Sobre a integração indefinida de funções racionais complexas: teoria e implementação de algoritmos racionais

We present indefinite integration algorithms for rational functions over subfields of the complex numbers, through an algebraic approach. We study the local algorithm of Bernoulli and rational algorithms for the class of functions in concern, namely, the algorithms of Hermite; Horowitz-Ostrogradsky; Rothstein-Trager and Lazard-Rioboo-Trager. We also study the algorithm of Rioboo for conversion of logarithms involving complex extensions into real arctangent functions, when these logarithms arise from the integration of rational functions with real coefficients. We conclude presenting pseudocodes and codes for implementation in the software Maxima concerning the algorithms studied in this work, as well as to algorithms for polynomial gcd computation; partial fraction decomposition; squarefree factorization; subresultant computation, among other side algorithms for the work. We also present the algorithm of Zeilberger-Almkvist for integration of hyperexpontential functions, as well as its pseudocode and code for Maxima. As an alternative for the algorithms of Rothstein-Trager and Lazard-Rioboo-Trager, we yet present a code for Benoulli’s algorithm for square-free denominators; and another for Czichowski’s algorithm, although this one is not studied in detail in the present work, due to the theoretical basis necessary to understand it, which is beyond this work’s scope. Several examples are provided in order to illustrate the working of the integration algorithms in this text

Neuroscience and education: prime time to build the bridge

As neuroscience gains social traction and entices media attention, the notion that education has much to benefit from brain research becomes increasingly popular. However, it has been argued that the fundamental bridge toward education is cognitive psychology, not neuroscience. We discuss four specific cases in which neuroscience synergizes with other disciplines to serve education, ranging from very general physiological aspects of human learning such as nutrition, exercise and sleep, to brain architectures that shape the way we acquire language and reading, and neuroscience tools that increasingly allow the early detection of cognitive deficits, especially in preverbal infants. Neuroscience methods, tools and theoretical frameworks have broadened our understanding of the mind in a way that is highly relevant to educational practice. Although the bridge’s cement is still fresh, we argue why it is prime time to march over it.

Democracia participativa e regulação econômica: uma questão de legitimidade

This work presents an analysis about the legitimation of independent regulatory commission`s rulemaking power by participation procedure. It is observed that political and administrative decentralization and fragmentation of State, with the purpose of approaching citizens and provide, more efficiently, the functions acquired by the passage of the Welfare State, leads to a deficit of legitimacy (democratic crisis), which is noticeable in the making of legal norms by directors of independent regulatory commission to regulate specific economic sector. However, we understand that this crisis stems from the observation of the contemporary world from dogmas and legal institutions of the eighteenth century, without their evolution and adaptation to the modern world. The legitimacy must be perceived as the justification of power, relation command /obedience, which, from the Modern State, has the democracy as standard. Therefore, just as the world has evolved and demanded political and administrative decentralization to accompany him, it is necessary to the development of the idea of representative democracy (formal legitimacy) to participatory democracy (legitimacy stuff). Legitimacy is not confused with the legality: as the legality is on observance to internal legal system, the "rules of play"; legitimacy, as inputs to be fed into this system, the selection of the different expectations in the environment. Nevertheless, the legitimacy will take place by legality, through introduction of rational and communicative procedures: procedures get fundamental importance because these will be the means to select the expectations to be introduced in the legal system in order to make decisions more fair, rational and qualified towards society. Thus, it is necessary to its opening to the environment for dialogue with the government. In this context, we try to make an analysis of constitutional norms based on systematic and teleological interpretation of these norms to build these arguments. According to the Constitution of 1988, participatory democracy is a result of the democratic principle (sole paragraph of art. 1 of the Constitution), and it is an expression of citizenship and political pluralism, both foundations of Republic (respectively Art. 1st, inc . V and II of the Constitution), as well as the national consciousness. From another point of view, that principle consists of an evolution in the management public affairs (principle of Republic). The right of interested participate in the rulemaking process derives both the principle of popular participation (part of the democratic principle) and the republican principle as the due process constitutional (art. 5, LIV and LV, CF/88) and the right to petition (Art . 5 °, inc. XXXIV, "a", CF/88), and it is the duty of the State not only be open to participation and encourage it. Ignoring stakeholder involvement in procedures and / or expressions compiled can be causes of invalidation of the rule of law produced by addiction of procedure, motive, motivation and/or because of the administrative act. Finally, we conclude that the involvement of stakeholders in the process of making rules within the independent regulatory commission is the legitimacy and the validity of rules; and that, despite of the expressions do not bind the decision making, they will enter the system as juridical fact, balancing the field of technical discretionary of agencies

A metafísica de Isaac Newton

The general objective of this dissertation is to analyze the metaphysical aspects of "rational mechanics" of Isaac Newton, clarifying, by scientific and philosophical discourse, their main elements, with emphasis to the presence of one entity infinitely rational behind all the phenomena of nature, and to the Newton's insight as certain empiricist which, however, accepts deductions metaphysics; a philosopher-scientist. The specific objectives are detailed below: a) brief presentation of the development of modern science, since the Pre-Socratics, seeking to understand the historical conjecture that enabled the rise of Newtonian mechanics; b) presentation of the elements of scientific methodology and philosophical, aimed at comprehension of certain "Newtonian methodology", understanding how this specific methodology able to present empirical aspects, mathematics, philosophic and religious in communion; c) to understand, from the Newtonian concepts, both concerning man's role in the world as the "notional notions" of mass, space, time and movement, necessary for analysis and understanding of certain metaphysical aspects in the Newtonian physics; d) to present the Newtonian concepts related to the ether, to understand why it necessarily assumes metaphysics characteristics and mediation between the bodies; e) to present and understand the factors that lead the empiricist Newton to assume the religion in his mechanics, as well as, the existence and functions of God in nature, to object to the higher content of his metaphysics; f) to highlight the metaphysical elements of his classical mechanics, that confirm the presence of concepts like God Creator and Preserver of the natural laws; g) at last, to analyze the importance of Newton to the modern metaphysics and the legacy to philosophy of science at sec. XVII to science contemporary