Evidence Algorithm and Processing Formalized Mathematical Texts

The goal of a research programme Evidence Algorithm is a development of an open system of automated proving that is able to accumulate mathematical knowledge and to prove theorems in a context of a self-contained mathematical text. By now, the first version of such a system called a System for Automated Deduction, SAD, is implemented in software. The system SAD possesses the following main features: mathematical texts are formalized using a specific formal language that is close to a natural language of mathematical publications; a proof search is based on special sequent-type calculi formalizing natural reasoning style, such as application of definitions and auxiliary propositions. These calculi also admit a separation of equality handling from deduction that gives an opportunity to integrate logical reasoning with symbolic calculation.

Monismo do corpo: único ponto de partida atualmente possível para o desenvolvimento de uma psicologia científica

Inicia-se o trabalho, reconstituindo-se, sob um ponto de vista histórico, o problema do dualismo e do monismo, na Psicologia. A reconstituição é feita partindo-se de uma origem situada em Sócrates e, dai, desenvolvendo-se até os dias atuais, onde, demonstra-se, a questão permanece. A identificação daquela origem foi determinada pela circunstância de, alí, o problema ter merecido um estudo sistematizado e ter se caracterizado como metafísico. Entendendo-se, com isso, que a questão a resolver era a respeito do que existiria como entidade autônoma. Neste caso, então, se apenas o "corpo", se apenas a "mente" ou se os dois. As soluções que propunham a existência só da mente (monistas da mente), ou de mente e corpo, enquanto entidades distintas (dualistas) viriam a ser, portanto, decisivas para a própria concepção da Psicologia. Como se afirma ser, a partir de uma decisão referente ao problema anterior, que se deva desenvolver uma Psicologia cientifica, estabelece-se, no capítulo II, as concepções adotadas para Ciência, conhecimento científico e método científico. Ali, aproveita-se para justificar porque parte do estudo deve cair sob o domínio da Filosofia da Ciência, como um todo e da Filosofia da Psicologia, em particular. No capítulo III, volta-se a demonstrar com maior ênfase, que o problema "mente-corpo" é, ainda hoje, metafísico e requer uma tomada de decisão, naqueles termos. Mostra-se que a decisão é sempre tomada quando nada como pressuposto, senão explícito, pelo menos implícito. Uma vez tendo-se demonstrado que só o corpo pode ser afirmado como representando alguma coisa que exista, em termos reais, no sentido metafísico, parte-se para o estabelecimento daquele que seria o autêntico objeto de estudo da Psicologia. Fazendo-se, então, uso de uma Semântica Filosófica "crítico-realista", demonstra-se que ele termina sendo: o conjunto de propriedades do objeto real representado pelo corpo e responsáveis pelas manifestações pelas quais a Psicologia, por uma tradição de investigação, sempre se interessou. Finalmente, no capítulo IV, concebe-se um modelo sistêmico para representar a Natureza. Nele vige a 'lei' da transformação, que resulta da' interação entre os subsistemas. Entre os subsistemas existem aqueles que representam objetos reais e são designados como "Corpo Humano". Estes estão sujeitos à mesma 'lei'. A partir da transformação do U23592 em Pb20782, constrói-se duas funções matemáticas, com base na teoria dos conjuntos, para demonstrar-se como funciona a lei da transformação ou a função transformação, aplicável a todos os subsistemas, que são elementos do Sistema que representa a Natureza. Dessas construções e mais algumas, ao serem aplicadas aos subsistemas que representam os objetos reais denotados como Corpo Humano, extrai-se um grande número de consequências para a Psicologia. Termina-se apresentando um modelo específico para representar o objeto real denotado por Corpo Humano. Este, como subsistema, também é um sistema e composto de quatro subsistemas: Motor, Emocional, Perceptivo e Cognitivo. O todo e as partes passam a funcionar regidos pela lei da Transformação.

Towards an ontology for mathematical modeling with application to epidemiology

EMAp - Escola de Matemática Aplicada

Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I- 100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Investigação etnomatemática em contextos indígenas: caminhos para a reorientação da prática pedagógica

From the investigation, analysis, discussion and pondering about the activities developed by the lndians from the Porteira hamlet, members of the Xerente community, in the Tocantins state, we developed an investigative and descriptive study about the reality of this people with the aim of helping in the conceptual formation and in the reorientation of the pedagogical practice of the local teachers. In this sense, the undertaken research involved the teachers, the main representatives and experts in that cultural tradition, in order to investigate how the everyday activities (agriculture, food handling, assets distribution among the community members, etc.) and the cultural tradition (log race, body painting, clan division, Xerente numeration, Indian myths and histories, etc.), may enable the contextualization of the mathematics teaching in the lndian School Srêmtôwê of this hamlet, under a more transversal and globalizing perspective of the local and school knowledge. We based this research in the sociocultural conceptions of knowledge generation proposed by D Ambrosio (1990; 2002); Vergani (2007); Oliveras (1996); Gerdes (1991; 2002); Bishop (1999) e Sebastiani Ferreira (1997; 2004). ln the process of this study we propose some viable ways so that the Indian teachers may reorganize their classroom knowledge and actions, based in the strengthening of their history and culture. The observation of some social practices and knowledge as well as of the Xerente traditions helped us to point some possibilities of projection of a didacticalpedagogical dimension of these activities and practices, in the development of the school mathematical knowledge in this community

Possibilidades de exploração da história da ciência na formação do professor de matemática: mobilizando saberes a partir da obra de Nicolau Copérnico de revolutionibus orbium coelestium

This study aims to analyze the implications that the knowledge of an important work for the History of Science, De revolutionibus orbium coelestium , by Nicholas Copernicus, can bring for the formation of Mathematics professors. The study focuses on Book I of Copernicus s work, where, in the final part, is found the Table of the Subtense Straight Lines in a Circle, a true sine table constructed by the author. The study considers two theoretical references, the History of Science and of Mathematics, in the professor s formation searched amongst others in Miguel and Miorm, Brito, Neves and Martins, and Radford, and the necessary teaching knowledge professors mst have, on the basis of Gauthier, Schulman and Imbernón amongst others, through which it is established a net of knowledge grouped in dimensions such as mathematical, psycho pedagogical, cultural and practical diversity, that guide the study analysis. In the search for more necessary elements to enrich the analysis, beyond the theoretical research in Book I, it is carried through, with under graduation pupils, future Math professors, the construction of a sine table following the project used in De revolutionibus . The study still makes a description of the life and work of Nicholas Copernicus, detaching the historical context where the author lived and the conceptions about the Universe existing at that time. The research reveals that the studied work is an important source of culture, able to provide to the Mathematics professor in formation, beyond the conceptual and procedural mathematical knowledge, a cultural knowledge that allows him to be opened to the knowledge of other areas that not his specific area, and so to acquire knowledge about the world history, the development of sciences and of the society

A etnomatemática em uma cerâmica da região do Seridó/RN

This work has as objective to describe mathematical knowledge used as tools in the manufacture and marketing of tiles of red ceramic by potters of the Currais Novos village/ RN, located 250 km from the capital of Rio Grande do Norte. For us to reach our objective, we rely on conceptions ambrosianas of Ethnomatematics, besides of the qualitative research in an ethnographic approach. In the empirical part of the research, that went it accomplishes in the period from 2009 to 2012 in the Currais Novos Village, we support the following tools for data collection, semi-structured interviews, field diary, photographs, audio recordings and participant observations. In the analysis of the collected data, we can conclude that there are mathematical knowledge in the management of manufacture and marketing of tiles, often different from the academic mathematics, mainly in the wood cube, on cube of the clays, in the handler with the measures time, the count method , in the arrangement of tiles, in the preparation of the ceramic mass and sale of tiles. Theses knowledge were described and analyzed in the light of the theoretical Ethnomatematics, also supported in official documents, such as Parameters Nacional Curriculares. The analyzes of these knowledge generated subsidies for elaboration of an educational product - a proposal of didactic sequence destined to the Teaching of Mathematics in Elementary and Middle levels for the community schools and region, this proposal is in the Appendix to this work

Dificuldades na construção de gráficos de funções

This study describes about graduation s students difficulties of to draw functions graph. Specifically, we intend to observe their abilities evolution, as well as their difficulties during Calculus I subject in engineering course. For that, we show them publications about the elaboration of graphs and its difficulties in obstacle terms and some researches witch contain this subject and that it was done during postgraduate studies in mathematical education. It shows by research methodology aspects related to French didatic s mathematic and some theories of cognitive psychology considering the high value between theoretical-methodological relation that was evidenced in both theoretical conceptions about ways to understand and teach mathematic. This methodology is based on didactic engineering purpose, that consist in preliminaries analysis, conception and didactic sequence analysis prior, trials by application followed analysis up and conclusion. We had also used pedagogicals actions and analysis of results achieved, to classify types of errors made by the 2005 s students during second semester, from conceptions related to the episthemologic and didactics obstacles

GPS Satellite Kinematic Relative Positioning: Analyzing and Improving the Functional Mathematical Model Using Wavelets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Mathematical tests about the existence and applications of PPS-wavelets in function approximation problems

Neural networks and wavelet transform have been recently seen as attractive tools for developing eficient solutions for many real world problems in function approximation. Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. So, mathematical model is a very important tool to guarantee the development of the neural network area. In this article we will introduce one series of mathematical demonstrations that guarantee the wavelets properties for the PPS functions. As application, we will show the use of PPS-wavelets in pattern recognition problems of handwritten digit through function approximation techniques.

Um ensaio sobre as concepções de professores de Matemática: possibilidades metodológicas e um exercício de pesquisa

Este artigo tem como tema principal as concepções dos professores de Matemática. Considerando o termo concepção a partir do pragmatismo de Peirce, elabora-se um conjunto de parâmetros metodológicos - chamado de método indireto - a ser aplicado no estudo das concepções de professores de Matemática. Trata-se, em síntese, de investigar as concepções dos professores interpelando-os não sobre suas crenças, mas sobre suas práticas. Fundamentando essa abordagem indireta e explicitando-a em sua natureza qualitativa, o artigo segue apresentando, como exemplo, um exercício desse método indireto: um estudo sobre os critérios que os professores utilizam quando escolhem livros-texto para sua sala de aula, abordando, conseqüentemente, quais concepções de Matemática e de seu ensino e aprendizagem tais critérios desvendam. Partindo de depoimentos de professores de Matemática, o estudo indica que os professores agem com certa independência quando escolhem os materiais utilizados em suas atividades docentes. Buscam, ao mesmo tempo, apoio em uma vasta gama de livros didáticos, desconsiderando as particularidades de cada obra e as abordagens e perspectivas defendidas por seus autores. Embora submetam-se ao livro didático - considerado uma referência legítima e segura -, os professores o subvertem, buscando adequá-lo ao que consideram correto. Dessa constatação, algumas das concepções dos professores podem ser realçadas: o aluno, via de regra, é avaliado e classificado pelas lacunas que apresenta em relação aos conteúdos. Dessa postura, segue a valorização da precedência lógica dos conteúdos, de sua apresentação linear, e a defesa de pré-requisitos que viabilizariam o ensino e, conseqüentemente, implicam a legitimidade de aulas predominantemente expositivas.

Alumina porous ceramics: mathematical behavior at different commercial starch concentration

Several researches have been developed in order to verify the porosity effect over the ceramic material properties. The starch consolidation casting (SCC) allows to obtain porous ceramics by using starch as a binder and pore forming element. This work is intended to describe the porous mathematical behavior and the mechanical resistance at different commercial starch concentration. Ceramic samples were made with alumina and potato and corn starches. The slips were prepared with 10 to 50 wt% of starch. The specimens were characterized by apparent density measurements and three-point flexural test associated to Weibull statistics. Results indicated that the porosity showed a first-order exponential equation e(-x/c) increasing in both kinds of starches, so it was confirmed that the alumina ceramic porosity is related to the kind of starch used. The mechanical resistance is represented by a logarithmic expression R = A + B/1+10((Log(x0)-P)C).

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems. Part I. Mathematical modeling

The conventional Newton and fast decoupled power flow (FDPF) methods have been considered inadequate to obtain the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. It is well known that the PV and Q-theta decoupling assumptions of the fast decoupled power flow formulation no longer hold in the vicinity of the critical point. Moreover, the Jacobian matrix of the Newton method becomes singular at this point. However, the maximum loading point can be efficiently computed through parameterization techniques of continuation methods. In this paper it is shown that by using either theta or V as a parameter, the new fast decoupled power flow versions (XB and BX) become adequate for the computation of the maximum loading point only with a few small modifications. The possible use of reactive power injection in a selected PV bus (Q(PV)) as continuation parameter (mu) for the computation of the maximum loading point is also shown. A trivial secant predictor, the modified zero-order polynomial which uses the current solution and a fixed increment in the parameter (V, theta, or mu) as an estimate for the next solution, is used in predictor step. These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained with the new approach for the IEEE test systems (14, 30, 57 and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that parameters can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. (C) 2003 Elsevier B.V. All rights reserved.