to all the learning-teaching process.

Plásticos reforçados a base de tecidos híbridos: efeitos da anisotropia e geometria normativa na caracterização mecânica e da fratura

As most current studies, reinforced plastics have been, in recent years, a viable alternative in building structural elements of medium and large, since the lightness accompanied by high performance possible. The design of hybrid polymer composites (combination of different types of reinforcements) may enable structural applications thereof, facing the most severe service conditions. Within this class of composite materials, reinforced the underlying tissues hybrid high performance are taking space when your application requires high load bearing and high rigidity. The objective of this research work is to study the challenges in designing these fabrics bring these materials as to its mechanical characterization and fracture mechanisms involved. Some parameters associated with the process and / or form of hybridization stand out as influential factors in the final performance of the material such as the presence of anisotropy, so the fabric weave, the process of making the same, normative geometry of the specimens, among others. This sense, four laminates were developed based hybrid reinforcement fabrics involving AS4 carbon fiber, kevlar and glass 49-E as the matrix epoxy vinyl ester resin (DERAKANE 411-350). All laminates were formed each with four layers of reinforcements. Depending on the hybrid fabric, all the influencing factors mentioned above have been studied for laminates. All laminates were manufactured industrially used being the lamination process manual (hand-lay-up). All mechanical characterization and study of the mechanism of fracture (fracture mechanics) was developed for laminates subjected to uniaxial tensile test, bending in three and uniaxial compression. The analysis of fracture mechanisms were held involving the macroscopic, optical microscopy and scanning electron microscopy