A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

Questões objetivas sobre funções das provas de matemática do vestibular da UFRN dos anos de (2001 a 2008): um diagnóstico sobre os erros que os candidatos cometem

La dificultad que los alumnos encuentran en el aprendizaje de matemática viene siendo objeto de investigación por estudiosos en educación matemática, tanto en Brasil como en el exterior. El objetivo de este estudio consiste em investigar las dificuldades en el aprendizado sobre funciones matemáticas y la influencia de las concepciones alternativas a partir de los errores que los candidatos acerca de las cuestiones sobre funciones en la prueba objetiva de matemática del acceso a la universidad de los años de 2001 a 2008. Teniendo como cuestiones de estudio para alcanzar el objetivo propuesto: identificar la relevancia del tema funciones que son contemplados en las pruebas de acceso a la Universidad; asi como cuáles han sido los tipos de funciones más privilegiados y menos privilegiados; analizar si la contextualización de la pregunta y la presencia de elementos no textuales han influenciado en el aumento de tal dificultad; analizar si la representación semiótica agrega mayor exigencia a la pregunta; analizar respecto a la exigencia matemática de la pregunta; analizar lo que se refiere al desempeño de los candidatos para verificar cuál pregunta tuvo mejor desempeño y cuál el peor e identificar los errores más frecuentemente cometidos por los candidatos en esas pruebas. Las reflexiones de los estudiosos como: Radatz (1980), Cury (1994), Socas (1997), Borasi (1997), Franchi e Rincón (2004), Pochulu (2004) presentan las dificultades en el aprendizaje matemático, que aparecen a partir de los errores cometidos por los alumnos, quando estos errores reciben la influencia de las concepciones alternativas. El estudio que se presenta en esta disertación configura un análisis de los errores que los candidatos han cometido en las preguntas objetivas sobre el tema funciones de las pruebas de acceso a la Universidad de los años de 2001 a 2008, a partir de los relatorios de la Comissão Permanente do Vestibular COMPERVE/UFRN. Con la intención de alcanzar los objetivos propuestos para este estudio, fueran sido construidas categorías de análisis. Los resultados encontrados han sido: El tema funciones es el más frecuente entre los demás con (28,1%); el tipo de función priorizada durante esos años ha sido la función logarítmica con (24%); la contextualización de las preguntas exige una mayor comprensión por parte del candidato de lo que las situaciones directas; la caracterización semiótica posee elementos que estructuran esas preguntas que el educando debe saber asociar al texto; la exigencia matemática posibilitó analizar que el procedimiento medio ha sido el más requisitado; el desempeño de los candidatos ha sido en la mayoría bajo (50%); y los principales errores que ellos han cometido han sido de realizar traducciones incorrectas de las expresiones que aparecen en las situaciones-problema; utilizar todos los datos que aparezcan en el problema sin tomar en cuenta si el cálculo realizado responde a la pregunta solicitada; no interpretar coherentemente las informaciones del gráfico; decodificar incorrectamente los valores representados por literales en una recta numérica. Los resultados señalizan la necesidad de una revisión didáctico-metodológicas de la enseñanza de funciones a raíz de las cuales las dificultades en el aprendizaje se han presentado

A fotossíntese vegetal no 3º ano do Ensino médio: concepções alternativas, erros conceituais e uma proposta de unidade didática baseada no Desenvolvimento Sustentável.

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Infografia interativa na redação: o processo de produção no Diário do Nordeste à luz da teoria do jornalismo

The infographics historically experience the process of evolution of journalism, from the incipient models handmade in the eighteenth century to the inclusion of computers and sophisticated software today. In order to face the advent of TV against of the partiality readers of the printed newspaper, or to represent the Gulf War, where not allowed photography, infographics reaches modern levels of production and publication. The technical devices which enabled the infographics to evolve the environment of the internet, with conditions for the manipulation of the reader, incorporating video, audio and animations, so styling of interactive infographics. These digital models of information visualization recently arrived daily in the northeast and on their respective web sites with features regionalized. This paper therefore proposes to explore and describe the processes of producing the interactive infographics, taking the example of the Diário do Nordeste, Fortaleza, Ceará, whose department was created one year ago. Therefore, based on aspects that guide the theory of journalism, as newsmaking, filters that focus on productive routine (gatekeeping) and the construction stages of the news. This research also draws on the theoretical framework on the subject, in concepts essential characteristics of computer graphics, as well as the methodological procedures and systematic empirical observations in production routines of the newsroom who can testify limitations and / or advances

As origens históricas do Zaratustra nietzcheano: o espelho de Zaratustra, a correção do mais fatal dos erros e a superação da morte de Deus

Through a careful examination of the relationship between Zoroastrianism and the Western tradition, and a detailed and critical reading of the writings of Nietzsche, this work aims at showing to what extent the character Zarathustra , his discourses and poetical-philosophical thoughts, and related passages from many distinct Nietzschean works, directly or undirectly reflect a philosophy that harvests contributions from the Zoroastrian tradition or its headways (in the Judeo-Greco-Christian tradition, and furthermore in the whole Western philosophical tradition). Supplied with this provisions, and with the interpretation cast upon them, Nietzschean philosophy questions the entire Western tradition of thought, and proposes its replacement by a new attitude towards life. This work also intends to show the way the Nietzschean Zarathustra was built up, in the writings of the German philosopher, together with the idea of making, out of the namesake character of the ancient Iranian prophet (Zarathushtra or Zoroaster, the founder of Zoroastrianism), the herald of that important text that intended to bring the German language to its highest perfection , clumping together, and leading to a prophetic-poetic climax consonant with the meaning of the Earth , Nietzsche s key ideas about the rectification of the most fatal of errors and about the death of God . An elaborate investigation has been pursued after the reasons and manners of the building up of Nietzsche s Zarathustra mirroring its Iranian namesake (sections 1.1 to 1.6), and a survey of the works of Nietzsche has suggested unquestionable relations with the Zoroastrian tradition, mostly through the Jewish, Greek or Christian repercussions of this tradition. These relations have been put in context, in many framings (sections 2.1 to 2.3.2), in the ambit of the most fatal of errors - the - creation of morals in the very occasion of its transposition to metaphysics (Ecce Homo, Why I am a destiny , 3). Through an evaluation of the possible circumstances and repercussions of the death of God , the relations between Nietzsche s writings and Zoroastrian tradition have been investigated (sections 3.1 to 3.7), allowing the understanding of this event as an essential component, and tragic outcome, of the rectification of the most fatal of errors

Interpretação e análise do problema da indução sob uma visão fundamentada em teorias de conjuntos e teoria de probabilidades

The following work is to interpret and analyze the problem of induction under a vision founded on set theory and probability theory as a basis for solution of its negative philosophical implications related to the systems of inductive logic in general. Due to the importance of the problem and the relatively recent developments in these fields of knowledge (early 20th century), as well as the visible relations between them and the process of inductive inference, it has been opened a field of relatively unexplored and promising possibilities. The key point of the study consists in modeling the information acquisition process using concepts of set theory, followed by a treatment using probability theory. Throughout the study it was identified as a major obstacle to the probabilistic justification, both: the problem of defining the concept of probability and that of rationality, as well as the subtle connection between the two. This finding called for a greater care in choosing the criterion of rationality to be considered in order to facilitate the treatment of the problem through such specific situations, but without losing their original characteristics so that the conclusions can be extended to classic cases such as the question about the continuity of the sunrise

Aplicações da teoria da percolação à modelagem e simulação de reservatórios de petróleo

In this thesis we study some problems related to petroleum reservoirs using methods and concepts of Statistical Physics. The thesis could be divided percolation problem in random multifractal support motivated by its potential application in modelling oil reservoirs. We develped an heterogeneous and anisotropic grid that followin two parts. The first one introduce a study of the percolations a random multifractal distribution of its sites. After, we determine the percolation threshold for this grid, the fractal dimension of the percolating cluster and the critical exponents ß and v. In the second part, we propose an alternative systematic of modelling and simulating oil reservoirs. We introduce a statistical model based in a stochastic formulation do Darcy Law. In this model, the distribution of permeabilities is localy equivalent to the basic model of bond percolation

Um estudo na teoria do movimento brownianno com viscosidade variável

In this work we investigate the stochastic behavior of a large class of systems with variable damping which are described by a time-dependent Lagrangian. Our stochastic approach is based on the Langevin treatment describing the motion of a classical Brownian particle of mass m. Two situations of physical interest are considered. In the first one, we discuss in detail an application of the standard Langevin treatment (white noise) for the variable damping system. In the second one, a more general viewpoint is adopted by assuming a given expression to the so-called collored noise. For both cases, the basic diffententiaql equations are analytically solved and al the quantities physically relevant are explicitly determined. The results depend on an arbitrary q parameter measuring how the behavior of the system departs from the standard brownian particle with constant viscosity. Several types of sthocastic behavior (superdiffusive and subdiffusive) are obteinded when the free pamameter varies continuosly. However, all the results of the conventional Langevin approach with constant damping are recovered in the limit q = 1

Teoria cinética não extensiva: efeitos físicos em gases e plasmas

The standard kinetic theory for a nonrelativistic diluted gas is generalized in the spirit of the nonextensive statistic distribution introduced by Tsallis. The new formalism depends on an arbitrary q parameter measuring the degree of nonextensivity. In the limit q = 1, the extensive Maxwell-Boltzmann theory is recovered. Starting from a purely kinetic deduction of the velocity q-distribution function, the Boltzmann H-teorem is generalized for including the possibility of nonextensive out of equilibrium effects. Based on this investigation, it is proved that Tsallis' distribution is the necessary and sufficient condition defining a thermodynamic equilibrium state in the nonextensive context. This result follows naturally from the generalized transport equation and also from the extended H-theorem. Two physical applications of the nonextensive effects have been considered. Closed analytic expressions were obtained for the Doppler broadening of spectral lines from an excited gas, as well as, for the dispersion relations describing the eletrostatic oscillations in a diluted electronic plasma. In the later case, a comparison with the experimental results strongly suggests a Tsallis distribution with the q parameter smaller than unity. A complementary study is related to the thermodynamic behavior of a relativistic imperfect simple fluid. Using nonequilibrium thermodynamics, we show how the basic primary variables, namely: the energy momentum tensor, the particle and entropy fluxes depend on the several dissipative processes present in the fluid. The temperature variation law for this moving imperfect fluid is also obtained, and the Eckart and Landau-Lifshitz formulations are recovered as particular cases

Teoria semi-clássica para super rede magnética formada por materiais ferromagnético e antiferromagnético

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O uso de analogias para o ensino de equilíbrio químico no ensino médio: facilitação da aprendizagem ou transmissão de erros conceituais?

The use of analogies in high school is often useful for chemistry teaching, either on textbooks or by teachers in the classroom.This use is justified by the large number of abstract concepts that rules this course. Analogies are conceptualized by several authors, which converge on the idea that these are tools that seek a way to elucidate an unknown concept by comparing it to a familiar one, relating their similar and dissimilar features. An analysis on a survey of analogies found in high school chemistry textbooks and chemical equilibrium studies is performed in order to verify whether they are leading to misconceptions for their use by students and/or for their use by teachers in the classroom, or whether they promote a learning facilitation

Prova automática de satisfatibilidade módulo teoria aplicada ao método B

Este trabalho apresenta uma extensão do provador haRVey destinada à verificação de obrigações de prova originadas de acordo com o método B. O método B de desenvolvimento de software abrange as fases de especificação, projeto e implementação do ciclo de vida do software. No contexto da verificação, destacam-se as ferramentas de prova Prioni, Z/EVES e Atelier-B/Click n Prove. Elas descrevem formalismos com suporte à checagem satisfatibilidade de fórmulas da teoria axiomática dos conjuntos, ou seja, podem ser aplicadas ao método B. A checagem de SMT consiste na checagem de satisfatibilidade de fórmulas da lógica de primeira-ordem livre de quantificadores dada uma teoria decidível. A abordagem de checagem de SMT implementada pelo provador automático de teoremas haRVey é apresentada, adotando-se a teoria dos vetores que não permite expressar todas as construções necessárias às especificações baseadas em conjuntos. Assim, para estender a checagem de SMT para teorias dos conjuntos destacam-se as teorias dos conjuntos de Zermelo-Frankel (ZFC) e de von Neumann-Bernays-Gödel (NBG). Tendo em vista que a abordagem de checagem de SMT implementada no haRVey requer uma teoria finita e pode ser estendida para as teorias nãodecidíveis, a teoria NBG apresenta-se como uma opção adequada para a expansão da capacidade dedutiva do haRVey à teoria dos conjuntos. Assim, através do mapeamento dos operadores de conjunto fornecidos pela linguagem B a classes da teoria NBG, obtem-se uma abordagem alternativa para a checagem de SMT aplicada ao método B

Contribuição da teoria do caos para a gestão do turismo: uma análise a partir da percepção dos gestores da hotelaria de Natal/RN

O presente estudo tem como objetivo analisar como os gestores da hotelaria percebem a relação da teoria do caos e turismo, descrever como é pensada e concebida a gestão do turismo; mostrar as características caopléxicas do turismo e sua gestão e identificar os elementos do padrão estratégico de gestão e planejamento na visão dos gestores dos Meios de Hospedagem. Os dados foram obtidos através da observação direta intensiva e aplicação de entrevistas aplicadas junto aos hoteleiros da cidade de Natal/RN. Constata que as teorias da mudança e do caos proporcionam visão do conjunto de relações, aspectos e implicações do turismo, com base nas incertezas e instabilidades ambientais e de mercado. Mostra que a maioria dos modelos de análise, planejamento e gestão do turismo ainda é limitada, em razão do seu caráter linear e unidimensional. Destaca que o objetivo da teoria do caos é fornecer explicações dos fenômenos, não é fazer previsões, pois é impossível prever o futuro a longo prazo. Trata das estratégias de gestão como geradoras de novas fontes de incerteza, pois a realidade não pode ser completamente representada por modelos. Ter consciência desses fatos significa, entretanto, considerar o campo de múltiplas possibilidades e oportunidades da mudança e do caos na gestão do desenvolvimento do turismo. Essas idéias foram aplicadas à análise da gestão do turismo na localidade investigada. Os questionamentos levantados no estudo pautaram-se em pesquisa bibliográfica, fundamentada, principalmente, em autores como Beni, Prahalad, Mintzberg, Ritto, Senge e Hamel. Conclui-se que na era do conhecimento, as organizações que continuam presas ao paradigma mecanicista têm dificuldade de acompanhar as mudanças do mercado e sendo a hotelaria uma indústria de serviços que tem características organizacionais complexas e adaptativas, é imprescindível que os empreendimentos hoteleiros funcionem como sistemas interativos, que acompanhem as mudanças de um mercado tão turbulento e instável tendo na teoria do caos e da complexidade uma das possibilidades de compreender a realidade fora do modelo mecanicista.

O planejamento turístico e o comércio ambulante : uma análise à luz da teoria das representações sociais

The Social Representation Theory provides subsidies to scientifically analyze what is called common sense, suggesting that thought be given credibility to the individual, from the assignment of logic to it. The Representations allow us to interpret, understand, explain and thus classify information, events and people. In this sense, this study aimed to analyze how social representations of the actors of the intinerant traders who operate in Ponta Negra/RN can be used as an element for tourism planning. To achieve the desired goals, we conducted a qualitative study, from a descriptive study, using methods of data collection the research literature, the technique of free association of words and the questionnaire, applied with 90 intinerant traders who work in Ponta Negra/RN beach. As tools of data analysis were used to analyze literature, and software EVOC and SPHINX. This research has revealed the predominance of people in itinerant male, between 18 and 28 years, with incomplete primary education, no contributors of Previdência Social and working seven days a week. The core elements of representations brings that explain that their knowledge is guided by collectively shared knowledge in the culture of tourism, which is seen as something that brings economics benefits (money) to the society, from the travel and entertainment. The plan represents the forward thinking, based on development plans that seek improvements and organization. The structure and operation of tourism planning in Natal/RN, there were no representation of intinerant traders. It is concluded that understanding the needs of itinerant traders provides grants to developing strategies for the development of tourism. This is achieved from its inclusion in tourism planning, since it enables tourism managers to understand how they are capturing, interpreting and acting on their next reality, since these representations are fundamental in forming opinions and the establishment of individual attitudes and collective. Thus, it is an important theory to be used to subsidize social research with individuals living reality and local needs, but which is the margin of decision-making processes of economic in the Brazil

A teoria da ruína aplicada em um modelo de empresa financeira com risco de crédito

In this work we study a new risk model for a firm which is sensitive to its credit quality, proposed by Yang(2003): Are obtained recursive equations for finite time ruin probability and distribution of ruin time and Volterra type integral equation systems for ultimate ruin probability, severity of ruin and distribution of surplus before and after ruin