Euler e os números pentagonais

The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem

A produção do mobiliário urbano nos espaços públicos :o desenho do mobiliário urbano nos projetos de reordenamento das orlas do Rio Grande do Norte

This work aims to analyze and evaluate the Urban furniture designed to public areas according to the Revitalization planning for Rio Grande do Norte coastland, defining visual relations among urban elements in the landscape of revitalized public urban areas with cultural, paisagistic and touristic values and the design process used for developing urban furniture to those areas, observing the incoming consequences use to that process in a specific urban context which alters use, functions, cultural images as well as social values attributed to each particular place. Environmental perceptions, legibility of local cultural references and their representation through the design of urban elements, act in a positive or negative manner over the inhabitants cognition process of some particular revitalized area, determining new use and attributions to those areas. Designs for coastal urban interventions try excessively to standardize technical media, construction materials and planning configurations, creating artificial sceneries that segregates users, imposing new structures and usage, generating, consequently, the so called non-places and burlesque regionalism. The research is divided into 4 chapters: 1) Theoretical support (Industrial design; Urban furniture; Public urban spaces; Urban image and environmental perception; Urban occupation and interventions in coastland areas); 2) Methodological procedures and data collection; 3) Analysis of Rio Grande do Norte coastal areas and their urban interventions; 4) Final considerations and Industrial Design contributions to the subject

Supressão do ruído de rolamento superficial utilizando a transformada Curvelet

Among the many types of noise observed in seismic land acquisition there is one produced by surface waves called Ground Roll that is a particular type of Rayleigh wave which characteristics are high amplitude, low frequency and low velocity (generating a cone with high dip). Ground roll contaminates the relevant signals and can mask the relevant information, carried by waves scattered in deeper regions of the geological layers. In this thesis, we will present a method that attenuates the ground roll. The technique consists in to decompose the seismogram in a basis of curvelet functions that are localized in time, in frequency, and also, incorporate an angular orientation. These characteristics allow to construct a curvelet filter that takes in consideration the localization of denoise in scales, times and angles in the seismogram. The method was tested with real data and the results were very good

Identificação fuzzy-multimodelos para sistemas não lineares

This paper presents a new multi-model technique of dentification in ANFIS for nonlinear systems. In this technique, the structure used is of the fuzzy Takagi-Sugeno of which the consequences are local linear models that represent the system of different points of operation and the precursors are membership functions whose adjustments are realized by the learning phase of the neuro-fuzzy ANFIS technique. The models that represent the system at different points of the operation can be found with linearization techniques like, for example, the Least Squares method that is robust against sounds and of simple application. The fuzzy system is responsible for informing the proportion of each model that should be utilized, using the membership functions. The membership functions can be adjusted by ANFIS with the use of neural network algorithms, like the back propagation error type, in such a way that the models found for each area are correctly interpolated and define an action of each model for possible entries into the system. In multi-models, the definition of action of models is known as metrics and, since this paper is based on ANFIS, it shall be denominated in ANFIS metrics. This way, ANFIS metrics is utilized to interpolate various models, composing a system to be identified. Differing from the traditional ANFIS, the created technique necessarily represents the system in various well defined regions by unaltered models whose pondered activation as per the membership functions. The selection of regions for the application of the Least Squares method is realized manually from the graphic analysis of the system behavior or from the physical characteristics of the plant. This selection serves as a base to initiate the linear model defining technique and generating the initial configuration of the membership functions. The experiments are conducted in a teaching tank, with multiple sections, designed and created to show the characteristics of the technique. The results from this tank illustrate the performance reached by the technique in task of identifying, utilizing configurations of ANFIS, comparing the developed technique with various models of simple metrics and comparing with the NNARX technique, also adapted to identification

Um ambiente integrado para manipulação de tráfego multicast

In the two last decades of the past century, following the consolidation of the Internet as the world-wide computer network, applications generating more robust data flows started to appear. The increasing use of videoconferencing stimulated the creation of a new form of point-to-multipoint transmission called IP Multicast. All companies working in the area of software and the hardware development for network videoconferencing have adjusted their products as well as developed new solutionsfor the use of multicast. However the configuration of such different solutions is not easy done, moreover when changes in the operational system are also requirede. Besides, the existing free tools have limited functions, and the current comercial solutions are heavily dependent on specific platforms. Along with the maturity of IP Multicast technology and with its inclusion in all the current operational systems, the object-oriented programming languages had developed classes able to handle multicast traflic. So, with the help of Java APIs for network, data bases and hipertext, it became possible to the develop an Integrated Environment able to handle multicast traffic, which is the major objective of this work. This document describes the implementation of the above mentioned environment, which provides many functions to use and manage multicast traffic, functions which existed only in a limited way and just in few tools, normally the comercial ones. This environment is useful to different kinds of users, so that it can be used by common users, who want to join multimedia Internet sessions, as well as more advenced users such engineers and network administrators who may need to monitor and handle multicast traffic

Desenvolvimento de um ambiente para projeto de controladores fuzzy para dispositivos móveis

Fuzzy intelligent systems are present in a variety of equipment ranging from household appliances to Fuzzy intelligent systems are present in a variety of equipment ranging from household appliances to small devices such as digital cameras and cell phones being used primarily for dealing with the uncertainties in the modeling of real systems. However, commercial implementations of Fuzzy systems are not general purpose and do not have portability to different hardware platforms. Thinking about these issues this work presents the implementation of an open source development environment that consists of a desktop system capable of generate Graphically a general purpose Fuzzy controller and export these parameters for an embedded system with a Fuzzy controller written in Java Platform Micro Edition To (J2ME), whose modular design makes it portable to any mobile device that supports J2ME. Thus, the proposed development platform is capable of generating all the parameters of a Fuzzy controller and export it in XML file, and the code responsible for the control logic that is embedded in the mobile device is able to read this file and start the controller. All the parameters of a Fuzzy controller are configurable using the desktop system, since the membership functions and rule base, even the universe of discourse of the linguistic terms of output variables. This system generates Fuzzy controllers for the interpolation model of Takagi-Sugeno. As the validation process and testing of the proposed solution the Fuzzy controller was embedded on the mobile device Sun SPOT ® and used to control a plant-level Quanser®, and to compare the Fuzzy controller generated by the system with other types of controllers was implemented and embedded in sun spot a PID controller to control the same level plant of Quanser®